Class 6 Whole Number

Natural Numbers

Whole Numbers

Successor of a Whole Number

Predecessor of a Whole Number

Properties of Addition

Properties of Subtraction

Properties of Multiplication

Properties of Division

Whole Number Test

Whole Number Worksheet

Answer Sheet

Natural Numbers

Counting numbers for example one, two, three, four, five, six etc. Are known as natural numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9....

Whole Numbers

The natural numbers along with zero form the collection of whole numbers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9...

1. All Natural numbers are whole numbers

2. All whole numbers are not natural numbers

Successor of a Whole Number

If we add 1 to a whole number then we get the next whole number, which is known as it’s successor. For example, successor of 0 is 1, successor of 1 is 2 and successor of 2 is 3.

Predecessor of a Whole Number

One less than a given whole number is known as its predecessor. For example, predecessor of 1 is 0, predecessor of 2 is 1 and predecessor of 3 is 2. Whole number 0 does not have it predecessor.

Properties of Addition

We have various properties of addition of whole numbers.

1. Closure property of addition

2. Commutative property of addition

3. Additive property of zero

4. Associative law of addition

Closure Property of Addition

If we add two whole numbers, then the result will be a whole number. Let us see some examples.

Example 1. Add 5 and 7, check if the sum is a whole number.

Solution. 5 + 7 = 12
12 is a whole number.

Example 2. Add 15 and 12, check if the sum is a whole number.

Solution. 15 + 12 = 27
27 is a whole number.

Commutative Property of Addition

If we add two whole numbers with different orders, then the sum will remain same.

A + B = B + A
Let us see some examples.

Example 1. Check if 7 + 8 = 8 + 7.

Solution. 7 + 8 = 15 and 8 + 7 = 15
Thus, 7 + 8 is equal to 8 + 7.

Example 2. Check if 12 + 13 = 13 + 12.

Solution. 12 + 13 = 25 and 13 + 12 = 25
Thus, 12 + 13 is equal to 13 + 12.

Additive Property of Zero

Sum of any whole number and zero is the number itself.

5 + 0 = 0 + 5 = 5
12 + 0 = 0 + 12 = 12

Associative Law of Addition

In addition of whole numbers, the manner of associating the numbers does not affect the sum.

(a + b) + c = a + ( b + c)
Let's consider some examples.

Example 1. Find the sum of 5, 8, 10.

Solution. (5 + 8) + 10 = 13 + 10 = 23
5 + (8 + 10) = 5 + 18 = 23
So, (5 + 8) + 10 = 5 + (8 + 10)

Properties of Subtraction

We have various properties of subtraction of whole numbers.

Property 1. If A and B are two whole numbers such that A > B or A = B, then A − B is a whole number. Otherwise subtraction is not possible in whole numbers.

Property 2. If A and B are two whole numbers, then in general A − B is not equal to B − A.

Property 3. If A is any whole number, then A − 0 = A but 0 − A is not defined.

Property 4. If A, B, C are three whole numbers then, (A − B) − C is not equal to A − (B − C).

Properties of Multiplication

We have various properties of multiplication of whole numbers.

1. Closure property of multiplication

2. Commutative property of multiplication

3. Multiplicative property of zero

4. Multiplicative property of 1

5. Associative law of multiplication

6. Distributive law of multiplication over addition

7. Distributive law of multiplication over subtraction

Closure Property of Multiplication

If A and B are any two whole numbers, then product of A and B is also a whole number. Let's see some examples.

Example 1. Product of 5 and 7.

Solution. 5 x 7 = 35
35 is a whole number

Example 2. Product of 8 and 11.

Solution. 8 x 11 = 88
88 is a whole number.

Commutative Property of Multiplication

If A and B are any two whole numbers, then A x B = B x A. Let's see some examples.

Example 1. Check if 3 x 5 = 5 x 3.

Solution. 3 x 5 = 15 and 5 x 3 = 15
Thus 3 x 5 is equal to 5 x 3.

Example 2. Check if 5 x 15 = 15 x 5.

Solution. 5 x 15 = 75 and 15 x 5 = 75
Thus, 5 x 15 is equal to 15 x 5.

Multiplicative Property of Zero

Any whole number multiplied by zero gives the product zero.

5 x 0 = 0 x 5 = 0

Multiplicative Property of 1

Any whole number multiplied with 1 gives the number itself.

7 x 1 = 1 x 7 = 7

Associative Law of Multiplication

If A, B, C are any whole numbers then (A x B) x C = A x (B x C). Let's see some examples.

Example 1. Multiply 4, 5 and 6.

Solution. 4 x 5 x 6 = (4 x 5) x 6 = 20 x 6 = 120
Changing the arrangement, we have:

4 x 5 x 6 = 4 x (5 x 6) = 4 x 30 = 120
Thus, (4 x 5) x 6 = 4 x (5 x 6)

Distributive Law of Multiplication Over Addition

If A, B, C are any whole numbers then A x (B + C) = A x B + A x C
Let's see some examples.

Example 1. Check: 4 x (5 + 7) = 4 x 5 + 4 x 7

Solution. 4 x (5 + 7) = 4 x 12 = 48
And 4 x 5 + 4 x 7 = 20 + 28 = 48
Thus, 4 x (5 + 7) = 4 x 5 + 4 x 7.

Distributive Law of Multiplication Over Subtraction

If A, B, C are nay whole numbers then A x (B − C) = A x B − A x C.

Let's see some examples.

Example 1. Check: 5 x (6 − 2) = 5 x 6 − 5 x 2.

Solution. 5 x (6 − 2) = 5 x 4 = 20
And 5 x 6 − 5 x 2 = 30 − 10 = 20
Thus, 5 x (6 − 2) = 5 x 6 − 5 x 2.

Properties of Division

We have various properties of multiplication of whole numbers.

1. Division by zero

2. Zero divided by a natural number

Division by zero

If A and B are whole numbers, then A ÷ B is not always a whole number.

Let us consider 5 ÷ 0. Clearly, we must find a whole number which when multiplied by zero gives 5. We are sure that no such number can be obtained.
Hence, we conclude that division by zero is not defined.