6 th Grade Fractions Chapter Questions
1. Explain how to add, subtract, multiply and divide fractions.
2. Explain why you multiply by the inverse when dividing.
3. What is the GCF and how do you determine it?
4. What is the LCM and how do you determine it?
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Chapter Problems
Greatest Common FactorClassworkFind the Greatest Common Factor of each set of numbers.
1) 72 and 64
2) 15 and 16
3) 14 and 49
4) 15 and 75
5) 66 and 147
6) 78 and 42
7) 75 and 18
8) 98 and 66
9) 27 and 72
10) 18 and 21
HomeworkFind the Greatest Common Factor of each set of numbers.
11) 30 and 45
12) 70 and 130
13) 98 and 30
14) 45 and 66
15) 77 and 21
16) 63 and 45
17) 36 and 63
18) 21 and 40
19) 6 and 51
20) 63 and 99
Least Common MultipleClassworkFind the Least Common Multiple of each set of numbers.
21) 9 and 21
22) 12 and 80
23) 6 and 10
24) 14 and 12
25) 15 and 36
26) 8 and 20
27) 9 and 6
28) 15 and 10
29) 8 and 14
30) 55 and 22
HomeworkFind the Least Common Multiple of each set of numbers.
31) 9 and 15
32) 4 and 7
33) 12 and 15
34) 10 and 9
35) 8 and 14
36) 11 and 13
37) 42 and 21
38) 4 and 6
39) 14 and 63
40) 22 and 8
GCF/LCM ApplicationsClasswork
41) Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie.
a. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?
b. How many of each cookie will she put in each container?
42) Beginning at 8:30 A.M., tours of the National Capitol and the White House begin at a tour agency. Tours for the National Capitol leave every 8 minutes. Tours for the White House leave every 10 minutes. How often do the tours leave at the same time?
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43) Joe is making key chains with beads. He wants each key chain to have the same number of beads. He has 90 blue beads and 72 yellow beads.
a. What is the greatest number of key chains he can make that are exactly the same?b. How many of each color bead will be on each key chain?
44) A florist has 36 roses, 27 tulips, and 18 carnations she must use to create bouquets.a. What is the largest number of bouquets she can make without having any flowers left
over?b. How many of each flower will she put in each bouquet?
45) A radio station is giving away prizes to its callers. Depending on what number caller you are, you receive a different prize.
What number caller will be the first to receive all 3 prizes?
Homework46) Two neon lights are turned on at the same time. One blinks every 4 seconds and the other blinks
every 6 seconds. In 60 seconds, how many times will they blink at the same time?
47) Shannon is making identical balloon arrangements for a party. She has 32 maroon balloons, 24 white balloons, and 16 orange balloons. She wants each arrangement to have the same number of each color.
a. What is the greatest number of arrangements that she can make if every balloon is used?b. How many balloons of each color will be in each arrangement?
48) At a display booth at an amusement park, every visitor gets a gift bag. Some of the bags have items in them as shown in this table.
What number visitor will be the first to receive all 3 items in the gift bag?
49) There are 48 girls and 64 boys in the school choir. The choir teacher plans to arrange the students in equal rows. The same number of boys and the same number of girls will be in each row. What is the greatest number of rows the teacher can arrange?
50) Mike can buy red push pins in packages of 10 and yellow push pins in packages of 12. What is the least amount of packages of each color he must buy in order to have the same number of pins?
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Prizes CallerHat Every 3rd callerT-shirt Every 5th callerBackpack Every 6th caller
Items BagsHat Every 2nd visitorT-shirt Every 7th visitorBackpack Every 10th visitor
DistributionClassworkUse the Distributive Property to rewrite each expression:
51) 45 + 75
52) 18 + 27
53) 77 + 91
54) 32 + 44
55) 46 + 69
56) 51 + 17
57) 24 + 66
58) 38 + 95
59) 85 + 95
60) 35 + 22
HomeworkUse the Distributive Property to rewrite each expression:
61) 20 + 44
62) 30 + 400
63) 63 + 72
64) 9 + 12
65) 33 + 45
66) 34 + 51
67) 65 + 91
68) 102 + 42
69) 104 + 78
70) 26 + 13
Adding FractionsClassworkSimplify to lowest terms:
71)12+ 12
72)14+ 24
73)312
+ 1412
74)57+ 37
75)1232
+ 1632
76) 1 13+3 23
77) 1112
+2 512
78) 3 57+2 37
79) 6 19+4 49
80) 3 332+11 15
32
81)12+ 13
82)13+ 25
83)310
+ 512
84)56+ 37
85)1218
+ 26
86) 1 12+2 13
87) 4 14+5 17
88) 9 312
+5 1120
89) 6 111+4 49
90) 3 324+1116
32
HomeworkSimplify to lowest terms:
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91)14+ 34
92)26+ 36
93)618
+ 618
94)1112
+ 1512
95)416
+ 616
96) 316+2 36
97) 1 38+3 58
98) 5 118
+2 718
99) 2 413+3 1113
100) 7 1112+ 512
101)28+ 49
102)38+ 712
103)1112
+ 1522
104)20100
+ 30150
105) 1 14+2 35
106) 1 38+3 59
107) 4 27+4 25
108) 10 1730
+1 512
109) 7 1112
+ 516
Subtracting FractionsClasswork
110)52−32
111)57−27
112)78−38
113)1520
− 920
114) 2 34−1 1
4
115) 3 1422
−3 322
116) 7 56−4 3
6
117) 43 1314
−13 1114
118) 11 19−10 1
9
119)712
− 312
120)710
−35
121)34−23
122)1112
−29
123)1520
− 712
124)70120
−3090
125) 2 34−1 13
126) 5 25−2 17
127) 7 35−4 5
6
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128) 43−13 110
129) 11 38−10 1
9
Homework
130)72−32
131)65−35
132)810
− 210
133)238
−118
134)84120
− 22120
135) 3 24−1 1
4
136) 6 1221
−5 521
137) 13 1524
−11 624
138) 15 35−6 25
139) 79 3350
−56 850
140)78−37
141)45−13
142)814
− 210
143)2340
−38
144)810
−2255
145) 3 25−1 14
146) 6 16−5 1221
147) 7 49−7 16
148) 41 1320
−30 615
149) 15−6 35
150) 79 3350
−56 720
Multiplying FractionsClasswork
151)14• 23
152)25• 56
153)310• 512
154)16• 39
155)1215• 612
156) 2 • 12
157) 8 • 35
158) 6 • 49
159) 2 • 516
160) 3 • 1532
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161) 1 12• 2 12
162) 1 13•3
163) 8 •1 35
164) 9 12• 45
165) 3 310•2 311
Homework
166)26• 37
167)28• 49
168)38• 712
169)513• 710
170)1112• 1522
171) 3• 56
172) 2 • 58
173) 5 • 718
174) 10 • 1430
175) 7 • 512
176) 316• 2 25
177) 1 38•3
178) 2 45•3 47
179) 6 14• 45
180) 2 110•4 27
Dividing Fractions Classwork
181) Use the model below to demonstrate: 2÷ 12
182) Use the model below to demonstrate: 56÷ 23
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183) Use the model below to demonstrate:4 12÷ 12
184)12÷ 13
185)25÷ 56
186)1218÷ 26
187)1215÷ 612
188) 6÷ 49
189) 2÷ 516
190) 3÷ 1532
191) 8÷ 35
192) 5 14÷ 18
193) 3 57÷2
194) 6 411÷4 49
195) 3 13÷4 15
Homework
196) Use the model below to demonstrate: 3÷ 56
197) Use the model below to demonstrate: 23÷ 56
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198) Use the model below to demonstrate: 2 12÷ 12
199)38÷ 712
200)410÷ 27
201)312÷ 520
202) 26÷ 37
203) 2÷ 58
204) 5÷ 718
205) 10÷ 1430
206) 7÷ 512
207) 5 14÷2 13
208) 2 18÷3 34
209) 2 110÷ 38
210) 3 19÷ 56
Fraction Operations ApplicationClasswork
211) How much candy will each person get if 5 people share 6 ½ pounds of Swedish Fish?
212) How many
23 cup servings are in 1½ cups of cheese?
213) How long is a rectangle if its width is 2 310 feet and its area is
83750 square feet?
214) A recipe calls for
34 cup of brown sugar. If you want to make
14 of the recipe, how many
cups of brown sugar do you need?
215) For a party, you buy 8 34 lbs of salt water taffy. If 150 people are attending, how much
salt water taffy does each person get?
216) A cook has
35 ounce of pepper. A recipe for a steak marinade requires
115 ounce of
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pepper. How many batches of marinade can the cook produce from
35 ounce of pepper?
217) Max wants to run 5 12 miles to train for track season. If the total length around the track
is
34 mile, how many laps does Max need to run around the track?
218) You are making hamburgers for a barbeque with your family and bought2 12 pounds of
ground beef. If you want to make
13 pound hamburgers, how many can you make from
2 12 pounds of ground beef?
219) Annie is baking cupcakes. The recipe calls for 13
cup of butter, 27
cup of sugar, and 23
cup of milk. How many cups of ingredients is that altogether?
220) Ben has 55 baseball cards. He will give 15 of his cards to his younger brother, Phil. How
many cards will Phil get?
221) Kelly has 45 cookies. She plans on bringing 23
of the cookies to school to share with her
class. How many cookies is she not bringing to school?
222) Jim needs 4 12 cups of bleach for every ten gallons of water for cleaning. How many
cups of bleach should he use if he is making 5 gallons?
223) If x4=5 is true, is
x5=4 also true? Why or why not?
224) Evaluate the expression 4d+ 23
if d = 5.
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225) Sue has a picture that is 7 12
inches across and 8 inches long. She wants to put a border
that is 1 14
inches around the picture. What is the new perimeter of the picture, including
the border?
Homework
226) How many nuts will each person get if 9 people share 28 45 pounds of nuts?
227) How many 1 23 cup servings are in
15 14 cups of salsa?
228) How long is a rectangle if its width is 3 38 feet and its area is 27 square feet?
229) A recipe calls for 4 34 cups of flour. If you want to make
3 12 of the recipe, how many
cups of flour do you need?
230) For the first day of school, you buy 51 34 lbs of cookies. If you share with the 23 people in
homeroom, how many pounds of cookies do you give each person?
231) A cook has
47 ounce of baking powder. A recipe for chocolate chip cookies requires
128
ounce of baking powder. How many batches of cookies can the cook produce from
47
ounce of baking powder?
232) Anthony wants to run 8 12miles to train for track season. If the total length around the
track is
34 mile, how many laps does Anthony need to run around the track?
233) You are making a cake for a friend’s birthday and bought2 35 pounds of
butter. If each layer of the cake requires
13 pound of butter, how many layers can you
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make from2 35 pounds of butter?
234) Pamela is baking muffins. She will put 34
cup of dried cranberries, 23
cup of sliced
almonds, 18
cup of raisins, and 1 14
cup of milk. How many cups of ingredients is that
altogether?
235) Brenda has 120 stickers. She will use 14
of them to decorate her folder. How many
stickers will she put on her folder?
236) Melanie works with 33 people. 13 of her coworkers are male. How many are female?
237) Krista uses 2 23
tablespoons of drink mix for every liter of fruit punch. How many
tablespoons does she need if she is making 5 liters for her class party?
238) If 7t=21 is true, is t=21 ∙7 also true? Why or why not?
239) Evaluate the expression 56+ v7
if v = 3.
240) Karla has a painting that is 20 inches across and 11 12 inches tall. She wants to put a 2 23
inch border around the painting. What is the area of the painting, including the border?
Fractions Multiple Choice Questions
1) Find the Greatest Common Factor of 24 and 72.a. 12b. 24c. 6d. 72
2) What is the Least Common Multiple of 3 and 18?a. 36b. 6c. 3d. 18
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3) A cookie recipe calls for 234
cups of chocolate chips. If you want to make 14
of the recipe, how
many cups of chocolate chips should you use?a. 11 cups
b.1116cup
c. 3 cups
d. 1 38 cups
4) Use the distributive property to rewrite 16 + 64a. 16(1 + 4)b. 8(2 + 8)c. 4(4 + 16)d. 2(8 + 32)
5) 4 is the GCF of which two numbers?a. 8 and 16b. 16 and 32c. 8 and 12d. 24 and 36
6) 48 is the LCM of which two numbers?a. 16 and 48b. 12 and 4c. 6 and 8d. 2 and 24
7) How many 25
ounce servings are in 3 47
ounces?
a. 1 37
servings
b. 4 37 servings
c. 3 835
servings
d. 8 1314
servings
8) Use the distributive property to rewrite 12 + 74a. 6(2 + 13)b. 4(3 + 19)c. 2(6 + 37)d. 12(1 + 6)
9) 1 56
+ 3 79
a. 4 354
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b. 5 1118
c. 4 34
d. 4 2918
10)58
• 49
a.518
b.2072
c. 11332
d.418
11)78
−35
a.43
b. 1 13
c.1140
d. 1940
12) 1 15 ÷ 34
a.910
b. 1320
c. 1415
d. 135
Fractions Short Constructed Response Questions
13)14+ 25 = ______ 14)
59−16 = ______
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15) 6 58−3 4
5= ______
16) 413•3 45 = ______
17)67• 1011
=______
18)67÷ 38
= ______
19) 3 29÷1 23 = ______
20) Use the distributive property to rewrite
56 + 72 ______
21) What is the GCF of 15 and 54? ______
22) What is the LCM of 16 and 36? ______
Extended Constructed Response Questions
23) In order to buy wall paper, Abby needed to find the perimeter (total distance around the outside) of her bedroom. She measured each of the following lengths of her walls
East wall: 1038 ft North Wall: 12
716 ft West Wall: 10
38 ft South Wall: 8
516 ft
What is the perimeter of Abbey’s room?
Her sister Anna’s room is a square (four equal sides) of walls that are 1038
ft. Will Anna need to
buy more or less wallpaper than Abbey? Show all of your work to support your answers.
24) Nick wants to order enough food for his party. He knows medium pizzas come in slices of 6, and large pizzas come in slices of 8. He wants enough pizza for each of his friends to have 3 slices.
Write a fraction to show how many slices per large pizza each of his friends will eat.
If Nick wants to invite 10 friends over, how many large pizzas should he order? If he wants to order medium pizzas instead, how many will he need? A large pizza costs $12 and a medium pizza costs $9. Which type of pizza should Nick buy for
his party? Show all of your work to support your answers.
25) To find the volume of a swimming pool, you must multiply the length, width, and depth of the pool together. Michelle wants to find out how much water she needs to fill her pool.
She measured a length of 20 12
ft, a width of 12 23
ft, and a depth of 6 12
ft.
What is the volume of Michelle’s pool in cubic feet?
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If she needs to buy 6 13
gallons of water for each cubic foot of space, how many gallons of water
will it take to fill her pool? Show all of your work to support your answers.
26) For a science project, Ms. States asked each of her students to measure how much gas they used driving to school each week. The students measured the amount of gas in
fractions of a tank. Mike used 25 of a tank, Jamie used
516 of a tank, Josh used
49 of a
tank, Adam used 37
of a tank, and Kate used 14
of a tank.
Rank the amount of gas used by each student, from least to greatest
If a tank of gas costs 24 12
dollars, how much money did Josh and Kate spend on gas combined?
Show all of your work to support your answers.
27) Miriam’s uncle donated 120 cans of juice and 90 packs of cheese crackers for the school field trip. Each student is to receive the same number of cans of juice and the same number of packs of crackers. What is the greatest number of students that can go on the field trip and share the food
equally with no food left over?
How many cans of juice and how many packs of crackers will each student receive? Explain.
28) Jeremy and his little sister, Deborah, are at a carnival. There are both a large and a small Ferris wheel. Jeremy gets on the large Ferris wheel at the same time his sister gets on the small Ferris wheel. The rides begin at the same time. The large wheel makes one revolution in 10 seconds and the small wheel makes one revolution in 7 seconds.
How many seconds will pass before Jeremy and Deborah are at the bottom at the same time
again?
How many times will each Ferris wheel go around before Jeremy and his sister are both on the
ground again?
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Answer Key
1) 8
2) 1
3) 7
4) 15
5) 3
6) 6
7) 3
8) 2
9) 9
10) 3
11) 15
12) 10
13) 2
14) 3
15) 7
16) 9
17) 9
18) 1
19) 3
20) 9
21) 63
22) 240
23) 30
24) 84
25) 180
26) 40
27) 18
28) 30
29) 56
30) 110
31) 45
32) 28
33) 60
34) 90
35) 56
36) 143
37) 42
38) 12
39) 126
40) 88
41) a. 6 containersb. 5 oatmeal and 8
chocolate chip
42) Every 40 minutes
43) a. 18 key chainsb. 5 blue, 4 yellow
44)
a. 9 bouquetsb. 4 roses, 3 tulips, 2
carnations
45) 30th caller
46) 5 times
47) a. 8 arrangementsb. 4 maroon, 3
white, 2 orange
48) 70th visitor
49) 16 rows
50) 6 packages of red, 5 packages of yellow
51) 15(3 + 5)
52) 9(2 + 3)
53) 7(11 + 13)
54) 4(8 + 11)
55) 23(2 + 3)
56) 17(3 + 1)
57) 6(4 + 11)
58) 19(2 + 5)
59) 5(17 + 19)
60) 1(35 + 22)
61) 4(5 + 11)
62) 10(3 + 40)
63) 9(7 + 8)
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64) 3(3 + 4)
65) 3(11 + 15)
66) 17(2 + 3)
67) 13(5 + 7)
68) 6(17 + 7)
69) 26(4 + 3)
70) 13(2 + 1)
71) 1
72)34
73) 1 512
74) 1 17
75)78
76) 5
77) 3 ½
78) 6 17
79) 10 59
80) 14 916
81)56
82)1115
83)4360
84) 1 1142
85) 1
86) 3 56
87) 9 1128
88) 14 45
89) 10 5399
90) 14 58
91) 1
92)56
93)23
94) 2 16
95)58
96) 5 23
97) 5
98) 7 49
99) 6 213
100) 8 13
101)2536
102)2324
103) 1 79132
104)25
105) 3 1720
106) 4 6772
107) 8 2435
108) 11 5960
109) 8 1148
110) 1
111)37
112) ½
113)310
114) 1 ½
115) ½
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116) 3 13
117) 30 17
118) 1
119)13
120)110
121)112
122)2536
123)16
124)14
125) 1 512
126) 3 935
127) 2 2330
128) 29 910
129) 1 1972
130) 2
131)35
132)35
133) 112
134)3160
135) 2 14
136) 1 13
137) 2 38
138) 9 15
139) 23 12
140)2556
141)715
142)1335
143)15
144)25
145) 2 320
146)2542
147)518
148) 11 14
149) 8 25
150) 23 31100
151)16
152)13
153)18
154)118
155)25
156) 1
157) 4 45
158) 2 23
159)58
160) 1 1332
161) 3 34
162) 4
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163) 12 45
164) 7 35
165) 7 12
166)17
167)19
168)732
169)726
170)58
171) 2 12
172) 1 14
173) 1 1718
174) 4 23
175) 2 1112
176) 7 35
177) 4 18
178) 10
179) 5
180) 9
181) 4
182) 1 14
183) 9
184) 1 12
185)1225
186) 2
187) 1 35
188) 13 12
189) 6 25
190) 6 25
191) 13 13
192) 42
193) 1 67
194) 1 1944
195)5063
196) 3 35
197)45
198) 5
199)914
200) 1 25
201) 1
202)79
203) 3 15
204) 12 67
205) 21 37
206) 16 45
207) 2 14
208)1730
209) 5 35
210) 3 1115
211) 1 310 lbs
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212) 2 14 servings
213) 3 45 feet
214)316 cups
215)7120 lbs
216) 9 batches
217) 7 13 laps
218) 7 12 burgers
219) 1 27 cups
220) 11cards
221) 15 cookies
222) 2 14 cups
223) Yes, because
x=5 ∙4=20
224) 1 715
225) 41 inches
226) 3 15 lbs
227) 10 1320
servings
228) 8 feet
229) 16 58 cups
230) 2 14 lbs
231) 16 batches
232) 1113 laps
233) 7 45 layers
234) 2 1924 cups
235) 30 stickers
236) 22 workers
237) 13 13
tablespoons
238) It is false
because t= 721
∨13
239) 1 1142
426 49
Multiple Choice Questions
1) b
2) d
3) b
4) a
5) c
6) a
7) d
8) c
9) b
10) a
11) c
12) d
Short Constructed Response Questions
13)1320
14) 718
15) 23340
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16) 16 715
17)6077
18) 227
19) 11415
20) 8(7 + 9)
21) 3
22) 144
Extended Constructed Response Questions
23) 10 38+12 7
16+10 3
8+8 516
= 10 616
+12 716
+10 616
+8 516
= 40 2416
= 41 12
feet
Anna's Room: 4 (10 38 )=41 x 838 =41 12
ft She needs to buy the same amount.
24)10x 38
=308
=3 34 so he should buy 4 large pizzas
10x 36
=306
=5 so he should buy 5 medium pizzas
12 x4=$ 48∧9 x5=$45 so he should buy medium pizzas
25) 20 12x12 2
3x6 12= 412x 383x 132
= 2025412
=1687 56
ft3
6 13x1687 5
6=193x 10127
6=10689 11
18 gallons
26)25=3280, 516
=2580, 49=2863, 37=2763, 14=2080
Least to greatest: 14, 516, 25, 37, 49
49+ 14=1636
+ 936
=2536
2536x 24 1
2=2536x 492
=122572
=17 172= $17.02
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27) 30 students can go on the field trip
Each student will get 4 cans of juice and 3 packs of crackers.
30 is the GCF, so 4 x 30 = 120 (juice) and 3 x 30 = 90 (crackers)
28) It will be 70 seconds before they are both on the bottom again. The large Ferris Wheel will go
around 7 times, small will go 10 times.
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