**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:**

(a) Addition

(b) Multiplication

(c) Subtraction

(d) Division

Read Solution

**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

**Option (b) is correct**