The Associative Property of Multiplication - Examples, Exercises and Solutions

The associative property of multiplication allows us to multiply two factors and then multiply the product by the third factor, even if they're not in order from left to right.

A - The Associative Property of Multiplication

We can use this property in three ways:
1. We start by multiplying the first and the second factors, solving, and then multiplying the third factor by the result.
2. We start by multiplying the second and the third factors, solving, and then multiplying the first factor by the result.

  1. We start by multiplying the first and the third factors, solving, and then multiplying the second factor by the result.


We will place in parentheses around the factors that we want to group first in order to give them priority in the order of operations.

Note: The associative property of multiplication also works in algebraic expressions, but not in division expressions.


Let's define the associative property of multiplication as:

a×b×c=(a×b)×c=a×(b×c)=(a×c)×b a\times b\times c=(a\times b)\times c=a\times(b\times c)=(a\times c)\times b

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 The Associative Property of Multiplication

examples with solutions for the associative property of multiplication

Exercise #1

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 #2

3×5×4= 3\times5\times4=

Video Solution

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

Exercise #3

3+211= 3+2-11=

Video Solution

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

Exercise #4

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

Video Solution

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

Exercise #5

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

Video Solution

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

examples with solutions for the associative property of multiplication

Exercise #1

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 #2

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 #3

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 #4

12×5×6= 12\times5\times6=

Video Solution

Step-by-Step Solution

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

12×5=60 12\times5=60

60×6=360 60\times6=360

Answer

360

Exercise #5

94+12+6= 94+12+6=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, you can use the substitution property and organize the exercise in a more convenient way for calculation:

94+6+12= 94+6+12=

Now, we solve the exercise from left to right:

94+6=100 94+6=100

100+12=112 100+12=112

Answer

112

examples with solutions for the associative property of multiplication

Exercise #1

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

Exercise #2

7×5×2= 7\times5\times2=

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 comfortably calculate:

5×2=10 5\times2=10

7×10=70 7\times10=70

Answer

70

Exercise #3

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 #4

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 #5

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

Topics learned in later sections

  1. The Associative Property
  2. The Associative Property of Addition
  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