Equivalent Expressions using Number Properties Worksheets

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Equivalent Expressions using Number Properties

Examples, solutions, videos, and worksheets to help Grade 8 students learn how to use the commutative and associative properties to recognize structure within expressions and to prove equivalency of expressions.

The commutative and associative properties represent key beliefs about the arithmetic of real numbers. These properties can be applied to algebraic expressions using variables that represent real numbers.

Two algebraic expressions are equivalent if we can convert one expression into the other by repeatedly applying the commutative, associative, and distributive properties and the properties of rational exponents to components of the first expression.

How to find Equivalent Expressions using Number Properties?

We can use arithmetic properties to demonstrate that two expressions are equivalent. When we manipulate an expression using these properties, we create an expression that has the same value, showing equivalency. Here’s how to apply each property to confirm that two expressions are equivalent.

1. Using the Commutative Property
   

• Addition: Suppose we have the expressions 𝑎 + 𝑏 and 𝑏 + 𝑎. Using the commutative property of addition:
  𝑎 + 𝑏 = 𝑏 + 𝑎
  So, if we start with 𝑎 + 𝑏, we can rearrange it as 𝑏 + 𝑎, showing these two forms are equivalent.
  
• Multiplication: Similarly, if we have 𝑎 × 𝑏 and 𝑏 × 𝑎, we can rearrange the factors to show equivalency:
  𝑎 × 𝑏 = 𝑏 × 𝑎
  

2. Using the Associative Property
   

• Addition: The associative property lets us group numbers differently without changing their sum. For example:
  (𝑎 + 𝑏) + 𝑐 = 𝑎 + (𝑏 + 𝑐)
  
• Multiplication: Similarly,
  (𝑎 × 𝑏) × 𝑐 = 𝑎 × (𝑏 × 𝑐)
  

3. Using the Distributive Property
   The distributive property allows us to distribute multiplication over addition:
   𝑎 × (𝑏 + 𝑐) = 𝑎 × 𝑏 + 𝑎 × 𝑐

Have a look at this video if you need to review how to the Equivalent Expressions using Number Properties.

• Equivalent Expressions using Number Properties

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Equivalent Expressions using Number Properties Worksheet #5 (Exponents)

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