Associative Property Practice Problems & Solutions

Master the associative property of addition with step-by-step practice problems. Learn to group addends efficiently and solve complex expressions.

📚Practice Associative Property Skills
  • Apply associative property to group addends in different ways
  • Solve addition problems using parentheses to change order of operations
  • Work with algebraic expressions containing variables and coefficients
  • Calculate sums efficiently by grouping compatible numbers first
  • Verify that different groupings produce equivalent results
  • Use associative property with fractions and decimal numbers

Understanding The Associative Property of Addition

Complete explanation with examples

The associative property of addition allows us to group two addends and then add the third addend to the result.


We can use this property in three ways:
1. We start by adding the first and the second addend, solve the sum and add the third addend to the result.
2. We start by adding the second and third addends, solve the sum and then add the first addend to the result.

  1. We start by adding the first and the third addend, solve the sum and then add the second addend to the result.


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

The associative property of addition also works in algebraic expressions, but not in subtraction operations.
Let's define the associative property of addition as:
a+b+c=(a+b)+c=a+(b+c)=(a+c)+ba+b+c=(a+b)+c=a+(b+c)=(a+c)+b

A - The Associative Property of Addition

Detailed explanation

Practice The Associative Property of Addition

Test your knowledge with 21 quizzes

\( 9:3-3= \)

Examples with solutions for The Associative Property of Addition

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 addition?

+
The associative property states that when adding three or more numbers, you can group them in any way and get the same result. It's written as (a + b) + c = a + (b + c) = (a + c) + b.

How do you use parentheses with the associative property?

+
Parentheses show which numbers to add first. For example, in 7 + 8 + 12, you could write (7 + 8) + 12 = 15 + 12 = 27, or 7 + (8 + 12) = 7 + 20 = 27.

Does the associative property work with subtraction?

+
No, the associative property does not work with subtraction. For example, (10 - 3) - 2 = 5, but 10 - (3 - 2) = 9. The results are different.

When is the associative property useful in math?

+
The associative property is useful when you want to group numbers that are easier to add together first. It's particularly helpful with: 1) Mental math calculations, 2) Algebraic expressions with variables, 3) Working with fractions and decimals.

Can you use associative property with variables?

+
Yes, the associative property works with algebraic expressions. For example, 2 + 10x + 2x can be regrouped as 2 + (10x + 2x) = 2 + 12x.

What's the difference between associative and commutative properties?

+
The commutative property changes the order of numbers (3 + 5 = 5 + 3), while the associative property changes how numbers are grouped ((3 + 5) + 2 = 3 + (5 + 2)). Both properties help make calculations easier.

How do you solve associative property problems with fractions?

+
Convert mixed numbers to improper fractions, find common denominators, then group the fractions strategically. For example, group fractions that add up to whole numbers first to simplify calculations.

What are common mistakes when using the associative property?

+
Common mistakes include: 1) Trying to use it with subtraction or division, 2) Forgetting to follow order of operations, 3) Not converting fractions to common denominators first, 4) Confusing it with the commutative property.

More The Associative Property of Addition Questions

Continue Your Math Journey

Practice by Question Type