# Associative Property of Multiplication : Definition, Examples & Problems

## What is Associative Property of Multiplication?

According to the property, forming different groups in the multiplication will not affect the end result.

The property can be expressed as:

Where A, B & C can be any possible real number

Note that forming different groups using parenthesis will not affect the final result of the calculation

### Why the property is named “Associative”?

In English, Associative means ” forming group or relation“.

Through the name the property conveys the message that forming different group will not affect the multiplication outcome.

### Associative Property of Multiplication Example

Given below are some examples of associative property for your understanding

Example 01
Let A = 4, B =2 & C = 5

Calculate (A x B) x C
⟹ ( 4 x 2 ) x 5
⟹ 8 x 5
⟹ 40

Now Calculate A x (B x C)
⟹ 4 x (2 x 5)
⟹ 4 x 10
⟹ 40

Hence (A x B) x C = A x (B x C) = 40
The associative property of multiplication is verified

Example 02
Let A = 11, B = 5 & C = 15

Calculate (A x B) x C
⟹ ( 11 x 5 ) x 15
⟹ 55 x 15
⟹ 825

Now calculate A x (B x C)
⟹ 11 x (5 x 15)
⟹ 11 x 75
⟹ 825

Hence, (A x B) x C = A x (B x C) = 825
The associative property of multiplication is verified

### Frequently asked Question : Associative Property

#### How is associative property of multiplication different from Inverse property?

Inverse property of multiplication says that multiplying any number with its reciprocal results in number 1.

Inverse Property is expressed as:

On the other hand, distributive property is all about forming different groups in multiplication without affecting any outcome.

#### Will the associative property work for addition?

Yes!!
In fact, there is a separate associative property of addition which is expressed as:

It says that forming different groups in addition will not affect the final outcome

#### How is Commutative Property of multiplication different from associative property?

Commutative property is all about moving numbers in the multiplication without affecting the end result.

The property is expressed as:
A x B = B x A

On the other hand associative property is about forming different groups in multiplication without affecting the outcome
(A x B) x C = A x (B x C)

#### Does Associative property works in subtraction?

No!!

In subtraction the associative property does not work as forming different groups will produce different answers

For Example
Let A = 5, B = 3 & C = 2

Calculate (A – B) – C
⟹ (5 – 3) – 2
⟹ 2 – 2
⟹ 0

Now calculate A – (B – C)
⟹ 5 – (3 – 2)
⟹ 5 – 1
⟹ 4

Both the calculation produced different answers
Hence, the property does not work in subtraction

#### Will the associative property work in division?

No!
Associative property does not works in division as it will give different answer for different group formation

#### Is associative property application for rational numbers?

Yes!!
Rational numbers are the ones which can be expressed in the form of P/Q (i.e fractions)

Given below is the expression of associative property for rational number

\mathtt{\left(\frac{A}{B} \times \frac{C}{D}\right) \ \times \ \frac{E}{F} \ =\ \ \frac{A}{B} \ \times \ \left(\frac{C}{D} \times \frac{E}{F}\right)}

## Questions on Associative Property of Multiplication

(01) Use the associative property to write below expression in different manner
(7 x 6) x 3

(a) 7 + (3 x 6)
(b) 7 x (6 x 3)
(c) 7 x (6 + 3)
(d) (7 + 6) + 3

The associative property is expressed as:
(A x B) x C = A x (B x C)

Option (b) is the correct representation

(02) Find the value of Q using associative property
7 x (6 x Q) = (7 x 6) x 9

(a) 7
(b) 10
(c) 9
(d) 11

Option (c) is correct

(03) Associative property is applicable in:

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

Option (a) & (b) are correct
Associative property works in addition and multiplication

(04) Find the value of y in below expression
(\mathtt{6.\ y) \ .7\ =\ 126}

(a) 3
(b) 4
(c) 5
(d) 6

Option (a) is correct

Using\ associative\ property\ we\ can\ write\\\ \\ ( 6.\ 7) \ .\ y\ =\ 126\\\ \\ 42\ .\ y\ =\ 126\\\ \\ y\ =\ \frac{126}{42} \ =\ 3

Hence, value of y = 3

(05) Identify the property
A x ( B – C ) = AB – AC

(a) Associative property
(b) Distributive Property
(c) Commutative Property
(d) Inverse property