Associative Property - Examples, Exercises and Solutions

Understanding Associative Property

Complete explanation with examples

What is the associative property?

The associative property tells us that that we can change the grouping of factors (in multiplication) or addends (in addition) in an expression without changing the end result.

Typically, we use parentheses to associate, since they come first in the order of operations (PEMDAS).

A - The Associative Property

For example:

The expression

15×2×9= 15\times 2\times 9=

Can be associated as

(15×2)×9=15×(2×9)=270 \left(15×2\right)×9=15×\left(2×9\right)=270

Detailed explanation

Practice Associative Property

Test your knowledge with 21 quizzes

\( 8+2+7= \) ?

Examples with solutions for Associative Property

Step-by-step solutions included
Exercise #1

6:2+94= 6:2+9-4=

Step-by-Step Solution

According to the order of operations, we first solve the division exercise, and then the subtraction:

(6:2)+94= (6:2)+9-4=

6:2=3 6:2=3

Now we place the subtraction exercise in parentheses:

3+(94)= 3+(9-4)=

3+5=8 3+5=8

Answer:

8 8

Video Solution
Exercise #2

3×5×4= 3\times5\times4=

Step-by-Step Solution

According to the order of operations, we must solve the exercise from left to right.

But, this can leave us with awkward or complicated numbers to calculate.

Since the entire exercise is a multiplication, you can use the associative property to reorganize the exercise:

3*5*4=

We will start by calculating the second exercise, so we will mark it with parentheses:

3*(5*4)=

3*(20)=

Now, we can easily solve the rest of the exercise:

3*20=60

Answer:

60

Video Solution
Exercise #3

3+211= 3+2-11=

Step-by-Step Solution

According to the order of operations, we solve the exercise from left to right:

3+2=5 3+2=5

511=6 5-11=-6

Answer:

6 -6

Video Solution
Exercise #4

4+5+13= 4+5+1-3=

Step-by-Step Solution

According to the order of operations, we solve the exercise from left to right:

4+5=9 4+5=9

9+1=10 9+1=10

103=7 10-3=7

Answer:

7

Video Solution
Exercise #5

24:8:3= 24:8:3=

Step-by-Step Solution

According to the order of operations, we solve the exercise from left to right since the only operation in the exercise is division:

24:8=3 24:8=3

3:3=1 3:3=1

Answer:

1 1

Video Solution

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