Skill: Multiply a fraction by a whole number

Explanation and Free Practice Resources

Multiplying a fraction by a whole number means taking that many equal groups of the fraction, or scaling the fraction by a whole-number factor; a number line, bar model, or area model can show the repeated addition and resulting quantity, including products greater than one. The calculation $n \times \frac{a}{b}=\frac{na}{b}$ preserves the denominator because the unit fraction remains the same, with results simplified when appropriate; multiplication of two fractions and more generalized cases are not included.

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Detailed Explanation: Multiply a fraction by a whole number

To multiply a fraction by a whole number, think of the whole number as telling you how many equal groups of the fraction to take.

For example, find:

3 \times \frac{2}{5}

The number $3$ means three groups of $\frac{2}{5}$ :

\frac{2}{5}+\frac{2}{5}+\frac{2}{5}

Since all the fractions have the same denominator, multiply the numerator by $3$ and keep the denominator:

3 \times \frac{2}{5}=\frac{3\times 2}{5}=\frac{6}{5}

Simplify the improper fraction:

\frac{6}{5}=1\frac{1}{5}

So,

\boxed{3\times\frac{2}{5}=1\frac{1}{5}}

The denominator stays $5$ because you are still counting fifths. You are taking three groups of two fifths, which makes six fifths altogether.

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Fraction Multiplication - Simple by Whole

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