### Math Notes

Subjects
Basic Mathematics Solved Problems | Topics - Contents

# Division of Fractions

All fractions should be in improper or proper form.

#### Procedures:

1. Take the reciprocal of the denominator or the divisor.
The reciprocal of $$\frac{2}{3}$$ is $$\frac{3}{2}$$, the reciprocal of $$\frac{1}{5}$$ is 5.
2. Multiply the reciprocal to the numerator.

#### Examples:

1. Find the quotient of $$\frac{2}{3}$$ ÷ $$\frac{5}{6}$$
1. Reciprocal of the denominator $$\frac{5}{6}$$ is $$\frac{6}{5}$$
2. Multiply $$\frac{6}{5}$$ to the numerator $$\frac{2}{3}$$
3. $$\frac{6}{5}$$ x $$\frac{2}{3}$$ = $$\frac{12}{15}$$
4. Simplify / Reduce
5. $$\frac{12}{15}$$ = $$\frac{4}{5}$$
2. Find the quotient of $$\frac{8}{3}$$ ÷ $$\frac{3}{5}$$
1. Reciprocal of the denominator $$\frac{3}{5}$$ is $$\frac{5}{3}$$
2. Multiply $$\frac{5}{3}$$ to the numerator $$\frac{8}{3}$$
3. $$\frac{5}{3}$$ x $$\frac{8}{3}$$ = $$\frac{40}{9}$$
4. Since the numerator and the denominator has no common factors $$\frac{40}{9}$$ is the simplest form