Chapter Contents

• Factoring and Fractions
• 1. Special Products
• 2. Common Factor and Difference of Squares
• 3. Factoring Trinomials
• 4. The Sum and Difference of Cubes
• 5. Equivalent Fractions
• 6. Multiplication and Division of Fractions
• 7. Addition and Subtraction of Fractions
• 8. Equations Involving Fractions
• Factoring and Fractions Problem Solver

• Comments, Questions?

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5. Equivalent Fractions

Recall the following fraction properties:

This is true because we have multiplied both the top (numerator) and the bottom (denominator) by 5. We say 3/4 and 15/20 are equivalent fractions.

This is true because we have divided both the numerator and the denominator by 7. We say 7/21 and 1/3 are equivalent fractions.

We now apply these ideas to fractions involving algebraic expressions.

Example 1

Divide the numerator and the denominator of by 3ab².

Answer:

NOTE: This answer is not in simplest form. We could divide top and bottom again by a².

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KNOW WHEN TO STOP!

The following expression cannot be simplified further because there is an addition sign in the numerator and a subtraction in the denominator:

We cannot cancel the x and the x².

However, if the terms in the numerator and denominator are multiplied, then we can do further simplifying like this:

Example 2

Reduce to simplest form:

Answer:

We start by factoring the numerator and then observe we can divide top and bottom by one of the factors:

Example 3

Reduce to simplest form:

Answer

Exercises

Simplify:

(1)

Answer

(2)

Answer

(3)

Answer

(4)

Answer