Question

what property allows variables to be taken out and replacement values to be put in an expression?

distributive property
substitution property
inverse property
associative property
commutative property

Explanation:

Analyze the question prompt

The question asks: "What property allows variables to be taken out and replacement values to be put in an expression?"

Define the algebraic properties

Let's review the definition of each option provided:

• Distributive Property: Allows multiplying a sum by multiplying each addend separately, e.g., \(a(b + c) = ab + ac\).
• Substitution Property: States that if \(a = b\), then \(a\) may be replaced by \(b\) in any equation or expression. This allows replacing variables with specific numerical values.
• Inverse Property: Relates to additive inverses (\(a + (-a) = 0\)) or multiplicative inverses (\(a \cdot \frac{1}{a} = 1\)).
• Associative Property: States that the grouping of numbers does not affect their sum or product, e.g., \((a + b) + c = a + (b + c)\).
• Commutative Property: States that the order of numbers does not affect their sum or product, e.g., \(a + b = b + a\).

Match the definition to the correct property

Replacing a variable with a specific value is the definition of substitution. Therefore, the property that allows variables to be replaced with numerical values is the Substitution Property.

Answer:

• Distributive Property
• Substitution Property (Correct answer)
• Inverse Property
• Associative Property
• Commutative Property