**What is Associative Property of Addition?**

Association means to “**join something**“

The property says that addition of three or more numbers will yield same results regardless of how numbers are grouped in the addition.

**According to associative property**

where A, B and C can be any number possible

**Conclusion**

In addition, you can group numbers as per your wish without affecting the end result

**Note**

Associative property always involves three or more numbers

**How to remember Associative Property**

You can easily remember the property if you can understand the meaning of word **“Associate”**

“Associate” means **forming a group or relation** with other entity.

Similar to its meaning, the property is saying that we can form different types of groups or association in addition without changing the end result.

**Associative Property of Addition Example**

Given below are some examples which will help you understand the concept better

**Example 01**

A = 5, B = 4 and C = 2

(i) Find (A + B) + C

⟹(5 + 4) + 2

⟹ 9 + 2

⟹ 11

(ii) Now find A + (B + C)

⟹ 5 + (4 + 2)

⟹ 5 + 6

⟹ 11

You can see both (i) and (ii) yield same result**hence, associative property is verified**

**Example 02**

A = 10, B = 13 and C =9

(i) Find (A + B) + C

⟹(10 + 13) + 9

⟹ 23 + 9

⟹ 32

(ii) Now find A + (B + C)

⟹ 10 + (13 + 9)

⟹ 10 + 22

⟹ 32

You can see both (i) and (ii) yield same result**hence, associative property is verified**

**Frequently Asked Question – Associative Property of Addition**

**How are associative and commutative property different?**

Commutative property deals with the movement of numbers in addition, while associative property is all about forming groups.

Commutative Property Expression

A + B = B + A

Associative Property Expression

(A + B) + C = A + (B + C)

**Does associative property works in subtraction?**

NO!!

In subtraction regrouping of numbers will yield completely different answer.

Let me explain this with example

If A =2, B = 3, C = 4

Then prove if associative property works for given subtraction

A – (B – C) & (A – B) – C

(i) A – (B – C)

⟹ 2 – (3 – 4)

⟹ 2 – (-1)

⟹ 2+1

⟹ 3

(ii) (A – B) – C

⟹ (2 – 3) – 4

⟹ – 1 – 4

⟹ – 5

you can see that both (i) and (ii) gives different results

**Hence, associative property does not work in subtraction**

**Does associative property works in multiplication?**

YES!!

In multiplication, we can form different groups/association without change in the final outcome.

The** associative property of multiplication** is represented as:

(A x B) x C = A x (B x C)

**How is associative property different from distributive property?**

Distributive property is all about simplification of multiplication and division operation.

The distributive property needs three or more elements in its operation.

**The property is shown as:**

The removal is parenthesis is replaced with multiplication operation with the element A

On the other hand, associative property is all about formation of groups in addition operation

**Does associative property works in division operation?**

NO!!

We cannot form different groups in division as it will change the end result

**Questions on Associative Property of Addition**

**(01) Which of the following example show associative property of addition**

(a) (6 + 3) + 4 = 6 + (3 + 4)

(b) (7 + 1) + 6 = 5 + (4 + 5)

(c) (3 + 2) + 1 = 4 + 2

Read Solution

**Option (a) is the right answer**

Option (a) form grouping of same set of numbers

**(02) Given below is the number which follow associative property. Find the missing numbers**

3 + (5 + 7) = (3 + 5) + _______

(a) 3

(b) 5

(c) 7

Read Solution

**Option (c) is the right answer**

The associative property states that:

a + (b + c) = (a + b) +c

On comparing the above number, you will find that missing number is 7

**(03) Using associative property of addition, find the missing number**

⟹ (10 +_______) + _________ = ___________

⟹ (10 + 25 ) + 32 = ___________

Read Solution

⟹ (10 + 25 ) + 32 = 67

**(04) Which property is defined by below expression**

a x (b + c) = ( a x b ) + ( a x c )

(a) Commutative Property

(b) Distributive Property

(c) Associative Property

(d) Identity Property

Read Solution

**Option (b) is the right answer**

the expression is of distributive property of addition

**(05) Use the associative property to simplify below expression and find right answer**

3x + (7y + 2x)

(a) 3x + 10 y

(b) 6x + 7y

(c) 5x + 7y

(d) 9x + 9y

Read Solution

3x + (7y + 2x)

Using associative property of addition

⟹ (3x + 2x) + 7y

⟹ 5x + 7y

**Option (c) is the right answer**

**(06) Associative property works in following operations**

(a) Division and Addition

(b) Multiplication and subtraction

(c) Division and Subtraction

(d) Addition and Multiplication

Read Solution

**Option (d) is the right answer**

**(07) The expression below follows associative property. Find the value of x**

6 + (x + 8)= (6 + 4) +8

(a) 4

(b) 8

(c) 6

(d) 2

**Option (a) is the right answer**