Associative Property Practice Problems & Solutions

Master the associative property of multiplication with step-by-step practice problems. Learn to regroup factors efficiently and solve complex expressions.

📚Practice Associative Property Problems
  • Apply associative property to regroup multiplication factors strategically
  • Solve multi-step expressions using parentheses to group factors
  • Work with whole numbers, decimals, and fractions using associative property
  • Identify when regrouping factors makes calculations easier and faster
  • Combine associative property with order of operations in complex expressions
  • Verify solutions by applying different grouping strategies to same problem

Understanding The Associative Property of Multiplication

Complete explanation with examples

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

Detailed explanation

Practice The Associative Property of Multiplication

Test your knowledge with 21 quizzes

\( 9:3-3= \)

Examples with solutions for The Associative Property of Multiplication

Step-by-step solutions included
Exercise #1

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

Step-by-Step Solution

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

8+2=10 8+2=10

Now we have an easier exercise to solve:

10+7=17 10+7=17

Answer:

17

Video Solution
Exercise #2

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

Step-by-Step Solution

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

5+5=10 5+5=10

Now we have an easier exercise to solve:

13+10=23 13+10=23

Answer:

23

Video Solution
Exercise #3

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

Step-by-Step Solution

First, solve the right-hand side of the exercise since adding these numbers together will give you a round number:

2+8=10 2+8=10

This leaves you with an easier exercise to solve:

38+10=48 38+10=48

Answer:

48

Video Solution
Exercise #4

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

Step-by-Step Solution

First, we'll solve the left-hand side of the exercise since adding these numbers together gives us a round number:

13+7=20 13+7=20

This leaves us with a much easier exercise to solve:

20+100=120 20+100=120

Answer:

120

Video Solution
Exercise #5

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

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

Video Solution

Frequently Asked Questions

What is the associative property of multiplication with examples?

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The associative property states that you can regroup factors in multiplication without changing the result: (a × b) × c = a × (b × c). For example, (4 × 5) × 2 = 4 × (5 × 2) = 40. This means you can multiply 4 × 5 = 20 first, then 20 × 2 = 40, or multiply 5 × 2 = 10 first, then 4 × 10 = 40.

How do you use parentheses with the associative property?

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Parentheses show which factors to multiply first in the order of operations. In the expression 7 × (5 × 3), you multiply 5 × 3 = 15 first, then 7 × 15 = 105. The associative property lets you move these parentheses: (7 × 5) × 3 also equals 105.

When should I use the associative property to make calculations easier?

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Use the associative property when regrouping creates easier mental math: 1) When factors multiply to make round numbers (like 25 × 4 = 100), 2) When you can create multiplication facts you know well, 3) When working with fractions that can cancel out. For example, in 9 × 25 × 4, group 25 × 4 = 100 first.

Does the associative property work with division?

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No, the associative property does NOT work with division. For example, (12 ÷ 4) ÷ 2 = 3 ÷ 2 = 1.5, but 12 ÷ (4 ÷ 2) = 12 ÷ 2 = 6. The results are different, so you cannot regroup division operations.

How is associative property different from commutative property?

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The associative property is about REgrouping factors using parentheses: (a × b) × c = a × (b × c). The commutative property is about REordering factors: a × b = b × a. Associative changes which operations you do first, while commutative changes the sequence of numbers.

Can you use associative property with algebraic expressions?

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Yes, the associative property works with algebraic expressions containing variables. For example, x × 5 × 3 = x × (5 × 3) = x × 15 = 15x. This helps simplify expressions by combining numerical coefficients first, then multiplying by the variable.

What are common mistakes students make with associative property?

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Common mistakes include: 1) Trying to apply it to division (it doesn't work), 2) Confusing it with commutative property, 3) Forgetting to follow order of operations with parentheses, 4) Not recognizing when regrouping would make calculations easier. Always remember: associative = regrouping, commutative = reordering.

How do you solve associative property problems with fractions?

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With fractions, look for opportunities to cancel: In (4/7) × (3/2) × (7/4), you can regroup as (4/7) × (7/4) × (3/2). The 4s and 7s cancel out: (4×7)/(7×4) × (3/2) = 1 × (3/2) = 3/2. Always look for common factors that can simplify the calculation.

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