Lesson 5: Multiply Two Fractions

Property

If $a$, $b$, $c$, and $d$ are numbers where $b \neq 0$ and $d \neq 0$, then

To multiply fractions, we multiply the numerators and multiply the denominators. Then we write the fraction in simplified form.

Examples

• To multiply $\frac{2}{3} \cdot \frac{4}{5}$, multiply the numerators ($2 \cdot 4 = 8$) and the denominators ($3 \cdot 5 = 15$). The result is $\frac{8}{15}$.
• Multiply $-\frac{4}{7} \cdot \frac{14}{16}$. The product will be negative. We can simplify before multiplying: $-\frac{4}{7} \cdot \frac{2 \cdot 7}{4 \cdot 4} = -\frac{1}{1} \cdot \frac{2}{4} = -\frac{2}{4}$, which simplifies to $-\frac{1}{2}$.
• To multiply $8 \cdot \frac{3}{4}$, first write 8 as $\frac{8}{1}$. Then multiply: $\frac{8}{1} \cdot \frac{3}{4} = \frac{24}{4}$. Simplifying this fraction gives 6.

Explanation

Multiplying fractions is straightforward: multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator. Remember to simplify the resulting fraction by canceling any common factors for the final answer.

Property

When an expression contains parentheses, perform the operation inside the parentheses first. For fractions, this means you add or subtract the fractions within the parentheses before multiplying.

Examples

• $(\frac{1}{2} + \frac{1}{2}) \times \frac{3}{8} = 1 \times \frac{3}{8} = \frac{3}{8}$
• $(\frac{5}{6} - \frac{1}{6}) \times \frac{1}{2} = \frac{4}{6} \times \frac{1}{2} = \frac{4}{12} = \frac{1}{3}$
• $(\frac{1}{3} + \frac{1}{4}) \times \frac{2}{5} = (\frac{4}{12} + \frac{3}{12}) \times \frac{2}{5} = \frac{7}{12} \times \frac{2}{5} = \frac{14}{60} = \frac{7}{30}$

Explanation

The order of operations (PEMDAS/BODMAS) also applies to fractions. This means you must solve any calculations inside parentheses before performing other operations like multiplication. First, find a common denominator if needed and perform the addition or subtraction within the parentheses. Then, multiply the resulting fraction by the fraction outside the parentheses to find the final answer.