## Reciprocals and Dividing by Fractions

## Formative Assessment

# Summary of the Math: Reciprocals and Dividing by Fractions

**Read and Discuss**

- The fractions $\frac{a}{b}$ and $\frac{b}{a}$, with numerators and denominators inverted, are called
*reciprocals*of each other. The key property of reciprocals is that their product is always 1.

$\frac{a}{b}\times \frac{b}{a}=\frac{a\times b}{b\times a}=1$Reciprocals are also called

$\frac{3}{4}\times 5=\frac{15}{4}$*multiplicative inverses*. This name refers to the fact that if you multiply a fraction by a number, and then multiply the result by the reciprocal of the fraction, the result is “undone.” For example:

$\frac{15}{4}\times \frac{4}{3}=\frac{15}{3}=5$- You can use the properties of reciprocals to help you divide by fractions. The general rule is:
*To divide by a fraction, multiply by the reciprocal of the fraction*. Algebraically, the rule looks like this: $\frac{a}{b}\xf7\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}=\frac{ad}{bc}$

Can you:

- Solve a problem that involves dividing a fraction by a fraction?
- Determine which operation is needed to solve a word problem?
- Explain what reciprocals are and how to use them to help you solve division problems involving fractions?