What are the properties of whole numbers part-2

Whole Numbers – Properties of Whole Numbers - Part 2

• Meaning of Commutative
• Commutative Property of Addition
• Commutative Property of Subtraction
• Commutative Property of Multiplication
• Commutative Property of Division
• What’s Learn Next?

In the previous segment, we learnt about the Closure property of whole numbers. In this segment, we will learn about the Commutative property of whole numbers.

What is the meaning of Commutative?

In mathematics, commutative means exchanging positions.

So when we say that a particular operation is commutative, it means that when the position of numbers is exchanged for that operation, the result will be the same in both the cases.

To understand this better, let us see if whole numbers are commutative w.r.t; addition, subtraction, division and multiplication.

Commutative property - Addition

Let us take an example. 70 + 80 = 150

Let us now interchange the positions of the two numbers and perform addition. 80 + 70 = 150

In both cases, the answer remains the same.

Let us check if this is true when we add more than two numbers.

2 + 3 + 4 = 9

4 + 3 + 2 = 9

3 + 2 + 4 = 9

Interchanging the position of whole numbers does not affect the result. Hence, we can say that commutative property of addition holds true for whole numbers.

Commutative property - Subtraction

Let us check whether whole numbers are commutative under subtraction. 7 - 5 = 2

On swapping the positions of numbers, 5 - 7 = -2

So, 7 - 5 ≠ 5 - 7

From this, we can conclude that the commutative property of subtraction does not hold true for whole numbers.

Commutative property - Multiplication

Just like in addition, the multiplication of two whole numbers does not alter the result.

For example,

10 × 9 = 90 and 9 × 10 = 90

Thus, we can say that the commutative property of multiplication holds true for whole numbers.

Commutative property - Division

Finally, let us see whether whole numbers are commutative for division.

24 ÷ 12 = 2

When their positions are interchanged, we get

12 ÷ 24 = 0.5

The answers are different in both cases.

We can therefore conclude that commutative property of division does not hold true for whole numbers.

Overview

What’s Learn next?

In our next segment of Class 6 Maths, we will learn about the Associative property of whole numbers.

Also Check

NCERT Solutions For Class 6 - All Subjects (2022-23)

CBSE Worksheets For Class 6 Maths (Chapter wise)