## Whole Numbers

The natural numbers along with zero are called the**Whole Numbers**

Since, the natural numbers are 1, 2, 3, 4, 5, . . . . .

Thus, 0, 1, 2, 3, 4, 5, . . . . . are the examples of **Whole Numbers**

## Solution of Try These Exercise

**Question (1)** Are all natural numbers also whole numbers?

**Answer**

*Yes, all natural numbers also whole numbers*.

**Explanation**

Since, whole numbers are the natural numbers along with zero. Hence ** All natural numbers also whole numbers**.

**Question (2)** Are all whole numbers also natural numbers?

**Answer**

No, *all whole numbers are not also natural numbers, because zero (0) is not a natural number but a whole number*.

**Explanation**

Since, zero is a whole number, but not a natural number.

Because natural numbers are , 2, 3, 4, 5, 6, . . . .

This means the first natural number is 1 and there is no predecessor of this natural number. That means zero (0) is not a natural number.

Hence, **all whole numbers are not also natural numbers**.

**Question (3)** Which is the greatest whole number?

**Answer**

*Whole numbers are countless; this means we can count whole numbers up to infinity. Thus no whole number is the greatest whole number*.

## Operation on Whole Numbers

All operations, such as addition, subtraction, multiplication, and division of whole numbers are done by using general rule or method.

### Properties of Operations on Whole Numbers

#### (1) **The sum of two whole numbers is also a whole number. **

**Example**

(a) 6 + 10 = 16

In the above example, 6 and 10 are the whole numbers. And their sum which is equal to 16 is also a whole number.

(b) 5 + 6 = 11

In the above example, 5 and 6 are the whole numbers. And their sum which is equal to 11 is also a whole number.

(c) 15 + 16 = 31

In the above example, 15 and 16 are the whole numbers. And their sum which is equal to 31 is also a whole number.

(d) 20 + 12 = 32

In the above example, 20 and 12 are the whole numbers. And their sum which is equal to 32 is also a whole number.

#### (2) **The subtraction, i.e. difference of two whole numbers is also a whole number. **

**Example**

(a) 10 – 4 = 6

In the above example, 10 and 4, both are whole numbers. And the difference between 10 and 4 is 6 which is also a whole number.

(b) 15 – 3 = 12

In the above example, 15 and 3, both are whole numbers. And the difference between 15 and 3 is 12. Here 12 is also a whole number.

(c) 25 – 11 = 14

In the above example, 25 and 11, both are whole numbers. And when we subtract 11 from 25 we get 14. Here 14 is also a whole number.

(d) 21 – 8 = 13

In the above example, 21 and 8, both are whole numbers. And when we subtract 8 from 21 we get 13. Here 13 is also a whole number.

(e) 35 – 6 = 29

In the above example, 35 and 6, both are whole numbers. And when we subtract 6 from 35 we get 29. Here 29 is also a whole number.

#### (3) **The results of multiplication of two whole numbers are also whole numbers. **

**Example**

(a) 2 × 3 = 6

In the above example, 2 and 3 are whole numbers. When we multiply 2 by 3, we get 6. Here 6 is also a whole number.

(b) 4 × 5 = 20

In the above example, 4 and 5 are whole numbers. When we multiply 4 by 5, we get 20. Here 20 is also a whole number.

(c) 15 × 10 = 150

In the above example, 15 and 10 are whole numbers. When we multiply 15 by 10, we get 150. Here 150 is also a whole number.

(d) 9 × 100 = 900

In the above example, 9 and 100 are whole numbers. When we multiply 9 by 100, we get 900. Here 900 is also a whole number.

#### (4) **The results of division of two whole numbers are not always whole numbers. **

**Example**

(a) ^{6}/_{2} = 3

In the above example, 6 and 2 are the whole numbers. When we divide 6 by 2, we get 3. Here 3 is also a whole number.

Thus, in this example (a) the result of division of two whole numbers is also a whole number.

(b) ^{32}/_{8} = 4

In the above example, 32 and 8 are the whole numbers. When we divide 32 by 8, we get 4. Here 4 is also a whole number.

Thus, in this example (a) the result of division of two whole numbers is also a whole number.

(c) ^{7}/_{4} = 1 ^{3}/_{7}

In the above example, 7 and 4 are the whole numbers. When we divide 7 by 4, we get 1 ^{3}/_{7} which is not a whole number.

Thus, in this example (a) the result of division of two whole numbers is not a whole number.

(d) ^{15}/_{2} = 7 ^{1}/_{2} or 7.5

In the above example, 15 and 2 are the whole numbers. When we divide 15 by 2, we get 7 ^{1}/_{2} or 7.5 which is not a whole number.

Thus, in this example (a) the result of division of two whole numbers is not a whole number.

(e) ^{100}/_{3} = 33 ^{1}/_{3} or 33.333

In the above example, 100 and 3 are the whole numbers. When we divide 100 by 3, we get 33 ^{1}/_{3} or 33.333 which is not a whole number.

Thus, in this example (a) the result of division of two whole numbers is not a whole number.

Thus, **the result of the division of two whole numbers is not always a whole number**.