Equivalent expressions

Concept

If two algebraic expressions are equivalent, then the two expressions have the same value.

Rules

Rewrite the expression using the distributive property.
a. Find the greatest common factor (GCF) to be distributed.
b. Put the GCF outside of the parenthesis with the other terms inside.
a x b + a x c = a(b + c)

Example

Use the distributive property to write the equivalent expression.
10 x 3 + 10 x 2

Solution

10 is the GCF to be distributed to each value in the parenthesis.
Put the GCF (10) outside of the parenthesis with the other terms inside.
Answer: 10(3 + 2)

Practice Equivalent Expressions

Practice Problem 1

Select the expression being modeled.

Practice Problem 2

Select the expression that is equivalent.
2 × 3.5 – 2 × 5.3

Practice Problem 3

Select the expression that is equivalent.
$\fn_phv \frac{1}{4}\times \frac{2}{7}+\frac{1}{4}\times0.1$

Equivalent expressions are expressions that work the same even though they look different.

Greatest Common Factor (GCF) – is the largest positive integer that divides evenly into all numbers with zero remainders.

Distributive Property – to multiply a sum or difference by a number, multiply each term inside the parentheses by the number outside the parentheses.

Pre-requisite Skill
Distributive Property of Multiplication