Multiply a fraction by a whole number

Multiplying a fraction by a whole number means finding that many equal fractional parts, so $n \times \frac{a}{b}$ can be interpreted as repeated addition and represented by equal jumps on a number line or groups of a fraction. The learner understands that the denominator names the size of each part while the numerator is multiplied by the whole number, including results greater than one; multiplication of two fractions and general fraction algorithms are beyond this scope.

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 find.

Example

Find:

3 \times \frac{2}{5}

Step 1: Write the fraction as repeated addition.

Three groups of $\frac{2}{5}$ are:

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

Step 2: Keep the denominator the same.

The denominator $5$ tells the size of the parts. There are still fifths, so the denominator stays $5$ .

Step 3: Multiply the numerator by the whole number.

There are $3$ groups of $2$ fifths:

3 \times 2=6

So:

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

Step 4: Understand the result.

Six fifths is one whole and one fifth:

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

Therefore:

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

On a number line, you could start at $0$ and make three equal jumps of $\frac{2}{5}$ : first to $\frac{2}{5}$ , then to $\frac{4}{5}$ , and finally to $\frac{6}{5}$ .

Learn by doing: Multiply a fraction by a whole number

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Fraction Multiplication - Simple by Whole Concept Intro - Picture to Answer - Don't Simplify

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