Multiplying fractions

Find a fraction of a whole number, multiply two fractions with an area model, and predict whether a product will be bigger or smaller than the number you started with.

A fraction of a number

$\frac{1}{3}$ of 12 means: cut 12 into 3 equal parts and take one. 12 ÷ 3 = 4. $\frac{2}{3}$ of 12 is two of those parts: 8.

"Of" means multiply: $\frac{2}{3}$ of 12 is $\frac{2}{3} \times 12 = \frac{24}{3} = 8$.

Fraction times fraction

To find $\frac{1}{2}$ of $\frac{3}{4}$, take half of three fourths. In an area model, shade $\frac{3}{4}$ one way and take $\frac{1}{2}$ of it the other way; the overlap is the answer.

Multiply the numerators and multiply the denominators: $\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}$.

The same rule gives the area of a rectangle with fraction sides: one $\frac{2}{3}$ m by $\frac{4}{5}$ m has an area of $\frac{8}{15}$ square meter.

Multiplying makes it bigger or smaller

Multiplying by a number bigger than 1 makes a number bigger. Multiplying by a fraction less than 1 makes it smaller: $\frac{3}{4}$ × 8 = 6, which is less than 8.

Try it yourself

Work each one on paper first, then open the answer to check.

1. What is $\frac{1}{4}$ of 24?

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   6.

2. What is $\frac{3}{4}$ of 16?

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   12.

3. What is $\frac{2}{5}$ × $\frac{1}{3}$?

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   $\frac{2}{15}$

4. What is $\frac{3}{4}$ × $\frac{2}{3}$?

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   $\frac{6}{12}$, which is $\frac{1}{2}$.

5. Is $1\frac{1}{4}$ × 6 more or less than 6?

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   More, because $1\frac{1}{4}$ is bigger than 1. It is $7\frac{1}{2}$.