Dividing fractions

To divide fractions, we can use the ‘keep, change, flip’ method. We keep the first fraction the same, change the division sign to a multiplication sign, and flip the second fraction (take its reciprocal).

This can be written as:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Example: Evaluate \frac{2}{3} \div \frac{4}{5}

• = \frac{2}{3} \times \frac{5}{4}
• = \frac{2 \times 5}{3 \times 4}
• = \frac{10}{12}
• = \frac{5}{6} - simplified by dividing both numerator and denominator by 2.
• Answer: \frac{5}{6}

Example: Evaluate \frac{3}{4} \div \frac{2}{7}

• = \frac{3}{4} \times \frac{7}{2}
• = \frac{3 \times 7}{4 \times 2}
• = \frac{21}{8}
• Answer: \frac{21}{8}

Example: Evaluate \frac{5}{6} \div 2

• = \frac{5}{6} \div \frac{2}{1}
• = \frac{5}{6} \times \frac{1}{2}
• = \frac{5 \times 1}{6 \times 2}
• = \frac{5}{12}
• Answer: \frac{5}{12}