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.

\[\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2}\]

Then multiply the fractions.

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