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

Suggested Topics to Practice in Advance

  1. The commutative property
  2. The Commutative Property of Addition
  3. The Commutative Property of Multiplication
  4. The Distributive Property
  5. The Distributive Property for Seventh Graders
  6. The Distributive Property of Division
  7. The Distributive Property in the Case of Multiplication
  8. The commutative properties of addition and multiplication, and the distributive property

Practice Associative Property

Examples with solutions for Associative Property

Exercise #1

13+5+5= 13+5+5=

Video Solution

Step-by-Step Solution

First, we'll solve the right-hand exercise, since adding the numbers will give us a round number:

5+5=10 5+5=10

Now we'll get an easier exercise to solve:

13+10=23 13+10=23

Answer

23

Exercise #2

38+2+8= 38+2+8=

Video Solution

Step-by-Step Solution

First, we'll solve the right-hand exercise, since adding the numbers will give us a round number:

2+8=10 2+8=10

Now we'll get an easier exercise to solve:

38+10=48 38+10=48

Answer

48

Exercise #3

8+2+7= 8+2+7=

Video Solution

Step-by-Step Solution

First, we'll solve the left exercise, since adding the numbers will give us a round number:

8+2=10 8+2=10

Now we'll get an easier exercise to solve:

10+7=17 10+7=17

Answer

17

Exercise #4

13+7+100= 13+7+100=

Video Solution

Step-by-Step Solution

First, we'll solve the left exercise, since adding the numbers will give us a round number:

13+7=20 13+7=20

Now we'll get an easier exercise to solve:

20+100=120 20+100=120

Answer

120

Exercise #5

13+2+8= 13+2+8=

Video Solution

Step-by-Step Solution

We will use the commutative property and first solve the addition exercise on the right:

2+8=10 2+8=10

Now we get:

13+10=23 13+10=23

Answer

23

Exercise #6

4+9+8= 4+9+8=

Video Solution

Step-by-Step Solution

Let's break down 4 into a smaller addition problem:

3+1 3+1

Now we'll get the exercise:

3+1+9+8= 3+1+9+8=

Since the exercise only involves addition, we'll use the commutative property and start with the exercise:

1+9=10 1+9=10

Now we'll get the exercise:

3+10+8= 3+10+8=

Let's solve the exercise from right to left:

10+8=18 10+8=18

18+3=21 18+3=21

Answer

21

Exercise #7

2+43= 2+4-3=

Video Solution

Step-by-Step Solution

We solve the exercise from left to right, we place the addition exercise in parentheses and then subtract:

(2+4)3= (2+4)-3=

63=3 6-3=3

Answer

3

Exercise #8

32+10= -3-2+10=

Video Solution

Step-by-Step Solution

First, we place the subtraction exercise in parentheses, and then we add:

(32)+10= (-3-2)+10=

5+10= -5+10=

We use the substitution property to make solving the exercise easier:

105=5 10-5=5

Answer

5

Exercise #9

5+2a+4= 5+2a+4=

Video Solution

Step-by-Step Solution

Given that in the exercise there is only one addition operation, the substitution property can be used:

5+4+2a= 5+4+2a=

We solve the exercise from left to right:

5+4=9 5+4=9

Now we obtain:

2a+9 2a+9

Answer

2a+9 2a+9

Exercise #10

2+610+302= 2+6-10+30-2=

Video Solution

Step-by-Step Solution

We solve the exercise according to the order of operations.

We place the addition and subtraction exercises in parentheses in the following way to make it easier to solve:

(2+6)10+(302)= (2+6)-10+(30-2)=

We solve the exercises in parentheses:

810+28= 8-10+28=

We place the subtraction exercise in parentheses:

(810)+28= (8-10)+28=

2+28=26 -2+28=26

Answer

26

Exercise #11

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

Video Solution

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

Exercise #12

9:33= 9:3-3=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, we first solve the division exercise:

9:3=3 9:3=3

Now we obtain the exercise:

33=0 3-3=0

Answer

0 0

Exercise #13

5+26:2= -5+2-6:2=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, we first solve the division exercise:

6:2=3 6:2=3

Now we get the exercise:

5+23= -5+2-3=

We solve the exercise from left to right:

5+2=3 -5+2=-3

33=6 -3-3=-6

Answer

6 -6

Exercise #14

4×25+4= 4\times2-5+4=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, we first solve the multiplication exercise:

4×2=8 4\times2=8

Now we obtain the exercise:

85+4= 8-5+4=

We solve the exercise from left to right:

85=3 8-5=3

3+4=7 3+4=7

Answer

7 7

Exercise #15

7+8+12= 7+8+12=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, you can use the substitution property and start the exercise from right to left to calculate comfortably:

8+12=20 8+12=20

Now we obtain the exercise:

7+20=27 7+20=27

Answer

27

Topics learned in later sections

  1. The Associative Property of Addition
  2. The Associative Property of Multiplication
  3. Advanced Arithmetic Operations
  4. Subtracting Whole Numbers with Addition in Parentheses
  5. Division of Whole Numbers Within Parentheses Involving Division
  6. Subtracting Whole Numbers with Subtraction in Parentheses
  7. Division of Whole Numbers with Multiplication in Parentheses