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Multiply a fraction by a whole number

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×ab=nabn \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.

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:

3×253 \times \frac{2}{5}

  1. The number 33 means three groups of 25\frac{2}{5}:

25+25+25\frac{2}{5}+\frac{2}{5}+\frac{2}{5}

  1. Since all the fractions have the same denominator, multiply the numerator by 33 and keep the denominator:

3×25=3×25=653 \times \frac{2}{5}=\frac{3\times 2}{5}=\frac{6}{5}

  1. Simplify the improper fraction:

65=115\frac{6}{5}=1\frac{1}{5}

So,

3×25=115\boxed{3\times\frac{2}{5}=1\frac{1}{5}}

The denominator stays 55 because you are still counting fifths. You are taking three groups of two fifths, which makes six fifths altogether.

Learn by doing: Multiply a fraction by a whole number

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    Fraction Multiplication - Simple by Whole

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