Lesson 9: Divide Rational Numbers

Property

To divide rational numbers that are in different forms, first convert them to the same form (usually fractions) and then divide.

• If the signs are the same (both positive or both negative), the quotient is positive
• If the signs are different (one positive, one negative), the quotient is negative

Examples

Property

A complex fraction is a fraction in which the numerator or the denominator contains a fraction. To simplify a complex fraction, remember that the fraction bar means division.
Step 1. Rewrite the complex fraction as a division problem.
Step 2. Follow the rules for dividing fractions.
Step 3. Simplify if possible.

Examples

• To simplify $\frac{\frac{1}{3}}{\frac{4}{9}}$, rewrite as $\frac{1}{3} \div \frac{4}{9}$. This becomes $\frac{1}{3} \cdot \frac{9}{4} = \frac{9}{12}$, which simplifies to $\frac{3}{4}$.

• To simplify $\frac{5}{\frac{2}{3}}$, rewrite as $5 \div \frac{2}{3}$. This becomes $\frac{5}{1} \cdot \frac{3}{2} = \frac{15}{2}$.