# Commutative Property of Multiplication : Definition, Examples and Problems

## What is Commutative Property of Multiplication?

The property says that in multiplication of numbers, if you change the order of numbers the end result will not change

According to commutative property:

Where A & B can be any possible real number

Note that we have changed the location of digits and still it has no effect on final outcome.

### Why this property is named “Commutative”?

In English, commutative means “to move

As the name suggests, in this property we can move the location of different numbers without affecting the final outcome.

### Commutative Property of Multiplication Example

Given below are some example of commutative property

Example 01
Let A = 5 and B = 2

Calculate A x B
⟹ 5 x 2
⟹ 10

Calculate B x A
⟹ 2 x 5
⟹ 10

Hence A x B and B x A = 10
Commutative property of multiplication is verified

Example 02
Let A = 6, B = 2 & C = 3

Calculate A x B x C
⟹ 6 x 2 x 3
⟹ 36

Now calculate B x C x A
⟹ 2 x 3 x 6
⟹ 36

Calculate C x A x B
⟹ 3 x 6 x 2
⟹ 36

Observe that changing the location of number does not effect the final result.
Hence, A x B x C = B x C x A = C x A x B

### Frequently asked Question – Commutative Property of Multiplication

#### (01) How is Commutative Property of Multiplication different from associative property?

Commutative property says that changing the location of digits does not effect the final outcome.
A x B = B x A

While Associative property says that forming of different groups in multiplication does not effect the outcome.
A x (B x C) = (A x B) x C

#### Is the commutative Property works in Addition?

Yes!!

There is a commutative property of addition which says that changing the location of digits in addition does not effect the outcome.

A + B = B + A

#### How Commutative Property of Multiplication is different from distributive Property?

Distributive property basically expand the expression containing both addition and multiplication.

The expression for distributive property is:
A x ( B + C ) = A.B + B.C

Commutative Property is all about changing the location of digits in multiplication without affecting the final result.

The expression for commutative property is :
A x B = B x A

#### Will Commutative Property works in subtraction of numbers?

No!!
The commutative property does not work in subtraction of number as will effect the end result

Let us understand this with help of example

Let A = 5 and B = 3
Calculate A – B
⟹ 5 – 3
⟹ 2

Now calculate B – A
⟹ 3 – 5
⟹ -2

Hence, A – B is not equal to B – A as the results produced are different,
So the commutative property doesn’t work in subtraction of numbers

#### Will the commutative property works in division of number?

NO!!
In division the commutative property doesn’t work

## Problems on Commutative Property of Multiplication

(01) Which of the following is an example of commutative property of multiplication

(a) 2 x 6 = 4 x 3
(b) 4 x 2 = 2 x 4
(c) 6 x 3 = 9 x 2
(d) 5 x 4 = 2 x 10

The general format for commutative property is
A x B = B x A
Option (b) is the right answer

(02) Find the value of x
(2x) . (x) . (3) = 24

(a) 3
(b) 4
(c) 5
(d) 2

Using commutative property of multiplication, the expression can be written as:

\mathtt{x.\ x.\ 2.\ 3\ \ =\ 24}\\\ \\ \mathtt{x^{2} .\ 6\ =\ 24}\\\ \\ \mathtt{x^{2} \ =\frac{24}{6}}\\\ \\ \mathtt{x^{2} \ =\ 4}\\\ \\ \mathtt{x\ =\ 2}

Option (d) is the right answer

(03) Complete the following equation
7 x 13 = _____ x 7

(a) 13
(b) 1
(c) 7
(d) 21

According to commutative property
A x B = B x A

7 x 13 = 13 x 7

Option (a) is correct

(04) Fill up the blanks using commutative property
19 x 7 = 7 x ______

(a) 7
(b) 19
(c) 13
(d) 20

Option (b) is correct

(05) Find the value of variable y
6 . y . 9 = 108

(a) 2
(b) 3
(c) 7
(d) 11

Using commutative property of multiplication we can write:
⟹ 6 . 9 . y = 108
⟹ 54 . y = 108
⟹ y = 108/54
⟹ y = 2

Option (a) is correct

(06) Commutative property works in following math operation

(b) Division
(c) Multiplication
(d) Subtraction

Option (a) & (c) is correct

Commutative property works only in addition and multiplication

(07) Using commutative property, write the below expression in different way
\mathtt{x^{\frac{3}{4}} \ .\ 6}