Lesson 4: The Standard Algorithm for Fraction Multiplication

Property

To multiply two fractions, multiply the numerators to find the new numerator and multiply the denominators to find the new denominator.

Examples

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

The commutative property of multiplication states that changing the order of the fractions does not change the product. For any two unit fractions:

Examples