Multiplying fractions

To multiply fractions, we multiply the numerators (the top parts) together and the denominators (the bottom parts) together.

This can be written as:

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

Example: Multiply \frac{2}{3} \times \frac{4}{5}

• = \frac{2 \times 4}{3 \times 5}
• = \frac{8}{15}
• Answer: \frac{8}{15}

Example: Multiply \frac{3}{4} \times \frac{2}{7}

• = \frac{3 \times 2}{4 \times 7}
• = \frac{6}{28}
• = \frac{3}{14} - simplified by dividing both numerator and denominator by 2.
• Answer: \frac{3}{14}

Example: Multiply \frac{5}{6} \times \frac{9}{10}

• = \frac{5 \times 9}{6 \times 10}
• = \frac{45}{60}
• = \frac{3}{4} - simplified by dividing both numerator and denominator by 15.
• Answer: \frac{3}{4}

Example: Multiply \frac{7x}{8y} \times \frac{16y}{21x}

• = \frac{7x \times 16y}{8y \times 21x}
• = \frac{112xy}{168xy}
• = \frac{2}{3} - simplified by dividing both numerator and denominator by 56xy.
• Answer: \frac{2}{3}

Example: Multiply \frac{4a^2}{-9b} \times \frac{27b^2}{16a}

• = \frac{4a^2 \times 27b^2}{-9b \times 16a}
• = \frac{108a^2b^2}{-144ab}
• = \frac{-3ab}{4} - simplified by dividing both numerator and denominator by 36ab.
• Answer: \frac{-3ab}{4} or -\frac{3ab}{4} or -\frac{3}{4}ab

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