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Multiplying and Dividing Rational Expressions

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- Multiplying and Dividing Numeric Fractions
- Multiplying Rational Expressions
- Dividing Rational Expressions

**Multiplying and Dividing Numeric Fractions**

Before we discuss how to multiply and divide rational expressions (or algebraic fractions), it is helpful to review how we multiply and divide numeric fractions, because the process is the same, no matter what kind of fractions we are working with.

Multiplying two fractions is very straight forward. We simply multiply across the numerators, and then multiply across the denominators. We should not forget to simplify the fraction if possible. Below is an example:

When dividing fractions, we write it as a multiplication problem, where we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is a fraction with the flipped quantities in the numerator and denominator. This is shown in the example below:

**Multiplying Rational Expressions**

We multiply algebraic expressions in the same way that we multiply numeric fractions: we multiply across the numerators, and multiply across the denominators. Once again, we make sure that our product is fully simplified by cancelling out common factors that appear in both the numerator and denominator:

**Dividing Rational Expressions**

Dividing algebraic fractions works the same way it does when dividing numeric fractions. First, we write the problem as multiplication, using the reciprocal of the second fraction. Then we can follow the same procedure for multiplying rational expressions: