Whole Numbers Examples, deals with various concepts which are as under:-

- Whole Numbers Definition
- Successor of a Whole Number
- Predecessor of a Whole Number
- Consecutive Whole Numbers
- Compare numbers on whole number line
- Division algorithm
- Distributive Law Of Multiplication Over Addition
- Distributive Law of Multiplication over Subtraction

#### Whole Numbers Definition

Whole Numbers are non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways: N = {0, 1, 2, 3……….}. So 0 is the smallest whole number and only non-negative natural numbers are known as whole numbers but all whole numbers are natural numbers.

#### Whole Numbers Examples – Successor of a Whole Number

The “Successor” of any whole number is the number, obtained by adding 1 to that number.

**Example 1**

Find the successor of 85265

**Explanation**

The “Successor” of any whole number is the number, obtained by adding 1 to that number

So, the successor of 85265 is 85265 + 1 = 85266

#### Whole Numbers Examples – Predecessor of a Whole Number

The “Predecessor” of any whole number is the number obtained by subtracting 1 from it

**Example 2**

Find the predecessor of 85265 ?

**Explanation**

The “Predecessor” of any whole number is the number obtained by subtracting 1 from it

So, the predecessor of 85265 is 85265 – 1 = 85264

#### Whole Numbers Examples – Consecutive Whole Numbers

**Example 3**

Write the three whole numbers occurring just after 40053

**Explanation**

The next three whole number of 40053 can be obtained by adding 1, 2 and 3 to 40053

that is,

40053 + 1 = 40054

40053 + 2 = 40055

40053 + 3 = 40056

Hence the next three whole numbers of 40053 are 40054 , 40055 , 40056 respectively

#### Whole Numbers Examples – Compare numbers on whole number line

The smaller number comes on the left side of the whole number line and bigger number comes on the right side of the whole number line.

**Example 4**

In the following pairs of number, state which number will be on right hand side of the whole number line?

( 589 , 362 )

**Explanation**

We know that the smaller number comes on the left and bigger number comes on right on the whole number line.

So between 589 and 362

362 is smaller number

So, 362 will be on left hand side while 589 will be on right hand side

362 < 589

Hence, 589 will be on right hand side of the whole number line

**Example 5**

In the following pairs state which number will be on left hand side of the whole number line?

( 563 , 693 )

**Explanation**

We know that the smaller number comes on the left and bigger number comes on right on the whole number line.

So, between 563 and 693

563 is smaller number

Since, 563 will be on left hand side while 693 will be on right hand side

563 < 693

Hence, the number on the left hand side would be 563

#### Whole Numbers Examples – Division algorithm

According to Division Algorithm,

dividend = (divisor x quotient) + remainder

**Example 6**

Find the number which when divided by 89 gives 4 as quotient and 6 as remainder

**Explanation**

Given,

Divisor = 89

Quotient = 4

Remainder = 6

In this question we have to use division algorithm

dividend = (divisor x quotient) + remainder

= ( 89 x 4 ) + 6

= 356 + 6

= 362

Hence, the dividend is 362

**Example 7**

If the Dividend = 6451 , quotient = 7 and remainder = 4 , find the Divisor ?

**Explanation**

Given,

Dividend = 6451

Quotient = 7

Remainder = 4

In this question we have to use division algorithm

dividend = (divisor x quotient) + remainder

dividend – remainder = divisor x quotient

Divisor =

= = 921

Hence, the divisor is 921

#### Whole Numbers Examples – Distributive Law Of Multiplication Over Addition

According to Distributive law of multiplication over addition, If a, b and c are Whole Numbers then,

a x (b + c ) = (a x b) + (a x c )

**Example 8**

Find the value of the following:-

( 635 x 63 ) + ( 67 x 635 )

**Explanation**

It follows Distributive law of multiplication over addition

Which states that a x (b + c ) = (a x b) + (a x c )

Here, a = 635

b = 63

c = 67

This question is in the form of (a x b) + (a x c )

That is, ( 635 x 63 ) + ( 67 x 635 )

( 635 x 63 ) + ( 635 x 67 ) **( NOTE : Whole number satisfy commutative property under multiplication) **

i.e (a x b) = (b x a)

Here, we have 67 x 635 = 635 x 67

By distributive law, = 635 x ( 63 + 67 )

= 635 x 130

= 82550

#### Whole Numbers Examples – Distributive Law of Multiplication over Subtraction

According to Distributive law of multiplication over subtraction, If a, b and c are Whole Numbers then,

a x ( b – c ) = (a x b) – (a x c)

**Example 9**

Solve:

11 x ( 9 – 5 )

**Explanation**

Here, we have two method to solve this question

By Distributive law of multiplication over subtraction a x ( b – c ) = (a x b) – (a x c)

here,

a = 11

b = 9

c = 5

**1 Method**

a x (b – c)

11 x ( 9 – 5 )

= 11 x 4

= 44

**2 Method **

(a x b) – (a x c)

( 11 X 9 ) – ( 11 x 5 )

= 99 – 55

= 44

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