Associative Property Practice Problems & Worksheets

Master the associative property with step-by-step practice problems for addition and multiplication. Interactive exercises with instant feedback and solutions.

📚Practice the Associative Property with Real Problems

Apply associative property to regroup addition problems like (4+5)+3 = 4+(5+3)
Use parentheses to group multiplication factors for easier calculation
Solve algebraic expressions using associative property with variables
Identify when associative property makes calculations simpler
Practice regrouping fractions using associative property of addition
Master complex expressions combining multiple operations with proper grouping

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).

For example:

The expression

$15\times 2\times 9=$

Can be associated as

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

Detailed explanation

Practice Associative Property

Test your knowledge with 21 quizzes

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

Examples with solutions for Associative Property

Step-by-step solutions included

Exercise #1

$3+2-11=$

Step-by-Step Solution

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

$3+2=5$

$5-11=-6$

Answer:

$-6$

Video Solution

Exercise #2

$4+5+1-3=$

Step-by-Step Solution

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

$4+5=9$

$9+1=10$

$10-3=7$

Answer:

Video Solution

Exercise #3

$7+8+12=$

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:

$8+12=20$

Now we obtain the exercise:

$7+20=27$

Answer:

Video Solution

Exercise #4

$94+12+6=$

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:

$94+6+12=$

Now, we solve the exercise from left to right:

$94+6=100$

$100+12=112$

Answer:

112

Video Solution

Exercise #5

$7\times5\times2=$

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:

$5\times2=10$

$7\times10=70$

Answer:

Video Solution

Frequently Asked Questions

Everything you need to know about Associative Property

What is the associative property of addition with examples?

The associative property of addition states that changing the grouping of addends doesn't change the sum. For example: (4+5)+3 = 4+(5+3) = 12. You can group any two numbers first, then add the third.

How do you use the associative property in multiplication?

The associative property of multiplication allows you to regroup factors: (a×b)×c = a×(b×c). For example: (7×2)×5 = 7×(2×5) = 70. Group numbers that are easier to multiply first.

Does the associative property work with subtraction and division?

No, the associative property only works with addition and multiplication. For subtraction: (8-3)-2 ≠ 8-(3-2). For division: (12÷4)÷2 ≠ 12÷(4÷2).

When should I use the associative property in math problems?

Use the associative property when regrouping makes calculations easier. Examples include: grouping numbers that sum to 10, multiplying by factors of 10, or combining like terms in algebra.

How is associative property different from commutative property?

Commutative property changes the order of numbers (a+b = b+a), while associative property changes the grouping ((a+b)+c = a+(b+c)). Both help simplify calculations but in different ways.

Can you use associative property with fractions?

Yes, the associative property works with fractions. For example: (1/2 + 1/4) + 1/4 = 1/2 + (1/4 + 1/4) = 1/2 + 1/2 = 1. This often makes fraction addition easier.

What are common mistakes when using associative property?

Common mistakes include: 1) Trying to use it with subtraction or division, 2) Forgetting to place parentheses correctly, 3) Not following order of operations after regrouping, 4) Confusing it with commutative property.

How does associative property help with algebraic expressions?

The associative property helps combine like terms in algebra. For example: 4 + 5x + 4x = 4 + (5x + 4x) = 4 + 9x. This simplifies expressions and makes solving equations easier.

Continue Your Math Journey

Master Associative Property first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

The Associative Property of Addition The Associative Property of Multiplication Advanced Arithmetic Operations Subtracting Whole Numbers with Addition in Parentheses Division of Whole Numbers Within Parentheses Involving Division Subtracting Whole Numbers with Subtraction in Parentheses Division of Whole Numbers with Multiplication in Parentheses

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Associative Property Practice Problems & Worksheets

Understanding Associative Property

What is the associative property?

Practice Associative Property

Examples with solutions for Associative Property

Frequently Asked Questions

What is the associative property of addition with examples?

How do you use the associative property in multiplication?

Does the associative property work with subtraction and division?

When should I use the associative property in math problems?

How is associative property different from commutative property?

Can you use associative property with fractions?

What are common mistakes when using associative property?

How does associative property help with algebraic expressions?

More Associative Property Questions