Multiplying and Dividing Fractions

Multiplying Fractions

Multiply straight across - numerator × numerator, denominator × denominator:

$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$

Simplify First!

You can cancel common factors before multiplying:

$\frac{3}{4} \times \frac{2}{9} = \frac{\cancel{3}^1}{4} \times \frac{2}{\cancel{9}^3} = \frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6}$

Multiplying Mixed Numbers

Convert to improper fractions first:

$2\frac{1}{2} \times 1\frac{1}{3}$

$= \frac{5}{2} \times \frac{4}{3}$

$= \frac{20}{6} = \frac{10}{3} = 3\frac{1}{3}$

Dividing Fractions

Keep, Change, Flip!

1. Keep the first fraction
2. Change division to multiplication
3. Flip the second fraction (reciprocal)

$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$

Why Does This Work?

Dividing by a fraction is the same as multiplying by its reciprocal.

"How many $\frac{1}{2}$'s fit in 3?" is the same as "$3 \times 2 = 6$"

Word Problem Example

"A recipe calls for $\frac{3}{4}$ cup of flour. You want to make half the recipe. How much flour?"

$\frac{3}{4} \times \frac{1}{2} = \frac{3}{8} \text{ cup}$