Convert Decimals to Fractions to Multiply

Property To multiply a decimal by a fraction, you can convert the decimal to its equivalent fraction and then multiply the two fractions. For a decimal $0.a$, the equivalent fraction is $\frac{a}{10}$. For a decimal $0.ab$, the equivalent fraction is $\frac{ab}{100}$.

Examples To calculate $0.5 \times \frac{3}{4}$, convert $0.5$ to $\frac{1}{2}$: $$\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$$ To find the value of $0.25$ of $\frac{4}{5}$, convert $0.25$ to $\frac{1}{4}$: $$\frac{1}{4} \times \frac{4}{5} = \frac{4}{20} = \frac{1}{5}$$ A recipe calls for $\frac{2}{3}$ cup of sugar. If you only make $0.75$ of the recipe, how much sugar do you need? $$0.75 \times \frac{2}{3} = \frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2} \text{ cup}$$.

Explanation This skill provides an alternative strategy for multiplying decimals and fractions. Converting a decimal to a fraction can sometimes make the calculation easier, especially if the decimal has a simple fractional equivalent like $0.5 = \frac{1}{2}$ or $0.25 = \frac{1}{4}$. Once both numbers are in fraction form, you can multiply the numerators and the denominators as usual. This method avoids decimal multiplication and allows for potential simplification before or after multiplying.