bull y
1 J
B ~ TOPH KAAC
YnpagtkHumeAHama mempagka ya ce Da YMHO)l(aBaM H lleJlR
e ogo6peHa om MUHucmepcmBomo Ha o6pa30BaHuemo Haykama u meXHoAoeuume c npomokoA N~ 6 om 02 12 1994 e
YB ce aB YMHO)f(BBBM
H aeJlR
Ha
om kAac
Y4uAuLUe ttK 3ulIliMllio IltlN
Da maka e Ho a3 LUe 6u 3a6ega caMO go 2paguHama Ha 3aMbka
AHU 6RPHO AU e
A 6bmpe mpR66a ga npogbAgtkume caMU
4e HaO-AecHO LUe ce HaY4UM ga YMHogtka6aMe U geAuM ako omugeM 6 3aMbka Ha
36e3g06poe~a
L
1 = 2
2 = 4
72=
= 1 0 VMHO)l(CHHC C 2
HRkbge koO 3HaO kbge komeHua gtku8eJu g8e Ho CbC Janu u onawku c6uJu ce 8egHbgtk IoHawku 6e3 o6a4e ga 6poumel Kagtkeme kOJko ca ywume
JI
~ I ~~1~- l
tfJ___ W~J rf====jl I I I I
I I I I - At I I
I I I shy
Vmiddot
- - -shy --~~----------shy TOH40 npogbJgtku
ga 3aka48aw no peg Ako npa8uJHo 3aka4uM
kbpnume u pewuM 3aga4ume owe gHec
we mpb2HeM kbM~_ ~ 3aMbka
bullge e Iku iawku le llume
I
1 I ~ ~ I ~ I I I
I ~ I
3a ga BAe3eme B apaguHama Ha 3aMbka
Hanuweme kOAko 4epewku e UMaAO Ha Bceku kAOH omgfl~HO Te ca 6UAU mOAkoBa kOAkomo Ha kAOHa omMIBo U~~--
e Hagnuweme u ma6eAk~~~~~~~~ Ha uBemfima
A~~
VnpilI(HeHHSI 3a YMHO)f(eHHe c 2
I
3a ga 6Ae3eme 6 3aMbka 6ceku mpR66a
npa6uAHo ga u36epe 2 3HaMeHa BHuMa6aOme To6a koemo e
HanucaHO Ha 3HaMemo omAR60 ga 6bge pa6Ho Ha 4UCAomo 6bPXY 3HaMemo omgRcHo CAeg kamo
npecMemHeme ou6ememe 3HaMeHama no g600ku
QYMama nbTEKA UMa 0 epu4ku BeRka epu4ka UMa 0 6yk6u KOAko ea 6yk6ume 6pORm UM e HanueaH Ha eguH om kAlo406eme OmkpuOme 20
2 = 2 2 2 = 4 32= 6 4 2= 8 5 2 = 10 6 2 = 12 7 2 = 14 8 2 = 16 9 2= 18 IIJ
1 2=
02=4 30= 6
42 = 8
2= 10
60= 12
2= 16
0= 18
11---1---- bull 0 =
VnpCl)KHCHMII 3a OTKpMoaHC Ha HCM38C(TCH MHO)l(HTCA
Eame HaCaM
2 3 = HO 2JegaOme 4UCJama
9 Kou om HanucaHume npou3shy6egeHusl ca om ma6Jullama 3a
3 2 YMHogtkeHue c 3 CaMo me3U
7 = cku ca go6pe 3ako6aHu Cmbn6aOme 6bPXY
4 3 = 1 5 KOJko
6 3 = 1 8 YMHO)l(eHllle c 3
6mopa u nog Mocma
3I 1 1 = I
KHwkkume Henpe6poeHu ca caMo nogpegeHu BMecmo mu ga au 6pouw Mogtkew ga au YMHOgtkUW
u06pe gowlu 6 3aMbka Ha 4uclamal 3ag ma3U 6u61uomeka
UMa maOHa 6pama Ho msl 1~___-w41~e ce om60pu ako 6egHaa
Hanuweme kOlko ca kHuaume Ha 6ceku
~IIIltpacpm
rn CbCTE3AHIf1E
C KOCTEHYPKIf1 Ha kOlko caHmushyMempa egHa om gpyaa ca nbp6ama u 4em6bpshymama kocmeHypka ako 3Haew 4e 6CU4ku me ce g6wkam Ha pa3shyCmOslHUe om no 3 CM
1 3 1 1 3 1 = f
3anuwu kak60 e pa3CmOslHUemO Megtkgy kocmeHypkume 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma
I I 1 1 1 1 1 1
B Hagnuca UMa 21 6ykBu no 3 Ha Bceku kaMbk
KOAko ca kaMbHume B Hagnuca
1211 I 1 3 1= I llgtkyggtkemo lUe u3Bagu om nellma 14 xMI6a TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo KOAko xAR6a lUe cepBupa gHec
3a mopmume UMa 18 4epewu C mRX ykpacu 2 mopmu kamo llgtkyggtkemama lle eAogtkam au pa3geAuw no paBHo nOAoBuHama ROua B 6aHuuashy
ma a oemaHaAume lle eBashyI I I I I I pRm KOAko ROua lle eBapRm
npeg ggtkyggtkemo UMa 27 pe3eH4ema no kOAko uBemR tUe noemaBu IUMOH nOMoaHU My ga au pa3g9JU ggtkyggtkemo BbB BeRka Ba3a ako au no paBHo 3a mpume Maeu pa3g9JU no paBHo
--1-r------------I ACICHHC C 2 H 3
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
YnpagtkHumeAHama mempagka ya ce Da YMHO)l(aBaM H lleJlR
e ogo6peHa om MUHucmepcmBomo Ha o6pa30BaHuemo Haykama u meXHoAoeuume c npomokoA N~ 6 om 02 12 1994 e
YB ce aB YMHO)f(BBBM
H aeJlR
Ha
om kAac
Y4uAuLUe ttK 3ulIliMllio IltlN
Da maka e Ho a3 LUe 6u 3a6ega caMO go 2paguHama Ha 3aMbka
AHU 6RPHO AU e
A 6bmpe mpR66a ga npogbAgtkume caMU
4e HaO-AecHO LUe ce HaY4UM ga YMHogtka6aMe U geAuM ako omugeM 6 3aMbka Ha
36e3g06poe~a
L
1 = 2
2 = 4
72=
= 1 0 VMHO)l(CHHC C 2
HRkbge koO 3HaO kbge komeHua gtku8eJu g8e Ho CbC Janu u onawku c6uJu ce 8egHbgtk IoHawku 6e3 o6a4e ga 6poumel Kagtkeme kOJko ca ywume
JI
~ I ~~1~- l
tfJ___ W~J rf====jl I I I I
I I I I - At I I
I I I shy
Vmiddot
- - -shy --~~----------shy TOH40 npogbJgtku
ga 3aka48aw no peg Ako npa8uJHo 3aka4uM
kbpnume u pewuM 3aga4ume owe gHec
we mpb2HeM kbM~_ ~ 3aMbka
bullge e Iku iawku le llume
I
1 I ~ ~ I ~ I I I
I ~ I
3a ga BAe3eme B apaguHama Ha 3aMbka
Hanuweme kOAko 4epewku e UMaAO Ha Bceku kAOH omgfl~HO Te ca 6UAU mOAkoBa kOAkomo Ha kAOHa omMIBo U~~--
e Hagnuweme u ma6eAk~~~~~~~~ Ha uBemfima
A~~
VnpilI(HeHHSI 3a YMHO)f(eHHe c 2
I
3a ga 6Ae3eme 6 3aMbka 6ceku mpR66a
npa6uAHo ga u36epe 2 3HaMeHa BHuMa6aOme To6a koemo e
HanucaHO Ha 3HaMemo omAR60 ga 6bge pa6Ho Ha 4UCAomo 6bPXY 3HaMemo omgRcHo CAeg kamo
npecMemHeme ou6ememe 3HaMeHama no g600ku
QYMama nbTEKA UMa 0 epu4ku BeRka epu4ka UMa 0 6yk6u KOAko ea 6yk6ume 6pORm UM e HanueaH Ha eguH om kAlo406eme OmkpuOme 20
2 = 2 2 2 = 4 32= 6 4 2= 8 5 2 = 10 6 2 = 12 7 2 = 14 8 2 = 16 9 2= 18 IIJ
1 2=
02=4 30= 6
42 = 8
2= 10
60= 12
2= 16
0= 18
11---1---- bull 0 =
VnpCl)KHCHMII 3a OTKpMoaHC Ha HCM38C(TCH MHO)l(HTCA
Eame HaCaM
2 3 = HO 2JegaOme 4UCJama
9 Kou om HanucaHume npou3shy6egeHusl ca om ma6Jullama 3a
3 2 YMHogtkeHue c 3 CaMo me3U
7 = cku ca go6pe 3ako6aHu Cmbn6aOme 6bPXY
4 3 = 1 5 KOJko
6 3 = 1 8 YMHO)l(eHllle c 3
6mopa u nog Mocma
3I 1 1 = I
KHwkkume Henpe6poeHu ca caMo nogpegeHu BMecmo mu ga au 6pouw Mogtkew ga au YMHOgtkUW
u06pe gowlu 6 3aMbka Ha 4uclamal 3ag ma3U 6u61uomeka
UMa maOHa 6pama Ho msl 1~___-w41~e ce om60pu ako 6egHaa
Hanuweme kOlko ca kHuaume Ha 6ceku
~IIIltpacpm
rn CbCTE3AHIf1E
C KOCTEHYPKIf1 Ha kOlko caHmushyMempa egHa om gpyaa ca nbp6ama u 4em6bpshymama kocmeHypka ako 3Haew 4e 6CU4ku me ce g6wkam Ha pa3shyCmOslHUe om no 3 CM
1 3 1 1 3 1 = f
3anuwu kak60 e pa3CmOslHUemO Megtkgy kocmeHypkume 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma
I I 1 1 1 1 1 1
B Hagnuca UMa 21 6ykBu no 3 Ha Bceku kaMbk
KOAko ca kaMbHume B Hagnuca
1211 I 1 3 1= I llgtkyggtkemo lUe u3Bagu om nellma 14 xMI6a TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo KOAko xAR6a lUe cepBupa gHec
3a mopmume UMa 18 4epewu C mRX ykpacu 2 mopmu kamo llgtkyggtkemama lle eAogtkam au pa3geAuw no paBHo nOAoBuHama ROua B 6aHuuashy
ma a oemaHaAume lle eBashyI I I I I I pRm KOAko ROua lle eBapRm
npeg ggtkyggtkemo UMa 27 pe3eH4ema no kOAko uBemR tUe noemaBu IUMOH nOMoaHU My ga au pa3g9JU ggtkyggtkemo BbB BeRka Ba3a ako au no paBHo 3a mpume Maeu pa3g9JU no paBHo
--1-r------------I ACICHHC C 2 H 3
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
L
1 = 2
2 = 4
72=
= 1 0 VMHO)l(CHHC C 2
HRkbge koO 3HaO kbge komeHua gtku8eJu g8e Ho CbC Janu u onawku c6uJu ce 8egHbgtk IoHawku 6e3 o6a4e ga 6poumel Kagtkeme kOJko ca ywume
JI
~ I ~~1~- l
tfJ___ W~J rf====jl I I I I
I I I I - At I I
I I I shy
Vmiddot
- - -shy --~~----------shy TOH40 npogbJgtku
ga 3aka48aw no peg Ako npa8uJHo 3aka4uM
kbpnume u pewuM 3aga4ume owe gHec
we mpb2HeM kbM~_ ~ 3aMbka
bullge e Iku iawku le llume
I
1 I ~ ~ I ~ I I I
I ~ I
3a ga BAe3eme B apaguHama Ha 3aMbka
Hanuweme kOAko 4epewku e UMaAO Ha Bceku kAOH omgfl~HO Te ca 6UAU mOAkoBa kOAkomo Ha kAOHa omMIBo U~~--
e Hagnuweme u ma6eAk~~~~~~~~ Ha uBemfima
A~~
VnpilI(HeHHSI 3a YMHO)f(eHHe c 2
I
3a ga 6Ae3eme 6 3aMbka 6ceku mpR66a
npa6uAHo ga u36epe 2 3HaMeHa BHuMa6aOme To6a koemo e
HanucaHO Ha 3HaMemo omAR60 ga 6bge pa6Ho Ha 4UCAomo 6bPXY 3HaMemo omgRcHo CAeg kamo
npecMemHeme ou6ememe 3HaMeHama no g600ku
QYMama nbTEKA UMa 0 epu4ku BeRka epu4ka UMa 0 6yk6u KOAko ea 6yk6ume 6pORm UM e HanueaH Ha eguH om kAlo406eme OmkpuOme 20
2 = 2 2 2 = 4 32= 6 4 2= 8 5 2 = 10 6 2 = 12 7 2 = 14 8 2 = 16 9 2= 18 IIJ
1 2=
02=4 30= 6
42 = 8
2= 10
60= 12
2= 16
0= 18
11---1---- bull 0 =
VnpCl)KHCHMII 3a OTKpMoaHC Ha HCM38C(TCH MHO)l(HTCA
Eame HaCaM
2 3 = HO 2JegaOme 4UCJama
9 Kou om HanucaHume npou3shy6egeHusl ca om ma6Jullama 3a
3 2 YMHogtkeHue c 3 CaMo me3U
7 = cku ca go6pe 3ako6aHu Cmbn6aOme 6bPXY
4 3 = 1 5 KOJko
6 3 = 1 8 YMHO)l(eHllle c 3
6mopa u nog Mocma
3I 1 1 = I
KHwkkume Henpe6poeHu ca caMo nogpegeHu BMecmo mu ga au 6pouw Mogtkew ga au YMHOgtkUW
u06pe gowlu 6 3aMbka Ha 4uclamal 3ag ma3U 6u61uomeka
UMa maOHa 6pama Ho msl 1~___-w41~e ce om60pu ako 6egHaa
Hanuweme kOlko ca kHuaume Ha 6ceku
~IIIltpacpm
rn CbCTE3AHIf1E
C KOCTEHYPKIf1 Ha kOlko caHmushyMempa egHa om gpyaa ca nbp6ama u 4em6bpshymama kocmeHypka ako 3Haew 4e 6CU4ku me ce g6wkam Ha pa3shyCmOslHUe om no 3 CM
1 3 1 1 3 1 = f
3anuwu kak60 e pa3CmOslHUemO Megtkgy kocmeHypkume 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma
I I 1 1 1 1 1 1
B Hagnuca UMa 21 6ykBu no 3 Ha Bceku kaMbk
KOAko ca kaMbHume B Hagnuca
1211 I 1 3 1= I llgtkyggtkemo lUe u3Bagu om nellma 14 xMI6a TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo KOAko xAR6a lUe cepBupa gHec
3a mopmume UMa 18 4epewu C mRX ykpacu 2 mopmu kamo llgtkyggtkemama lle eAogtkam au pa3geAuw no paBHo nOAoBuHama ROua B 6aHuuashy
ma a oemaHaAume lle eBashyI I I I I I pRm KOAko ROua lle eBapRm
npeg ggtkyggtkemo UMa 27 pe3eH4ema no kOAko uBemR tUe noemaBu IUMOH nOMoaHU My ga au pa3g9JU ggtkyggtkemo BbB BeRka Ba3a ako au no paBHo 3a mpume Maeu pa3g9JU no paBHo
--1-r------------I ACICHHC C 2 H 3
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
bullge e Iku iawku le llume
I
1 I ~ ~ I ~ I I I
I ~ I
3a ga BAe3eme B apaguHama Ha 3aMbka
Hanuweme kOAko 4epewku e UMaAO Ha Bceku kAOH omgfl~HO Te ca 6UAU mOAkoBa kOAkomo Ha kAOHa omMIBo U~~--
e Hagnuweme u ma6eAk~~~~~~~~ Ha uBemfima
A~~
VnpilI(HeHHSI 3a YMHO)f(eHHe c 2
I
3a ga 6Ae3eme 6 3aMbka 6ceku mpR66a
npa6uAHo ga u36epe 2 3HaMeHa BHuMa6aOme To6a koemo e
HanucaHO Ha 3HaMemo omAR60 ga 6bge pa6Ho Ha 4UCAomo 6bPXY 3HaMemo omgRcHo CAeg kamo
npecMemHeme ou6ememe 3HaMeHama no g600ku
QYMama nbTEKA UMa 0 epu4ku BeRka epu4ka UMa 0 6yk6u KOAko ea 6yk6ume 6pORm UM e HanueaH Ha eguH om kAlo406eme OmkpuOme 20
2 = 2 2 2 = 4 32= 6 4 2= 8 5 2 = 10 6 2 = 12 7 2 = 14 8 2 = 16 9 2= 18 IIJ
1 2=
02=4 30= 6
42 = 8
2= 10
60= 12
2= 16
0= 18
11---1---- bull 0 =
VnpCl)KHCHMII 3a OTKpMoaHC Ha HCM38C(TCH MHO)l(HTCA
Eame HaCaM
2 3 = HO 2JegaOme 4UCJama
9 Kou om HanucaHume npou3shy6egeHusl ca om ma6Jullama 3a
3 2 YMHogtkeHue c 3 CaMo me3U
7 = cku ca go6pe 3ako6aHu Cmbn6aOme 6bPXY
4 3 = 1 5 KOJko
6 3 = 1 8 YMHO)l(eHllle c 3
6mopa u nog Mocma
3I 1 1 = I
KHwkkume Henpe6poeHu ca caMo nogpegeHu BMecmo mu ga au 6pouw Mogtkew ga au YMHOgtkUW
u06pe gowlu 6 3aMbka Ha 4uclamal 3ag ma3U 6u61uomeka
UMa maOHa 6pama Ho msl 1~___-w41~e ce om60pu ako 6egHaa
Hanuweme kOlko ca kHuaume Ha 6ceku
~IIIltpacpm
rn CbCTE3AHIf1E
C KOCTEHYPKIf1 Ha kOlko caHmushyMempa egHa om gpyaa ca nbp6ama u 4em6bpshymama kocmeHypka ako 3Haew 4e 6CU4ku me ce g6wkam Ha pa3shyCmOslHUe om no 3 CM
1 3 1 1 3 1 = f
3anuwu kak60 e pa3CmOslHUemO Megtkgy kocmeHypkume 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma
I I 1 1 1 1 1 1
B Hagnuca UMa 21 6ykBu no 3 Ha Bceku kaMbk
KOAko ca kaMbHume B Hagnuca
1211 I 1 3 1= I llgtkyggtkemo lUe u3Bagu om nellma 14 xMI6a TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo KOAko xAR6a lUe cepBupa gHec
3a mopmume UMa 18 4epewu C mRX ykpacu 2 mopmu kamo llgtkyggtkemama lle eAogtkam au pa3geAuw no paBHo nOAoBuHama ROua B 6aHuuashy
ma a oemaHaAume lle eBashyI I I I I I pRm KOAko ROua lle eBapRm
npeg ggtkyggtkemo UMa 27 pe3eH4ema no kOAko uBemR tUe noemaBu IUMOH nOMoaHU My ga au pa3g9JU ggtkyggtkemo BbB BeRka Ba3a ako au no paBHo 3a mpume Maeu pa3g9JU no paBHo
--1-r------------I ACICHHC C 2 H 3
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
I
3a ga 6Ae3eme 6 3aMbka 6ceku mpR66a
npa6uAHo ga u36epe 2 3HaMeHa BHuMa6aOme To6a koemo e
HanucaHO Ha 3HaMemo omAR60 ga 6bge pa6Ho Ha 4UCAomo 6bPXY 3HaMemo omgRcHo CAeg kamo
npecMemHeme ou6ememe 3HaMeHama no g600ku
QYMama nbTEKA UMa 0 epu4ku BeRka epu4ka UMa 0 6yk6u KOAko ea 6yk6ume 6pORm UM e HanueaH Ha eguH om kAlo406eme OmkpuOme 20
2 = 2 2 2 = 4 32= 6 4 2= 8 5 2 = 10 6 2 = 12 7 2 = 14 8 2 = 16 9 2= 18 IIJ
1 2=
02=4 30= 6
42 = 8
2= 10
60= 12
2= 16
0= 18
11---1---- bull 0 =
VnpCl)KHCHMII 3a OTKpMoaHC Ha HCM38C(TCH MHO)l(HTCA
Eame HaCaM
2 3 = HO 2JegaOme 4UCJama
9 Kou om HanucaHume npou3shy6egeHusl ca om ma6Jullama 3a
3 2 YMHogtkeHue c 3 CaMo me3U
7 = cku ca go6pe 3ako6aHu Cmbn6aOme 6bPXY
4 3 = 1 5 KOJko
6 3 = 1 8 YMHO)l(eHllle c 3
6mopa u nog Mocma
3I 1 1 = I
KHwkkume Henpe6poeHu ca caMo nogpegeHu BMecmo mu ga au 6pouw Mogtkew ga au YMHOgtkUW
u06pe gowlu 6 3aMbka Ha 4uclamal 3ag ma3U 6u61uomeka
UMa maOHa 6pama Ho msl 1~___-w41~e ce om60pu ako 6egHaa
Hanuweme kOlko ca kHuaume Ha 6ceku
~IIIltpacpm
rn CbCTE3AHIf1E
C KOCTEHYPKIf1 Ha kOlko caHmushyMempa egHa om gpyaa ca nbp6ama u 4em6bpshymama kocmeHypka ako 3Haew 4e 6CU4ku me ce g6wkam Ha pa3shyCmOslHUe om no 3 CM
1 3 1 1 3 1 = f
3anuwu kak60 e pa3CmOslHUemO Megtkgy kocmeHypkume 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma
I I 1 1 1 1 1 1
B Hagnuca UMa 21 6ykBu no 3 Ha Bceku kaMbk
KOAko ca kaMbHume B Hagnuca
1211 I 1 3 1= I llgtkyggtkemo lUe u3Bagu om nellma 14 xMI6a TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo KOAko xAR6a lUe cepBupa gHec
3a mopmume UMa 18 4epewu C mRX ykpacu 2 mopmu kamo llgtkyggtkemama lle eAogtkam au pa3geAuw no paBHo nOAoBuHama ROua B 6aHuuashy
ma a oemaHaAume lle eBashyI I I I I I pRm KOAko ROua lle eBapRm
npeg ggtkyggtkemo UMa 27 pe3eH4ema no kOAko uBemR tUe noemaBu IUMOH nOMoaHU My ga au pa3g9JU ggtkyggtkemo BbB BeRka Ba3a ako au no paBHo 3a mpume Maeu pa3g9JU no paBHo
--1-r------------I ACICHHC C 2 H 3
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
2 = 2 2 2 = 4 32= 6 4 2= 8 5 2 = 10 6 2 = 12 7 2 = 14 8 2 = 16 9 2= 18 IIJ
1 2=
02=4 30= 6
42 = 8
2= 10
60= 12
2= 16
0= 18
11---1---- bull 0 =
VnpCl)KHCHMII 3a OTKpMoaHC Ha HCM38C(TCH MHO)l(HTCA
Eame HaCaM
2 3 = HO 2JegaOme 4UCJama
9 Kou om HanucaHume npou3shy6egeHusl ca om ma6Jullama 3a
3 2 YMHogtkeHue c 3 CaMo me3U
7 = cku ca go6pe 3ako6aHu Cmbn6aOme 6bPXY
4 3 = 1 5 KOJko
6 3 = 1 8 YMHO)l(eHllle c 3
6mopa u nog Mocma
3I 1 1 = I
KHwkkume Henpe6poeHu ca caMo nogpegeHu BMecmo mu ga au 6pouw Mogtkew ga au YMHOgtkUW
u06pe gowlu 6 3aMbka Ha 4uclamal 3ag ma3U 6u61uomeka
UMa maOHa 6pama Ho msl 1~___-w41~e ce om60pu ako 6egHaa
Hanuweme kOlko ca kHuaume Ha 6ceku
~IIIltpacpm
rn CbCTE3AHIf1E
C KOCTEHYPKIf1 Ha kOlko caHmushyMempa egHa om gpyaa ca nbp6ama u 4em6bpshymama kocmeHypka ako 3Haew 4e 6CU4ku me ce g6wkam Ha pa3shyCmOslHUe om no 3 CM
1 3 1 1 3 1 = f
3anuwu kak60 e pa3CmOslHUemO Megtkgy kocmeHypkume 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma
I I 1 1 1 1 1 1
B Hagnuca UMa 21 6ykBu no 3 Ha Bceku kaMbk
KOAko ca kaMbHume B Hagnuca
1211 I 1 3 1= I llgtkyggtkemo lUe u3Bagu om nellma 14 xMI6a TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo KOAko xAR6a lUe cepBupa gHec
3a mopmume UMa 18 4epewu C mRX ykpacu 2 mopmu kamo llgtkyggtkemama lle eAogtkam au pa3geAuw no paBHo nOAoBuHama ROua B 6aHuuashy
ma a oemaHaAume lle eBashyI I I I I I pRm KOAko ROua lle eBapRm
npeg ggtkyggtkemo UMa 27 pe3eH4ema no kOAko uBemR tUe noemaBu IUMOH nOMoaHU My ga au pa3g9JU ggtkyggtkemo BbB BeRka Ba3a ako au no paBHo 3a mpume Maeu pa3g9JU no paBHo
--1-r------------I ACICHHC C 2 H 3
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
Eame HaCaM
2 3 = HO 2JegaOme 4UCJama
9 Kou om HanucaHume npou3shy6egeHusl ca om ma6Jullama 3a
3 2 YMHogtkeHue c 3 CaMo me3U
7 = cku ca go6pe 3ako6aHu Cmbn6aOme 6bPXY
4 3 = 1 5 KOJko
6 3 = 1 8 YMHO)l(eHllle c 3
6mopa u nog Mocma
3I 1 1 = I
KHwkkume Henpe6poeHu ca caMo nogpegeHu BMecmo mu ga au 6pouw Mogtkew ga au YMHOgtkUW
u06pe gowlu 6 3aMbka Ha 4uclamal 3ag ma3U 6u61uomeka
UMa maOHa 6pama Ho msl 1~___-w41~e ce om60pu ako 6egHaa
Hanuweme kOlko ca kHuaume Ha 6ceku
~IIIltpacpm
rn CbCTE3AHIf1E
C KOCTEHYPKIf1 Ha kOlko caHmushyMempa egHa om gpyaa ca nbp6ama u 4em6bpshymama kocmeHypka ako 3Haew 4e 6CU4ku me ce g6wkam Ha pa3shyCmOslHUe om no 3 CM
1 3 1 1 3 1 = f
3anuwu kak60 e pa3CmOslHUemO Megtkgy kocmeHypkume 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma
I I 1 1 1 1 1 1
B Hagnuca UMa 21 6ykBu no 3 Ha Bceku kaMbk
KOAko ca kaMbHume B Hagnuca
1211 I 1 3 1= I llgtkyggtkemo lUe u3Bagu om nellma 14 xMI6a TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo KOAko xAR6a lUe cepBupa gHec
3a mopmume UMa 18 4epewu C mRX ykpacu 2 mopmu kamo llgtkyggtkemama lle eAogtkam au pa3geAuw no paBHo nOAoBuHama ROua B 6aHuuashy
ma a oemaHaAume lle eBashyI I I I I I pRm KOAko ROua lle eBapRm
npeg ggtkyggtkemo UMa 27 pe3eH4ema no kOAko uBemR tUe noemaBu IUMOH nOMoaHU My ga au pa3g9JU ggtkyggtkemo BbB BeRka Ba3a ako au no paBHo 3a mpume Maeu pa3g9JU no paBHo
--1-r------------I ACICHHC C 2 H 3
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
KHwkkume Henpe6poeHu ca caMo nogpegeHu BMecmo mu ga au 6pouw Mogtkew ga au YMHOgtkUW
u06pe gowlu 6 3aMbka Ha 4uclamal 3ag ma3U 6u61uomeka
UMa maOHa 6pama Ho msl 1~___-w41~e ce om60pu ako 6egHaa
Hanuweme kOlko ca kHuaume Ha 6ceku
~IIIltpacpm
rn CbCTE3AHIf1E
C KOCTEHYPKIf1 Ha kOlko caHmushyMempa egHa om gpyaa ca nbp6ama u 4em6bpshymama kocmeHypka ako 3Haew 4e 6CU4ku me ce g6wkam Ha pa3shyCmOslHUe om no 3 CM
1 3 1 1 3 1 = f
3anuwu kak60 e pa3CmOslHUemO Megtkgy kocmeHypkume 6mopa u 4em6bpma nbP6a u 4em6bpma mpema u 4em6bpma
I I 1 1 1 1 1 1
B Hagnuca UMa 21 6ykBu no 3 Ha Bceku kaMbk
KOAko ca kaMbHume B Hagnuca
1211 I 1 3 1= I llgtkyggtkemo lUe u3Bagu om nellma 14 xMI6a TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo KOAko xAR6a lUe cepBupa gHec
3a mopmume UMa 18 4epewu C mRX ykpacu 2 mopmu kamo llgtkyggtkemama lle eAogtkam au pa3geAuw no paBHo nOAoBuHama ROua B 6aHuuashy
ma a oemaHaAume lle eBashyI I I I I I pRm KOAko ROua lle eBapRm
npeg ggtkyggtkemo UMa 27 pe3eH4ema no kOAko uBemR tUe noemaBu IUMOH nOMoaHU My ga au pa3g9JU ggtkyggtkemo BbB BeRka Ba3a ako au no paBHo 3a mpume Maeu pa3g9JU no paBHo
--1-r------------I ACICHHC C 2 H 3
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
B Hagnuca UMa 21 6ykBu no 3 Ha Bceku kaMbk
KOAko ca kaMbHume B Hagnuca
1211 I 1 3 1= I llgtkyggtkemo lUe u3Bagu om nellma 14 xMI6a TpR6Ba ga au pa3geAu 3a 2 gHU no paBHo KOAko xAR6a lUe cepBupa gHec
3a mopmume UMa 18 4epewu C mRX ykpacu 2 mopmu kamo llgtkyggtkemama lle eAogtkam au pa3geAuw no paBHo nOAoBuHama ROua B 6aHuuashy
ma a oemaHaAume lle eBashyI I I I I I pRm KOAko ROua lle eBapRm
npeg ggtkyggtkemo UMa 27 pe3eH4ema no kOAko uBemR tUe noemaBu IUMOH nOMoaHU My ga au pa3g9JU ggtkyggtkemo BbB BeRka Ba3a ako au no paBHo 3a mpume Maeu pa3g9JU no paBHo
--1-r------------I ACICHHC C 2 H 3
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
pu geua HU
am Ha aocmu NIX cma6aMe 15 gywu 3a
06Ag
ina U4e cAogtllta m RQua B 6aHuuashy~aAume U4e cBashyQua U4e cBapRm
U4e nocmaBu Rka Ba3a ako au ~
I I I I
EgHO ggtlltyggtllte naAU mpu cBewu KOAko ggtlltyggtlltema ca 3anaAUAU cBewume B mpane3apuRma
nOAOBuHama ggtlltyggtlltema ca c 4epBeHu wanku KOAko ca CbC
3eAeHu I II I I I
Wecm ggtlltyggtlltema we nogpegtlltgam Macume KOAko ggtlltyggtlltema we nogpegRm egHa Maca Ha egHa om nokpuBkume e u36pogupaH omaoBopbm
llBeggtlltyggtlltemawe m16 4UHUU Bmpane3apuRma no kOAshyko mpR6Ba ga npeHece BCRko
I I I I I I I llgtlltyggtlltemama U meXHume aocmu we cegHam Ha 3 Macu no paBHo no kOAko cmOAa mpR6Bam 3a BCRka Maca Ha egHa om nokpuBkume e u36poshygupaH omaoBopbm Ha kOR
I I I I I I Om ggtlltyggtlltemama CbC 3eAeHUshyme wanku nOAoBuHama ca C04UshyAa KOAko om mRX uMam o4uAa
I I AeteHHe (2 H 3
~6bAkume ca 21 u ggtlltyggtlltemo mpR6Ba ga au pa3geAu no paBHo Bmpume cppykmuepu no kOAko R6bAku we
CAOgtlltU BbB BCRka I III I I I I 3BbH4emama no wanshy Om ggtlltyggtlltemama c OYUshykume Ha ggtlltyggtlltemama Aa nOAoBuHama ca ca 3AamHU cpe6bPHu u kbCOaAegu a gpyaume 6POH30Bu no paBeH 6poo UMam gaAekoaAegcmBo npe6poo 3BbH4emama KOAko ggtlltyggtlltema uuam KOAko ca 3AamHllme gaAekoaAegcmBo
I I I I I I I I I I I I I
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
A3 nbk aomBA MHoao nO-AeCHo om ggtkyggtkemama O~
BCU4ko CJaaaM no 4 kUJoapaMa HO Hukoaa He 3HaM kOJko AgeHe lle ce
nOJy4u L-1 Bce He YJY4BaM kOA meHggtkepa ga B3eMa Ule MU
nOMoaH9W JU
= 2
= 3
= 1
= 2
= 4 0
leA-e AyK 6ofi lyWKU opU3 Kapm(gu
Ha 2 paltjgtma
Ako cna3Baw Aomo Ha 6poela Hanu ko nbmu lle IlOHegeAHuk----shyIlOHeg8AHUk u ---shyn~g8AHUk 8mopHUk
nOH8g8A 48m8~mbk Anp83 npOA8mHam8 10 gHU
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
Peuenma N2 2 Kapmoffjll fiofi It Opll3
I I I
B kUAepa Ha 6060 6culiku nakemu U mop6u ca no 4 kUAoapaMa no kOAko kUAoapaMa om 6ceku npogykm UMa 6 kUAepa Ha 6060---------r--1---r-- 6paWHO - 9 nakema
Mopko6u - 5 mop6u
sl6bAku - 6 mop6u
3axap - 8 nakema
Ha 2 pacpma 6 kUAepa Ha 6060 UMa 4 pega no 4 6ypkaHa c kOMnom KOAko ca kOMnomume
~~I~I~I ~I~II~I~I~middot
Ha gpyau 2 pacpma UMa 4 pega no 3 6ypkaHa c mYPwuR KOAko ca 6ypkaHume c mYPwuR
~II~I~~I~I I~I~I~I~I~I~I_
KOAko ca 6culikume 6ypkaHu 6 kUAepa Ha 6060
I I I 1 I I I 1 1
Ako cna36aw npa6ushyAomo Ha 36e3goshy6poeua Hanuwu kOAshyko nbmu Ue Rgew 6 nOHegeAHuk-----------+-+---t---+--+--+---4
noH6geAHuk u 6mopHuk ------------+-f---+---+-+--+--4
nOHegeAHuk 6mopHuk u cpRga -----------+-+---+---+--+--+---4
nOHegeAHuk 6mopl-luk cpRga u 4em6~mbk _______ nn~nAHuk 6mopHuk cpRga
em6~mbk ~ebL ____ nOHegeAl-luk 6mopHuk cpRga 4em6~mbk nembk ~cb6oma __ nn~~(]Al-Iuk 6mopHuk cpRga
L4EIrllBlpmbk ~mbk~b6om~~eAR -t-+--+--+--+~I__-l A npu npOAeml-lama 6akaHuuR kORmo e 10 gl-lu
1
2
--t shy
--+shy
----
-t
-I
-f
--t shy
4
--t shy
--t shy --+
-+--+-
=
=
-+shy
--+
-+--
4
-+shy
--+shy
+~I__-l
--4
--4
Vnpil)I(HeHHSl 3a YMHO)KeHHC C 4
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
3Be3g06poeUbm e kynuA 28 3aaagb4Hu oaAegaAa U au e pa3geAuA no paBHo Ha 4emupume ema~a Ha 3aMbka no kOAko oaAegaAa UMa Ha Bceku ema~ BepHURm omaoBop e ckpum HRkbge HaMepu ao
AHU MU 6ewe ka3aAa 4e 6e3 ga 6POUM Mo~eM ga
n middotmiddotemHeM kOAko cBe~u naARm g~yg~emama B 3aMbka
BCRka Be4ep
Ako npou3BegeHuemo Ha 5 U 4 HaMaAUme 2 nbmu nOAY4eHomo YMHo~ume no 3 U npu6aBume 50 ~e nOAY4ume 6POR Ha cBe~ume B 3aMbka
j
I
5 = 5
2 = 1
3 = 1
5 = 2
5 5 = 6 5 = 7 = 3
5 = 4
9 = 4 VMHO)l(eH e c 5
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
npo onbAHU
CHamume 4UCAa
5 = 5
2 = 1 0
3 = 1 5
5 = 2 0
5 5 =
6 5 -7 = 3
5 = 4 0
9 = 4 5
Ha ma3U kapma 36e3g06poeshyUbm e Om6el~3al 36e3gume koumo e Ha61loga6al npe3 Howma c meleckona cu 3an04Hal ega au apynupa no 5 3a ga au npecMemHe nO-IeCHO OnumaO u mu
I I I I
geHuemo Ha 5 u 4 nbmu nOlY4eHomo 103 u npu6a6ume 50 Ie 6po~ Ha c6ewume
I
1shy
1
36e3g06poeUbm He e cnal URI8 HOW Ho kOlko MUHymu e aleg8l npe3 meleckona ~34UCIU no gHe6Huka My I I I I I I I
VMHO)l(eHHe c 5
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
3bullbullbull ~
KOAko e uHmepecHol Mogtke nbk kamo
nopacHa ga cmaHa acmpoHoM
npunoMHuM 4e koaamo B egHa 3aga4a UMa ck06u nbpBo ce u3BbpwBa geQcmBueshy
OuBemu c gtkbAmo me3U 3Be3gu Ha koumo UMa BepHU omaoBopu n03Ha AU koe e moBa cb3Be3gue
3Be3g06poeUbm epa3wucppoBaA cuaHaAU om kOCMoca U e Ha4epmaA no mAX me3U cpuaypku Ho 3a egHa cuaHaAbm e 6UA
53-15 HeAceH nOMoaHU My ga omaamHe kak u3aAegtkga AuncBaLUama cpuaypkafr t
V)27
)KumeAume Ha gaAe4Hama nAaHema He npUIU4am Ha 3eMHume Te ca 03Ha4UIU
54-20 ce6e cu c uucppu koumo ca npou3BegeHuA om ma6Auuama 3a YMHogtkeHue c 5
Ou6emu auAS cent A ------- V V l-136bH3eMHume ca om6eAA3alU
2 73_ 1 gtkumelume Ha 3eMAma c uuCPpu koumocent ca npou36egeHuA om ma6Auuama 3a
YMHogtkeHue c 3 Kou ca me
cent 52-10
23-8
3 -cent
-cent-BpeMe e ga cu
mo B ck06ume Ako HAMa ck06u nbpBo ce u36bpwBam geocmBuAma YMHogtkeHue u geAeHue
Vnpa)I(HeHHR 3a YMHOgtKeHHe c 1 3 4 H 5
OnumaO oUe npecMemHu HaOmiddot
HaO-MaAkama n nogpegu au no (
om HaO-aOMIMc HaO-MaAkal
4acmHO cbomBen
nAaHema I YacmHO I ~ no I
Hen1rH~~~~ =-~__ IOnumep 150 5 = I--------t--Mapc 130 5 = I ----- - ---i- shy
3eMR__I~~ ~ ~ j _ _ BeHepa 35 5 =
Macau
npaBUAHO AU nogp npoBepu Ako peWl gtkbAmama AeHma LMe nAaHema B CAbH4eBa caMo nem 3Haew AU
1 EgHa om nocokumf 3aAR3Ba CAbH~emo caMOAem 5 CBogbm ~ mo u 3Be3gume 6 n AeeHHe c 5
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
~Q28 8
06SA cuaHaJU no m~x me3U HSAbm e 6UA maamHe kak laypka
MaHema He ca 03HalUAU
Ipou36egeHuR raquokeHUe c 5
u$pu koumo 6Auuama 3a ~
)m6eAR3aAU
Map~ _I~~~ ~~_ _ Kamo u36bPWUW npeCMRmaHURma ~e nOAYlUW 3eM~ _I~~ ~ =---1 - _ IUCAO To noka36a 3a kOAko Meceua 3eMRma
B_e_H_ep_a_3_5__S_=I__ 06ukaAR OkOAO CAbHuemo
OnumaO o~e ceaa npecMemHu HaO-MaAkomo 4acmHO cbomBemcmBa Ha
HaO-MaAkama nAaHema nogpegu au no aOAeMUHa
om HaO-aOA~Mama go HaO-MaAkama
naHema I 4acmHO I Nv no peg
Hen~H-l~~~=--1-shyIOnumeEI~ ~ =-~__
f - 0-shy I
npa6UAHO AU nogpegu nAaHemume no 20AeMUHa npo6epu Ako peLUUUJ 6RPHO kpbcmocAo6uuama 6 gtkbAmama AeHma we nOAY4uLU UMemo Ha HaO-BOARMama nAaHema 6 CAbH4e6ama cucmeMa Ho 6 3aga4ama me ca caMO nem 3HaeLU AU kOAko ca Ha 6poO nAaHemume
1 EgHa om nocokume Ha c6ema 2 nocokama 6 kORmo 3aAR36a CAbHuemo 3 EgUH om ce30Hume 4 nUAom Ha CaMOAem 5 C60gbm Hag Hac Ha koOmo 6ugtkgaMe CAbHueshymo U36e3gume 6 nmuuama CMRmaHa 3a uap Ha He6emo
1
12 3
14 5
6
AeAeHllle c 5
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
I
MbHU4kume 4raquoeu om 3aMbka cb6upam 6uIku u au npeHacRm 8 mop6u4ku
I
no B apaMa KOAko 6UAku ca cb6pMU mpume cpeu 06LUO I KOAko ap 6UAku LUe cb6epe egHa cpe~ 6 9 mop6u4ku CAeg kamo u3cywam 6uAkume cpeume au HacunBam BaOAeMU kHUgtkHU nAuko6e U maka au cbxpaH~Bam npe3 3UMama Bceku nAuk cb6upa 7 mop6u4ku KOAko apaMa cb6upa 1 nAuk
nonbAHU nponycHamume 4UCAa
1 6 = 2 = 1 2
6 = 1 8
4 6 = 5 3 0 1
~ 3 6
= 4 2
8 = 4 8
9 6 =
Clgteume npoga6am cyweHume 6uAku EgUH apaM cmpy6a 6 cmomuHku Ako 3a cympewHuR 480 cu kynuw 4 apaMa kOAko ~e mu cmpy6a moO
I I I I I I I VnpagtKHCHMC la YMHO)l(C
VMHO)l(CtUtc c 6
6060 e nonpa6 kpaH06eme e 3a UMa npOU30e~Jelu
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
- --- --===
6060 e nonpaB~A BogonpoBoga 3a qgtoHmaHa Ho e 3a6paBuA koO om kpaHoBeme e 3a Heao nogckagtku My ToO e 3a mpb6ume BbPXY koumo UMa npou3BegeHuR caMo c 4UCAomo 6
I
~aCAm 6 mop6u~ku
I I II I I I I I
9MU kHUgtkHU l1Juko6e
I I I I
C-=III
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
426+9=0 0 7+606=0 0 546=0 0 48 (30 5) =00 9+486=0 0 186-2=0 0 36 6 + 5=0 0
6 6 =
HRk oO gtK uBee B kYAama Ha aaMbka LUe HaY4Uw koo e moO ako npaBuAHo pewuw aaga-4ume nOAY4eHomo 4UCAO we mu nokagtKe kOR no peg 6ykBa om a36ykama ga Hanuwew
_-u
54 6 =
24 6 =
12 6 =
ACtCHIitC C 6
TOH40 Mogtke ga ce ka4u go kYAama caMo ako npa6uAHo pewu aaga4ume Lr1Ha4e cmbnaAama we ce cpymAm
I I
I opaHgtk 36 4=
I AUAa6 9 3 =
1middot 1 1=1 I 1 1=1 I I +1 I 1= I
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
gbaama Ho ga
u3pa3ume
44epBeHo
10 Mogtke ga CS I go kYAama ) ako npaBUAHo U 3aga4ume ~e cmbnaAama e cpymAm
I
1 cAagoAsg om 9 AsBa
1 ltlgteume ca nOpb4aAU Ha luAu ~---- 2 ga ouBemu ~---1 3 nbpBo mpR6Ba--shy --I 4 npecMemHe
I opaHgtk36 4=
I 3SASH 15 3=
------I ~ nOMoaHu Q Hanuwu cpell-Y __----J 7 BCRka UUQgtpa cbomBemHuR
uBRm A nOCAe au ouBemu
9
6
5
___--- nOM08HU Ha ggtkyggtkemamaIga npscMemHam ueHume
===I AUAaB 9 3 =
I cB CUH 28 4=
= =
A a3 mpR6Ba ga cspBupaM 2 cynu no
5 AsBa 3 RcmUR no 4 AsBa 3 4aR no 6 AsBa U
+ = I I I L-I1-1LI+1I--L-~1+1---L-I_+1-1L-I-~-- Vnp()I(HeHIltSi 3a YMHO)l(eHllte lit AeAeHllte c 2 3 4 5 lit 6
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
6060 3an04HaA ga cnecmRBa napu B 2 kacu4ku nycHaA BbB BCRka no 7 AeBa KOAko AeBa UMa B gBeme kacu4ku
V1MaA B ggtko6oBeme cu OLUe 28 AB Cb6paA Bcu4kume napu B egHa kacu4ka KOAko AeBa ca cmaHaAu
Hamume 4UCAa
7 = 7 =
= 2 1
7 2 8
= 3 5
7 = 7 = 4 9
7 = 6 3
7
peCMemHU 3pa3ume U oapagu caMO me3U 4UCAa BbPXY 3HaMemo
Koumo ca paBHu Ha omaoBopume
3+34=
9-42=
26+4=
27+37shy
47+57shy
67+77shy
llgtkyggtkemama ~ MeAHuuama n aoguHu lile Hi kOAko om omaol+~
nonbAHU
1
2
3
6
8
=
VMHO)l(eHMe ChC 7
KoO AU cmou 3ag 6060 CbeguHu nocAegoBameAHO 3anUCaHUme 4UCAa U U(e pa36epew BCRko cAegBaU(o 4UCAO e CbC 7 noBe4e om npeguwHomo
49
56 Q Ggt
3a BCRka peg apugtkam 14 ltlgteu ltlgteu ce apwkam kowep
AeAeHMe (bC 7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
-28
r---------~------~~----------~~~~~~~~
7
npeCMemHU aume U oepagu
MO meau YUcJa pxy aHaMemO mo ca pa6HU Ha maoBopume
4 shy2=
4 shy37 shy5 7 shy7 7 -
ToBa e B~mbPHama MeJHU14a Ha aaMbka npeCMemHU UomkpuO koe om kpuJama mp~66a ga ce nonpa6u 0146emu eo
G BCU4kume cu napu 6060 kynuJ -_~ 7 6alttgtJu KOJko cmpy6a egHa
6alttgtJa
B apaguHama aag MeJHU14ama ca
3a 6c~ka pegU14a ce apugtkam 14 lttgteu KOJko lttgteu ce apugtkam 3a eguH kowep
II I I ACAeHHe CbC 7
kowepume Ha nyeJume Te ca 06wo 49 U ca 6 7 pegu14u no kOJko kowepa UMa 6b6 6c~ka pegu14a
I I I I I I I
ngtkyggtkemama ca nocmpouJu MeJHU14ama npegu MHoao aoguHu We HaY4uw npegu kOJko om oma060pa Ha 6~PHO peweHama aagaya
49 7 + 23 = 7 + 23 = 31
21 7 + 6 = 3 + 6 = 18
14 + 21 7 = 35 7 = 5
9 7 + 63 7 = 63 + 9 = 72
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
I i
I
CaMO egHa Bpama e omk04eHa T oBa e Bpamama Ha kORmo BCU4ku 3aga4u ca peweHu BRpHO Ako R omkpURm AUAU T0H40 U Becko we Moaam ga BAR3am B apaguHama c kowepume A mu we R om6eAegtkuw AU Oapagu apewHume omaoBopu
96==54 36 4 == 9 93== 18 35==25
60 60 ce e U3xumpUA 3an04 HaA e ga konae mYHeA nog cmeHama TpR6Ba ga u3konae 06wo 12 Mempa nog 3eMRma 3a eguH geH u3konaBaA 3 Mempa npecMemHu kOAko gHU mpR6Ba ga pa60mu 5060
VnpCl)I(HCHHSI 3a YMHOgtKCHHC H AeAcHHc C 2 3 4 5 6 H 7
nog4epmaO apeWHume omao6opl
2 8 = 1
6 8 = 6 I 3 8 = 2
5 8 = 4
8 8 = 7
6 8 = 4
4 8 = 3
9 8 = 7
2 8 = 1
VMHOgtKeHHe C 8
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
mkJ104eHa T o6a e 3CU4ku 3aga4u ca kpURm AUJu TOH40 IR3am 6 apaguHama R om6eJegtkuw JU
o6opu 3Haew JU
4e koaamo n4eJama gt---1 emu 6 kpba mR cbo6U4a6a
4e Hekmapbm e 6JU30 A koaamo onuc6a oCMopka
nog4epmaa apeWHume omao6opu
2 8 =
6 8 =
3 8 =
5 8 =
8 8 =
6 8 =
4 8 =
9 8 =
2 8 =
1
6
2
4
7
4
3
7
1
2
4
4
0
2
8
2
2
6
36e3go6poeUbm eomxJynuJ egUH kowep KOR om kUJuOkume ce pa3Ju4a6a om OCmaHaAUme Ou6emu R
06ukHo6eHo om eguH kowep ce nOJy4a6am
121 181= I I I kUJoapaMa Meg
Ho UMa U pekopgHu go6u6u om
11 101 middotlsl= I I I kUJoapaMa Meg
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
~
T03U koOmo e HapucyBaH
B M03aOkama U4e mu omkpue MaaURma Ha 4UCAomo 9 Ho mpR6Ba ga BHuMaBaw npu
ouBemRBaHemo
TaM kbgemo 4UCAomo ce geAu Ha 8 ouBemu CbC cBemAo CUHbO A kbgemo He ce geAu Ha 8 ouBeniu c kacpRBo
BHUMal11 noaAegHu gBe
CBuBaw m03U n noka3Ba koe 4UC Baw no 9 kamo ~
HagRcHo OmaoBo npbcmume omARB
noka3Bam gecel gRCHO noka3Ba
CBumuRm He ce 6
Kou npou3BegeHufi ca BepHu
9 9 = 9 1
4 9 = 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
1 5 9 = 4 0
9 9 = 8 1
VMHU)I(CHMe c 9
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
[3U HapucyBaH lwe mu omkpue UCAomo 9 Ho uMaBaw npu
BaHemo
Iomo ce geAu Ha 8 10 CUHbO A kbgemo oLBeniu c kacentRBo
BHUMameAHO n02AegHu gBeme MU Pbue
CBuBaw m03U npbCm koOmo noka3Ba koe 4UCAO we YMHogtkashyBaw no 9 kamo 6pouw omMIBo
HagRcHo Om20Bopbm e npeg me6 npbcmume omARBo Ha C2bHamUR
noka3Bam gecemuuume a omshygRCHO noka3Bam eguHuuume
CBumuRm npbcm __-li~ He ce 6pou
Kou npou36egeHuR ca 6epHu
9 9 = 9 1
4 9 3 6
2 9 = 1 9
7 9 = 6 3
3 9 = 2 7
8 9 = 7 2
2 9 = 1 8
5 9 = 4 0
9 9 = 8 1
Ako pewuw npaBuA-HO 3aga4ama we omkpuew Ha kOAko 20gUHU e Becko
59-49=
npecMemHu kOAko cmbnaAa u3ka4Ba npu3pakbm k02amo ce npu6upa B cBoRma kYAa
39+89 shyVMHO)l(CHHC C 9
Om20Bopu AU Ha Bbnpoca kOAko ca nAaHemume B CAbH4e6ama cucmeMa Ako He cu 3HaeA ce2a 3anOMHU Te ca 9
onumaM
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
6060 e BMI3bA B Aa60pamopuRma Ha 3Be3g06poeua 3a ga cu Hagye 6aAoHa Ako HanucaHume BbPXY kOA6ume 4UCAa ce geMlm Ha 9 6MoHbm My we nOAemu Ho ako UMa apewka we u36yxHe CnpaBUA AU ce e 6060
~~ Oapagu BepHUR omaoBop
BepHU AU CG paBeHcmBam
30 - 3 = 3 70 - 7 = 7 49=40-shy50 - 41 = 1 36-4=4 63-7=7 8 9=98 38=64
~~
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
A B Aa60pamopURma oe14a 3a ga CU Hagye HanucaHume BbPXY
Aa ce geARm Ha 9 ~e nOAemu Ho ako ~a U4e u36yxHe pe e 6060
~sectJ omaoBop
BepHU AU ca paBeHcmBama
30 - 3 = 3 9 70 - 7 = 7 9 49=40-4 50 - 41 = 1 9 36 - 4 = 4 8 63-7 = 78 89=98 38=64
~~
CAeg onuma c 6aAOHa 6060 e pewuA ga nOAemu c XBbp4uA a Ho XBbp4uAama lUe U3AemRm aka omaoBopume BbPXY rTmX ca BepHu
Vnpil)KHeHHSl 3a YMHO)l(eHHe H AeAeHHe c 8 H 9
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
ltbeume ca OpaaHU3UpaAU AOmapU R Bceku 6uAem ne4eAU m03U npegMem BbPXY koOmo e HanUCaH omaOBOpbm Ha 3aga4ama
9
6 1 0 = 5 1 0 = 7 0
8 1 0 = 8 0
3 1 0 = 3 0 Hanuwu koO kakBo cne4eAU
1 1 0 = 1 IUAU 5 1 0 = 5 0 Becko-------------shy
2 1 0 = 1 0 TOH40shy - ------shy - ---shy
6060- - ---- ------ -- shy4 1 0 = 4 0 5060- --shy - --shy- --shy - - -
HMC c 10
npu3pakbm e 3aMbkauce 3aga4ama U4e U4e ce cb6ygu
5 10 - 2 10 =
npegu ga 3acnu Ha 3aMbka
ToO mu npUnOMH~ UMa cb6upaHe U
geAeHue U HRMa cl geOcmBuRma YMHC ck06u nbpBo ce ck06ume
AeieHHe c 10
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
(ak60 cnSYSIU
Ako YUCAama BbPXY kaMbHume ca yaCmHU om ma6Auuama 3a geAeHue c 10 nupaMugama HRMa ga ce cpymu llo6pe AU au e u36pal TOHYo
~~ Oapagu BepHuR omaoBop
npu3pakbm e YMopeH om mOAkoBa WYM B 3aMbka U ce npu6upa ga cnu Ako pewuw BRPHO 3agayama we pa36epew cAeg kOAko aoguHu w e ce cb6ygu nak
5 10 - 2 10 =
npegu ga 3acnu moO 06ukaAR BcuYku cmau Ha 3aMbka npecMemHu kOAko ca cmaume
(12 - 7) 10 =
ToO mu npunoMHR ye koaamo B egHa 3agaya UMa cb6upaHe u3BagtkgaHe YMHogtkeHue u geleHus u HRMa cko6u nbpBo ce u3BbpwBam geOcmBuRma YMHogtkeHue u geAeHue Ako UMa cko6u nbpBo ce u3Bbpw Ba geOcmBuemo B cko6ume
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
W
Pewu 3aga4ume
5 1 = 1 1 = 9 1 =
6 1 = 5 1 =
TpA66a ga 3anOMHAI ToBa e MHoao BagtkHO Koaamo
eguHuRm om MHogtkumeiume e 0 mo u npou3BegeHuemo e O
50=05=0 C 4UCAomo 0 He MoJke ga ce geAul
5 0 e HeBb3MogtkHo geOcmBue
9 0 = 8 0 = 6 0 = 3 0 = 4 0 =
5
0
0
0
0
4 VMHO)KeHHe H AeAeHHC C 1 H 0
7(2+~
93-1=
6+60=
(6 + S) (
Vnp()I(HeHHII 3a I
72 + 3
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
Pewu 3aga4ume
5 1 = 5
1 1 =
9 1 =
6 1 = 5 1 =
Sue o6ukOAuxme
(HO Koaamo 1eAume e 0 mo lemo e O 5=0 ke g8 ce geAu IMO)(HO
Je
72+ 3 = 84+56=
7 (2 + 3) - 355+2=
9 3 - 1 shy =
6 + 60= 70 10 =
Ako HRMa cko6u nbP80 geAuM U
YMHo)(a8aMe a nOCAe u38a)(gaMe U
cb6upaMe
(6 + 6) 0 = 7 0 =
Vnpa)I(HeHHSl 3a pewaBaHe Ha 3aAa~H CbC CKo6H
9 0 =
8 0 =
6 0 =
3 0 =
4 0 =
0
0
0
0
4
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
bull
16=6 26 = 12 36=1 8 46=24 56=30
66=36 76=42 86=48 96=54
106=60
13=3 23=6 33=9 43=12 53=15 63 = 18 73=21 83=24 93=27
103 =30
17=7 27=14 37=21 47=28 57=35 67=42 77 = 49 87=56 97=63
107=70
14=4 24=8 34=12 44=16 54=20 64=24 74=28 84=32 9 4=36
104 =40
15=5 25=10 35=15 4 5=20 55=25 65=30 75=35 85=40 95=45
105=50
110=10 210=20 310=30 410=40 510=50 610=60 710=70 810=80 910=90 010=1
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
t=---shy
YnpagtkHUmelHama mempagka no MarneMamuka 3a Bm09u klac
YampfA CE fJA YMHOgtKABA M AEIA e He06xOguMO u nOllc33HO nOMaZalO 38 Yltiumelume YIeHUUUme u pogurnelume koumo g06pe nOOHaBam
u npegnollumam cepuAma om ynpa)(HumelHu mempagku Ha Vl K 3AamHOmO name
nognoMaeaHO om cBourne BpbCmHuuu om cmpaHuuume Ha mempagkama gememo C Iekoma OCMUCIR u ycBoABa geucmBuRma
YMHogtkeHue U geleHUe koumo ocBeH naMem u3uckBam u kOM6uHamuBHocm C me3U cBou npUAmelU Bawemo geme we npoHukHe B 3aMbka Ha iUCl8ma
om 1 go 100 kamo ce cnpaBR C Pa3IUllHU aaeagku no nbmR Clj
Tpound u B CAeyBawurne klac06e LL(e 6bgam 3oogHo C Heeo B ~IOCmHama cePUR om Yie6HU MamepUalu koumo ca 06Bbp3aHu B eguHHa
npoBepeHa a npakmukama Memoguka I OT CepIUITa Yge6HH nOMaraJ1a Ha 11 K 3J1aTHOTO naTe
Ta3H rO~HHa me HaMepHTe
Ja oeq(lma 6 llPERYfHJlHmHA Bb3PACT u flhPBH KJIAC A3 me 6bna nbpBoKRacHHK-l A3 lUI 6 blla flbpBoKRacHHK-2
A3 -leTa H CMRTaM Ilbpso 6yr(f~apte
3a YIenuqume 8 llhPBH KJlAC Yfa ce )la llHwa-l Y-Ia ce tla lIHilla-~ YIa ce na nHwa-3
POatH Kpaii 3a ITbpBH KRac - Yll pailltHI1TtJ1HH TeCTO Be Yfa ce lIa CMJlTaM t
3a yleHUqume 3M BTOPH KJlAC Yfa ce lIa YMHoxltaaaM H lIeRJI
npOlleH Kpaii 3a STOPH KRach - ynpa)KHI1TeRHH TeCTOBe Yta ce aa KOM6HHHpaM - 3aHlfMa1eRHa TeTpaJJKa
no MaleMaTHKa II TPYlI H TBopteCTBO
I Cocentw 199-1
IO( 3llJ1tJNlHlU1lWJ1W 0 Muwa K4JOJlIlOiJ4 - UllmlJp CmDJUI H_ _ dJltnOp
~ CIUIa Cmelfiwoo - C)IlKU e rfLWIltU 3JCll7UIIlIl - ClOmiddotemJUJ KDIUjIJuptJl DglOpUIUU
ISBN 954-431-082-7
Top Related