Multiply and Divide Fractions

Multiplying and dividing with fractions can be quite a simple process.

Multiplying proper fractions

To multiply fractions, multiply the numerators and the denominators.

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

Multiplying mixed numbers

$$2\frac{1}{2}\times 1\frac{3}{4}$$

To multiply mixed numbers, convert them into improper fractions.

$$2\frac{1}{2}\times 1\frac{3}{4}=\frac{5}{2}\times \frac{7}{4}$$

Then multiply the numerators and the denominators.

$$\frac{5}{2}\times \frac{7}{4}=\frac{5\times 7}{2\times 4}=\frac{35}{8}$$

Then convert back to a mixed number.

$$\frac{35}{8}=4\frac{3}{8}$$

Dividing Fractions

To divide fractions, flip the second fraction (find the reciprocal) and change the divide into a multiply.

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

Then multiply the fractions.

$$\frac{3}{4}\times \frac{5}{2}=\frac{15}{8}=1\frac{7}{8}$$