Multiplying whole numbers by fractions
I can multiply a whole number by a fraction and explain it as repeated addition or equal groups.
Learn
Each muffin needs 2/3 cup of flour. How much flour do 3 muffins need?
3 × 2/5 means 3 groups of 2/5: 2/5 + 2/5 + 2/5 = 6/5.
Multiply the whole number by the numerator and keep the denominator: 3 × 2/5 = (3 × 2)/5 = 6/5.
The answer can be more than one whole. 6/5 = 1 1/5.
Multiplying a whole number by a fraction less than 1 gives a smaller result than the whole number: 6 × 2/3 = 4, which is less than 6.
Worked examples
3 × 2/5
- Three groups of 2 fifths.
- 3 × 2 = 6 fifths.
- 6/5 = 1 1/5.
6 × 2/3
- 6 jumps of 2/3 on a number line.
- 6 × 2 = 12 thirds.
- 12/3 = 4.
Explore
Start at 2/3. Add 2 more thirds at a time to see 2 × 2/3, 3 × 2/3, and so on.
Guided practice
Use the hints as much as you like. You can try each question as many times as you need.
0 of 2 solved
3 × 2/5 = ? (any form)
4 × 3/4 = ?
Independent practice
Answers are checked exactly — equivalent fractions count unless a question asks for a particular form.
0 of 4 solved
5 × 1/6 = ?
6 × 2/3 = ?
Each muffin uses 2/3 cup of flour. How much do 3 muffins need?
Without calculating, is 8 × 3/4 more or less than 8?
Common mistakes
Multiplying both the numerator and the denominator by the whole number.
Why it happens: 3 × 2/5 ≠ 6/15 — that is just 2/5 rewritten.
What to do: Think “3 groups of 2 fifths” — only the count of fifths grows.
Thinking multiplication always makes bigger numbers.
Why it happens: Multiplying by a fraction less than 1 takes only part of each group.
What to do: Estimate first: is the fraction more or less than 1?
Lesson check
Three practice questions to check your understanding. Hints and retries are allowed, so this counts as practice — not mastery.
0 of 3 solved
7 × 1/3 = ? (any form)
10 × 3/5 = ?
4 × 5/8 = ? Write as a mixed number.
Show mastery on your own
Ready? Answer 4 new questions with no hints and one try each. This is the only way a lesson is marked as mastered.
Start mastery check