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Multiplying fractions by whole numbers
Multiplying a fraction by a whole number is repeated addition of the fraction. Three lots of 2/5 is 2/5 added three times. In the US, children learn this in 4th grade, then multiply a fraction by a fraction in 5th grade.
The quick rule: multiply the top number by the whole number and keep the bottom number. Then simplify or change to a mixed number if you like.
Worked examples
- As repeated addition. 2/5 + 2/5 + 2/5 = 6/5, so 3 × 2/5 = 6/5 = 1 1/5.
- As a fraction of a number. Two thirds of 12: one third of 12 is 4, so two thirds is 8. 2/3 × 12 = 8.
- Fraction times fraction (5th grade). Multiply the tops and multiply the bottoms: 2/3 × 4/5 = 8/15.
- Does the answer make sense? Multiplying by a fraction less than 1 gives a smaller answer: 8 is less than 12.
6 practice questions
- 1/3 × 4 = ?
- 3/4 × 3 = ?
- 2/5 × 5 = ?
- 2/3 × 9 = ?
- 3/8 × 4 = ?
- 1/2 × 3/4 = ?
Show answers
- 1/3 × 4 = 1 1/3
- 3/4 × 3 = 2 1/4
- 2/5 × 5 = 2
- 2/3 × 9 = 6
- 3/8 × 4 = 1 1/2
- 1/2 × 3/4 = 3/8
Tips for parents
- Draw it: three bars, each with 2/5 shaded, shows 3 × 2/5 = 6/5.
- Only the top number is multiplied by a whole number. The bottom stays the same.
- Simplify before multiplying when you can. It keeps the numbers small.
Questions parents ask
Do you multiply the denominator when multiplying a fraction by a whole number?
No. Multiply only the numerator (top number) by the whole number and keep the denominator the same. Then simplify if you can.