Lesson 2: Multiplying Fractions

Property

Division can be rewritten as multiplication by a reciprocal: $\frac{a}{b} = a \times \frac{1}{b}$ where $b \neq 0$
The reciprocal of a product equals the product of reciprocals: $\frac{1}{ab} = \frac{1}{a} \times \frac{1}{b}$ where $a, b \neq 0$

Examples

Property

When multiplying an integer by a fraction: $a \times \frac{c}{d} = \frac{ac}{d}$ where $d \neq 0$

Examples

Property

Taking $\frac{2}{3}$ of something means to divide the quantity into 3 equal parts, and then take 2 of them. This is the same as multiplying by $\frac{2}{3}$.

To multiply two fractions:

1. Multiply the numerators together.
2. Multiply the denominators together.

Examples

• What is $\frac{3}{4}$ of 24? We can calculate this by multiplying: $\frac{3}{4} \times \frac{24}{1} = \frac{3 \times 24}{4 \times 1} = \frac{72}{4} = 18$.