6. Whole numbers × fractions — Learner Route

Fractions · Step 6

Whole numbers × fractions

Multiplying a fraction by a whole number means taking several equal lots of that fraction. The pieces do not change size — we simply count more of them.

Start with what multiplication means

Two lots of two fifths

Read 2 × 25 as two lots of two fifths.

25
+
25
25 + 25 = 45
The denominator stays 5 because the pieces are still fifths. We have simply counted 4 fifth-sized pieces.
See the pattern

Multiply the numerator, keep the denominator

The whole number tells us how many lots we have. Each lot contributes the same number of fraction pieces.

3 × 27
3 × 2 → 6 pieces
The denominator 7 tells us the size of each piece, so it stays 7.
3 × 27 = 67
When the answer is bigger than one

The same idea still works

Sometimes repeated lots give us enough fraction pieces to make one or more complete wholes.

4 × 23
4 lots of 2 thirds
4 × 2 = 8 thirds
83 = 2 23
The multiplication gives 83. If it helps us understand the amount, we can rewrite it as the mixed number 2 23.
Interactive lab

How many pieces altogether?

Count the lots, then count the fraction pieces in each lot.

Choose an answer.
Method Trainer

Whole numbers × fractions

Try five fresh questions. Choose guided steps or type your final answer. Results feed into your Practice Lab log on this browser/device.

How would you like to answer?
Question 1 of 5 · 0 answered
1. Count all the fraction pieces: multiply the number of lots by the numerator
×=
2. Keep the denominator
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Need help with the whole-number multiplication? Open Times Tables: Develop strategies.

You have learned

A whole number multiplying a fraction means repeated equal lots of that fraction.

Multiply the whole number by the numerator, keep the denominator, and then interpret the result — including as a mixed number if it is bigger than one.

1 · Picture it2 · Equivalent3 · Add4 · Subtract5 · Mixed numbers6 · Whole × fraction7 · Fraction × fraction8 · Add any two9 · Divide10 · Simplify