My real folder of Maths Book ....................................... Work

8/13/2019 My real folder of Maths Book ....................................... Work

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After studying this unit, the students will be able to:Read numbers up to 1,000,000,000(one billion) in numerals

and in words.

Write numbers up to 1,000,000,000(one billion) innumerals and words.

Add numbers of complexity and of arbitrary size.

Subtract numbers of complexity and of arbitrary size.Multiply numbers up to 6 digits by 10,100 and1000.Multiply numbers up to 6 digits by a 2-digit and 3-digit

number.

Divide numbers up to 6-digits by a 2-digit and 3-digitnumber.

Recognize BODMAS rule, using only parenthesis ( ).

Carryout combined operations using BODMAS rule. Verify distributive laws.

Numbers And

ArithmeticOperationsUnit:1


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1.1 Numbers up to one billion.

1.1.1 Read the numbers up to one billion.

We know that 100000000 in international place value

system is written as:

Millions Thousands Ones

Hundred

Millions

Ten

Millions

Millions Hundred

Thousands

Ten

Thousands

Ten

Thousands

Hundreds Tens Ones

1 0 0 0 0 0 0 0 0

Commas are placed after three places from right most digits.

For example:

1.The number 200,000,000 is written in figures.It can be written as:

Two hundred million.

2.The number 100,000,000 is written in figures.It can be written as:

One hundred million.

Similarly, 345,267,982 is read as:

Three hundred forty five million, two hundred sixty seven

thousand, nine hundred eighty two.


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100,000,000 and 999,999,999 are respectively smallest and

largest 9-digits numbers.

999,999,999 is read as:

Nine hundred ninety nine million, nine hundred ninety nine

thousand, nine hundred ninety nine.

One more than 999,999,999 is one thousand million.

One thousand million is known as 1 billion.

1 billion is written as 1,000,000,000.

1 Billion=1000 million

Example 1 :

Read the following numbers and write in words.

I. 14,020,748.II. 843,658,952

III. 435,525,243.Solution:

I. 14,020,748:Fourteen million, twenty thousand, sevenhundred and forty eight.

II. 843,658,952:Eight hundred forty three million, sixhundred fifty eight thousand, nine hundred and fifty

two.

III. 435,525,243:Four hundred thirty five million, fivehundred twenty five thousand, two hundred and forty

three.


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1.1.2 Write numbers up to one billion

Example 2:

Write the following numbers in figures.

I.Seven hundred eight million, two hundred seventy two

thousand, nine hundred twenty six.

II.Eight hundred eighty six million , five hundred thousand, onehundred twenty six.

Solution:

I. 708,272,926.II. 886.500,126.

Activity

Place the commas in following numbers

according to international place value system:

1.705366935 2. 211435126

___________ ____________


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Exercise 1.1

1. Read the following numbers and write them in words:

I. 65,086,236II. 345,666,780

III. 980,765,455IV. 999,999,999V. 455.980,650

VI. 1,000,000,000VII. 455,678,999.

2. Write the following numbers in figures:

I. One hundred twenty million three hundred six thousandfour.

II. Ninety five million, sixteen thousand, fifty five.III. Sixty million.IV. Five hundred ninety million three hundred five

thousand five.


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1.2 .Addition and Subtraction:

We have learnt addition of numbers up to 6-digit numbers.

Addition of larger number (7,8 or 9-digit) is done similarly.

That is, addition of numbers is done by addition of digits

having same place values(starting from ones). We should be

very careful while placement of digits of numbers and

commas.

As an example, addition of 2,556,876,135 and 605,957

is performed as under:

1 1 1

2, 5 5 6 , 8 7 6 , 1 3 5

+ 6 0 5 , 9 5 2

2 , 5 5 7 , 4 8 2 , 0 8 7

Example 3 : Add 24,571,344 and 5,690,345.

1.2.1 Add numbers of complexity and ofarbitrary size :


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Solution:

1 1 1

2 4, 5 7 1, 3 4 4

+ 5, 6 9 0, 3 4 5

3 0 ,2 6 1 , 6 8 9

Activity

Answer the following in 10 seconds each!

208,070

+ 399,770

422,134

+ 533,450


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Exercise:1.2

Solve:

1. 3, 9 5 6, 2 3 4

+ 8 9 0, 1 2 4

2. 5 7 8, 9 8 0

+ 1 2 3, 6 7 0

3. 2, 8 9 0, 6 7 8

+ 7 8 3, 1 2 7

4. 6, 7 3 4, 5 6 7

+ 1 2 3, 6 8 0

5 . 4, 4 4 4, 4 4 4

+ 4 4 4,4 4 4


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6 . 7 , 6 8 0 , 7 8 1

+ 5 6 1 , 6 7 0

7 . 6 , 8 7 0 , 4 5 6

+ 6 7 5 , 3 2 1

8. 5 6 7 , 7 8 9 ,5 5 5

+ 2 3 4 , 5 6 7 , 6 5 7

Find the Sum:

9. 490,456 and 467,335.

10. 65,444,290 and 23,543,670.


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Same method is applied for subtraction of larger numbers (7, 8, 9)

as we have done for subtraction of numbers upto 6 digit numbers

. It is done by subtraction of digits having same place while

placement of digits of the numbers and commas .

Let us take an example :

Subtraction of 6, 567, 239 from 4,456, 112 is as under:

6 , 5 6 7, 2 3 9

- 4 , 4 5 6 , 11 2

2 , 1 1 1 ,1 2 7

Example 4:Subtract 4,567,887 from 5,678,997.

Solution:

1.2.2 Subtract numbers Of

complexity and Of arbitrary size.


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5 , 6 7 8 , 9 9 7

- 4, 5 6 7 , 8 8 71, 1 1 1 , 1 1 0

Exercise: 1. 3

Solve:

1. 7 8 9, 9 9 9 , 8 6 7

_3 2 1 , 8 9 0 , 7 6 6

2. 5 8 9, 7 9 0, 9 8 8

_ 4 7 8 , 8 9 0 ,3 2 2

3. 8 8 , 9 8 0 ,8 7 9

_ 6 7 , 7 8 0 , 3 4 5

4. 8 9 7, 8 9 9

_ 3 4 5, 7 7 8


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5. 3 3 9, 9 9 8, 9 8 4

_ 2 2 8, 7 8 0 , 2 1 3

Solve:

6. 5 8 8 , 9 8 94 6 7, 8 1 2

Multiplication by 10,100 and 1000.

Let us see the product of a number 22222 with 10,000 and

1000.22222 10 = 222220.

22222100=2222200.

222221000= 22222000.

1.3.1. Multiply

numbers up to 6

digits by 10 ,100 and

1000 :


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Example:

Multiply 3654 with 10,100 and 1000.Solution:

365410=36540.

3654100= 365400.

36541000=3654000.

Example 6 :Multiply 224222 by 14.

Solution:

1

2 2 4 2 2 2

1 4

8 9 6 8 8 8

2 2 4 2 2 2 0

3 1 3 9 1 0 8

1.3.2Multiply numbers upto 6 digits by a

2 digits and 3 digits number


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Exercise: 1.4

Multiply:

1. 512222 by 10.

2. 422116 by 13.

3. 112333 by 11

4. 310333 by 12.

Example:

Divide 537809 by 35 .Find the quotient and remainder as well.

1.3.3 Division Of numbers upto

6 digits by a 2-digit and 3-digitnumber:


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Solution:

15365 Quotient

35 537809

-35

187

- 175

128

- 105

230

- 210

209

- 175

34 Remainder

Note:The remainder at every step would be less than the

divisor.

Exercise: 1.5

Divide:

1. 425580 by 60


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2. 304480 by 40

3. 209800 by 20

4. 500800 by 40

5. 566700 by 30

BODMAS stands for Brackets, Of, Division, multiplications,

addition and subtraction. It helps remembering the order of

preferences of mathematical operators. We solve brackets

first if given in the question. In case of more brackets, we

solve from inner most bracket to the outer most bracket.

BODMAS given order of preferences as:

Preference No. Rule Operation Symbol

1 BODMAS Brackets ()

2 BODMAS Of Of

3 BODMAS Division +

4 BODMAS Multiplication

5 BODMAS Addition +

6 BODMAS Subtraction -

1.4 Order Of operations: BODMAS

rule :


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Order of Preferences is as under:

(), Of, , , + , - .

Now we simply 16+ (12 + 9 3) 5, using BODMAS rule,

16+ (12+ 93) 5

= 16 + (12+3) 5 (First divide within bracket)

=16+ 155 (After Addition remove Bracket)

= 16+75. (Multiplication)

= 91. (Addition)

Example 12:

Solve (18+6) 24.

Solution:

= (18+6) 24

=2424.

= 248.

= 3.

Exercise: 1.6

Solve:

1. 24 (126).

2. (510) 5.

1.4.1 Recognize BODMAS rule,using

only parenthesis ( ).


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3. (182+6) 3-2.

4. (85) 7+1.

We verify the distributive laws with the help of following

examples.

Example :

Verily Distributive laws.

a.10 (13+2) = (1013) + (102).

Solution:

L.H.S= 10 (13+2)

= 1015

= 150. (a)

R.H.S=(1013)+(102)

=130+20

=150. (b)From (a)and (b)

L.H.S=R.H.S.

b.(6+4) 4= (64) + (4 4).

Verification Of Distributive

Laws:


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Solution:

L.H.S= (6+4) 4.

= (6+4) 4

= 104.

= 40.

R.H.S= (64) + (4 4).

= 24+16.

=40.

Exercise:1.7

Verify distributive laws:

1. 14 (9+5) = (149)+ (145).

2. (12+5) 6= (126) + (56).

3.16 (10+4) = (1610) +(164).

4. 11 (12-7) = (1112)-(117).

5.16 (12-6) = (1612)-(166).

Review Exercise

1. Read the following numbers and write them in

words.I. 101,001,017.

II. 106,011,111.


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2. Multiply:

I. 244664 by 24.II.

993399 by 33.

3. Divide:

246444 by 22

4. Evaluate:

60-(4010-2) + 5.

5 .Multiple choice questions.

Encircle the correct answer:

1.1 billion= ?

a. 100 million b.10 million. c. 1000 million d.500

million.

2.Eight hundred twenty three million five hundred thirty eight

thousand two hundred seventy eight.

a. 800,23,538,208 b.823,538,278 c.804,567,278

d.893,567,278.

3.3566100= ?

a. 355600 b. 356600 c. 356000 d.344600.


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4.7 (4+4) = (74) + (74) is

a. Distributive law b. Associative law c. Commutative law

d. BODMAS rule.

5.5668-1333=?

a. 4335 b.4512 c. 4412 d. 4125.


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Answers:

Exercise 1.1

1.

i. Sixty-five million, eighty-six thousand, two hundred andthirty-six.

ii. Three hundred forty-five million, six hundred sixty-sixthousand ,seven hundred and eighty.

iii. Nine hundred eighty million, seven hundred and sixty-five , four hundred and fifty-five.

iv. Nine hundred ninety-nine million , nine hundredninety-nine thousand, nine hundred ninety-nine.

v. Four hundred and fifty-five, nine hundred and eighty, sixhundred and fifty.

vi. One thousand million.vii. Four hundred and fifty-five, six hundred and seventy-

eight, nine hundred and ninety nine.

Answers


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2.

i. 120,306,004.ii. 95,016,055.

iii. 60,000,000.iv. 590,305,005.

Exercise: 1.2

i. 4,846,358.ii. 702,650.

iii. 3,673,805.iv. 6,858,247.v. 4,888,888.

vi. 8,242,451.vii. 7,545,777.

viii. 802,357,212.ix. 957,791.x. 88,987,960.

Exercise: 1.3

i. 468,109,101.ii. 111,100,666.


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iii. 21,200,534.iv. 552,121.v. 111,218,771.

vi. 111,177.Exercise: 1.4

i. 5122220.ii. 5487508.

iii. 112344.iv. 3723996.

Exercise : 1.5

1.

i. 7093.ii. 7612.

iii. 10490iv. 12520v. 18890.

Exercise: 1.6

i. 48.ii. 10.iii. 15.iv. 5.


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Exercise: 1.7

i. 196.ii. 102.

iii. 224.iv. 55.v. 96.

Review exercise

1.

i. One hundred and one million, one thousand andseventeen.

ii. Six million ,eleven thousand , one hundred and eleven.2.

i. 5871936.ii. 32782167.

3.

11202.

4.

53.


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i. cii. b

iii. biv. av. a.

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