Fraction times a whole number

The idea

To multiply a whole number (the multiplicand) by a fraction (the multiplier), divide the multiplicand by the denominator of the multiplier, then multiply the result by the numerator of the multiplier.

A fraction of an hour

Aaron walks 3 km in one hour. We want to know how far he walks in just 1/5 of an hour.

How far does he walk in 1/5 hour?

• 3/5 km
• 5/3 km
• 15 km

Cut the bar, then take parts

The bar is the distance in one whole hour. The denominator of the multiplier tells how many equal parts to cut. The numerator tells how many parts to take.

Two steps: divide, then multiply

In 1/5 hour Aaron walks the length we get by dividing 3 km into 5 equal parts: that is 3 ÷ 5 = 3/5 km. In 2/5 hour he walks twice as much, because 2/5 is twice 1/5.

To multiply a whole number by a fraction, divide the whole number by the denominator of the fraction, then multiply the result by the numerator.

• Multiply | Divide by d | Multiply by n
• 1/5 × 3 | 3 ÷ 5 = 3/5 | 1 × 3/5 = 3/5
• 2/5 × 3 | 3 ÷ 5 = 3/5 | 2 × 3/5 = 6/5
• 5/4 × 8 | 8 ÷ 4 = 2 | 5 × 2 = 10

Notes

To multiply a whole number by a fraction, divide the whole number by the denominator of the fraction, then multiply the result by the numerator.

Check yourself

A ribbon is 20 metres long. How long is 3/4 of it? Type a whole number.

Answer: 15

20 ÷ 4 = 5, and 3 × 5 = 15 metres.

Which steps find 2/7 × 5?

Aaron walks 3 km in one hour. How far does he walk in 3/4 hour? Type a fraction or a mixed number, like 2 1/10.

Answer: 2 1/4

3 ÷ 4 = 3/4. Then 3 × 3/4 = 9/4 = 2 1/4 km.

Maya works out 2/5 × 3 and writes 6/15. What went wrong?

• Divide 5 by 7, then multiply by 2 — correct. Yes! The denominator 7 divides, the numerator 2 multiplies.
• Divide 5 by 2, then multiply by 7. The steps are the wrong way round. The denominator divides and the numerator multiplies.
• Multiply 5 by 7, then divide by 2. That swaps the two jobs. The denominator 7 is for cutting into parts.
• Nothing. 6/15 is right.. Check with the bar: 2 parts of 3/5 km is more than 1 km. But 6/15 is less than half a km.
• She multiplied the denominator 5 by 3. The 3 must be divided by 5: 3 ÷ 5 = 3/5, and 2 × 3/5 = 6/5. — correct. Yes! Only the numerator multiplies the result; the denominator divides the whole number.
• She should have added: 2 + 3 = 5.. This is a multiplication story. The steps are divide, then multiply.