Associative Property of Math

Introduction of associative Property of Math:

Associative is a property of some binary operations. It means that, within an expression containing two or more occurrences in a row of the same associative operator, That is, rearranging the parentheses in such an expression will not change its value. Consider for instance the equation.

(Source: Wikipedia)

Addition associative Property:

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

Multiplication associative Property:

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


Example problems for Associative Property of Mathematics:


Associative Property in math Example 1:

Find the values of given expression using associative property. 16 + (5 + 8)

Solution:

Step 1:

16 + (5 + 8)

Formula :

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

Step 2:

(16+5)+ 8 = 16 +(5+8)

21+8 = 16+13

29 = 29

Associative Property in math Example 2:

Find the values of given expression using associative property. 6 x (5 x 3)

Solution:

Step1:

The property in which altering the alignment of factors does not change the product is called associative property of multiplication.

Formula:

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

Step 2:

6 × (5 × 3) can be written as (6 × 5) × 3.

Step 3:

6 × (5 × 3) = (6 × 5) × 3 show the property of associative multiply

6 x 15 = 30 x 3

90     =   90

Associative Property in math Example 3:

Find the values of given expression 6 x (6 x 7) are associative or not.

Step 1:

Explanation:

Formula:

a x (b x c)
Step 2:

Using the multiplication property formula

6 x (6 x 7) = (6 x 6) x 7

6 x 42 = 36 x 7

252 =252

Associative Property in math Example 4:

Find the values of given expression using associative property. 6 x (3 x 15)

Solution:

Step1:

The property in which altering the alignment of factors does not change the product is called associative property of multiplication.

Formula:

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

Step 2:

6 × (3 × 15) can be written as (6 × 3) × 15.

Step 3:

6 × (3 × 15) = (6 × 3) × 15 show the property of associative multiply

6 x 45 = 18 x 15

270  =  270

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Practice Problems for associative Property of mathematics :-


1. Find the values of given expression using associative property 18 x (35 x 52)

Answer:

32760

2. Find the values of given expression using associative property. 61 + (56 + 64)

Answer:

181