Operation On Whole Numbers ICSE Class-6th RS Aggarwal Goyal Brothers Prakashan Chapter-2. We provide step by step Solutions of Exercise / lesson-2 Operation On Whole Numbers for ICSE Class-6 RS Aggarwal Mathematics  .

Our Solutions contain all type Questions with Exe-2 A, Exe-2 B,  to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6 Mathematics.

 Board ICSE Publications Goyal brothers Prakshan Subject Maths Class 6th Chapter-2 Operation On Whole Numbers Writer RS Aggrawal Book Name Foundation Topics Solution of Exe-2 A, Exe-2 B Academic Session 2021-2022

## Operation On Whole Numbers ICSE Class-6th RS Aggarwal Goyal Brothers Prakashan Chapter-2

–: Select Topics :–

Notes on Whole Numbers

Exe-2 A,

Exe-2 B,

### Properties of Whole Numbers

1. Addition and multiplication of any 2 whole number give a whole number.
2. Subtraction and division of any 2 whole number may or may not give a whole number.

### What is a Number line?

A number line is a picture of a graduated straight and horizontal line in which numbers are written. A number written on the left-hand side of the number line is lesser and number written on the right-hand side of the number line is greater.

#### Natural numbers

• Numbers that are used for counting and ordering are called natural Numbers.
• 1,2,3,4,5,6… are natural numbers

#### Whole numbers

• Natural numbers along with zero form the collection of whole numbers.
• 0,1,2,3,4,5… are called whole numbers.

Predecessor and Successor

• A successor of any number is the next number to it, which is obtained by adding 1.
• A predecessor of any number is the previous number to it, which is obtained by subtracting 1.
• For example, predecessor and successor of the number 12 is 12 – 1 and 12 + 1 which is 11 and 13

## Properties of Operators: Commutative Associative and Distributive

### Division by zero

Division of any whole number by 0 is not defined.

Mathematical operations are simplified due to certain properties that every number follows. They are:

• ### Commutative property

Addition and multiplication are commutative for whole numbers. i.e whole numbers can be added or multiplied in any order.

For e.g: 2 + 3 = 5 = 3 + 3 × 4 = 12 = 4 × 3

• ### Associative property

For eg: (5 +6) + 4 = 15 = 5 + (6 + 4)

(2 × 3) × 4 = 24 =2 × (3 × 4)

• ### Distributive Property

With distributivity property, 4 × (5 + 3) can be written as (4 × 5) + (4 × 3)

Here, 4 × (5 + 3) = 4 × 13 = 52

Also, (4 × 5) + (4 × 3) = 20 + 32 = 52

There exists certain numbers, when included in mathematical operations like addition and multiplication, the value of the operation remains unchanged. Such numbers are called as identities.

Additive identity gives the same whole number when added to another whole number.

Zero is the additive identity as a + 0 = a, (a is any whole number).

### Multiplicative Identity

Multiplicative identity gives the same whole number when multiplied by another whole number.

1 is the Multiplicative identity as a × 1 = a, (a is any whole number)

### Exercise – 2 A, Operation On Whole Numbers ICSE Class-6th RS Aggarwal Goyal Brothers Prakashan

Page 36-37

#### Question 1

fill in the blanks………

(i) 168 + 259 = …. + 168

(ii) …. + 317 =317

(iii) (37 + 18 ) + …. = 37 + (….. + 56)

(iv) 8 + 3 * 4 = ….

(v)18 * (….. + 23) = (18 * 17) + (18 * ….)

(i) 168 + 259 = 259  + 168

(ii) 0 + 317 =317

(iii) (37 + 18 ) + 56 = 37 + (68 + 56)

(iv) 8 + 3 * 4 = 20

(v)18 * (17 + 23) = (18 * 17) + (18 * 23)

#### Question 2

fill in the blanks………

(i) 237 * 1 = ……………………

(ii) 56 * ……….. = 0

(iii) 0/53 = ………………

(iv) 37 * 59 = 59 * ……………..

(v)  0 * 138 = ………………….

(vi)73/73 = …..

(i) 237 * 1 = 237

(ii) 56 * 0 = 0

(iii) 0/53 = 0

(iv) 37 * 59 = 59 * 37

(v)  0 * 138 = 0

(vi)73/73 = 1

#### Question 3

Divide 3605 by 29 and verify the division algorithm.

29 ) 3605 ( 124

Re = 9

Quotient = 124,

Reminder = 9

Dividend = (Divisor * Quotient ) + Reminder

= 29 * 124 + 9

= 3596 + 9 = 3605

#### Question 4

Find the number which when divided by 45 gives 16 as quotient and 9 as reminder.

Dividend = (Divisor * Quotient ) + Reminder

Here,

Deviser = 45,

Quotient = 16,

Reminder = 9

= (45 *16 ) + 9

720 + 9

= 729

#### Question 5

Find the ………………. by 57

Largest 5 digit number = 99999

on dividing by 57,

57 ) 99999 ( 1754

Reminder = 21

so Required number = 99999-21=99978

#### Question 6

Find the …………………. by 63

Smallest six digit number = 100000

On diving by 63,

63 ) 100000 ( 1587

Reminder = 19

#### Question 7

On dividing …….. find the divisor.

Dividend = (Divisor * Quotient ) + Reminder

Here,

Dividend – 1653,

Quotient = 45,

Reminder = 33

then divisor = 1653 = (divisor * 45) + 33

45 * divisor = 1653-33 = 1620

divisor = 1620/45

= 36

#### Question 8

Use distributive ……

(i) 576 ….

(ii) 385 …..

(iii) 365 …..

(iv) 407 …….

(i) Using distributive  law [a(b+c)]

= 576 (285 + 115)

= 576 (400)

230400

(ii) 385 * 178 – 385 * 78

Using distributive  law [a(b+c)]

= 85 (178 – 78)

= 385 (100)

= 38500

(iii) 365 * 645 + 135 * 645

Using distributive  law [a(b+c)]

= 645 (36 + 135)

= 645 (500)

= 322500

(iv) 407 * 168 – 307 * 168

Using distributive  law [a(b+c)]

= 168 (407 – 307)

168 (100)

16800

#### Question 9

Using the most ……… product :

(i) ……..

(ii) ………..

(iii) ……….

(iv) …………

(i) 5 * 648 * 20

= 5 * 20 * 648

=64800

(ii) 8 * 329 * 25

= 8 * 25 * 329

= 65800

(iii) 8 * 12 * 25 * 7

= 56 * 300

= 16800

(iv) 125 * 40 * 8 *  25

= 1000 * 1000

= 1000000

#### Question 10

Divide and ……. algorithm :

(i) ….

(ii) …..

(iii) ….

(i)  87 ) 3680 (42

Reminder = 26

Dividend = (Divisor * Quotient ) + Reminder

(87 * 42)+ 26

=3654 + 26

=3680

(ii) 327 ) 17368 (53

Reminder 37

Dividend = (Divisor * Quotient ) + Reminder

(327 * 53)+ 37

17331 + 37

= 17368

(iii) 265 ) 32679 (123

Reminder 84

Dividend = (Divisor * Quotient ) + Reminder

(265 * 123)+ 84

= 32595 + 84

= 32679

#### Question 11

Verify each of the following :

(i) ………..

(ii)………….

(ii)…………

(iv)……….

(i) 2867 + 986

= 986 – 2867

[so (a+b) = (b+a)]

2867 – 2867 = 986 – 986

0=0

(ii)

368 * 215

= 215 * 368

[so (a+b) = (b+a)]

Commutative law of multiplication

(iii) (156 + 273 ) + 74= 156 + (273 + 74)

[so (a+b) = (b+a)]

Associative law of multiplication

(iv)  (85 * 55) * 110 = 86 * (55 * 1110)

[so (a+b) = (b+a)]

Associative law of multiplication

#### Question 12

Simplify :

(i) ………..

(ii)………..

(ii)………..

(iv)………….

(v)…………..

(i)

39 – 18 / 3+ 2 * 3

= 39 – 6 + 2 * 3

= 39 – 6 + 6 = 39

(ii)

8 + 2 * 5

= 8 + 10 = 18

(iii)

5 + 8 – 6 / 2

= 5 * 8 –  3

(iv)

=19 – 9 * 2

= 19 – 18 = 1

(v)

15 / 5 * 4 / 2

= 3 * 2 = 6

### RS Aggarwal Solutions Operation On Whole Numbers ICSE Class-6th Goyal Brothers Prakashan Exercise – 2 B

Page 38-39

#### Question 1

Study following pattern, in each case write the next three step…………

(i)

111 / 3 = 37

222 / 6 = 37

333 / 9 = 37

444 / 12 = 37

(ii)

999999 * 1 = 0999999

999999 * 2 = 1999998

999999 * 3 = 2999998

999999 * 4 = 3999996

(iii) ……………..

(i)

111 / 3 = 37

222 / 6 = 37

333 / 9 = 37

444 / 12 = 37

555 / 15 = 37

666 / 18 = 37

777 / 21 = 37

(ii)

999999 * 5 = 4999995

999999 * 6 = 5999994

999999 * 7 = 6999993

(iii)

123456789 *  45 = 555555555

123456789 *  54 = 666666666

123456789 *  63 = 7777777777

123456789 *  36 = 444444444

#### Question 2

(i) ……….

(ii)…………

(iii)………..

(i) 5

(ii) 13 + 14 + 15 + 16 + 17 = 75

(iii) No, since the sum is a multiple of 5, and 92 is not a multiple of 5.

#### Question 3

Complete each one of the ……………. missing number :

(i) …….

(ii)……….

(iii)…………..

(iv)………..

(i)

 4 9 2 3 5 7 8 1 6

In each row/colum, the sum = 15

(ii)

 16 2 12 6 10 14 8 18 4

In each row/colum, the sum = 30

(iii)

 2 15 16 5 9 12 11 6 13 8 7 10 14 3 4 17

In each row/colum, the sum = 38

(iv)

 7 18 17 4 8 13 14 11 12 9 10 15 19 6 5 16

In each row/colum, the sum = 46

–: End of Operation On Whole Numbers ICSE Class-6th RS Aggrawal Solutions :–

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