**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**

(a) Addition

(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}

\mathtt{( a) \ \frac{6}{x^{3/4}}}\\\ \\ \mathtt{( b) \ 6.\ x^{\frac{3}{4}}}\\\ \\ \mathtt{( c) \ \frac{1}{6} .x^{\frac{3}{4}} \ }\\\ \\ \mathtt{( d) \ 6\ +\ x^{\frac{3}{4}} \ }

**Option (b) is correct**