# Associative Property of Addition – Definition, examples and problems

## 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

Read Solution

Option (a) is the right answer

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