Primary 5 maths · Fractions · About 12 minutes
Multiply proper and improper fractions by whole numbers
Identify the amount that acts as the whole, then one part, then the selected parts.
Start the interactive lesson →Practise: Fraction of a collection
What you will learn
- Multiply proper and improper fractions by whole numbers
Models used: number sentences, stories, tables.
Before you start
Find a fraction of a group
Here are 12 counters. We want two thirds of them.
Each dot stands for one object. A full row holds five; two full rows make ten.
Here are 12 counters. We want two thirds of them.
There are 3 groups, with 4 objects in each group. Count a group before counting them all.
Thirds means three equal groups. Each group has 4 counters.
4 + 4 + 4 = 3 × 4 = 12
There are 2 groups, with 4 objects in each group. Count a group before counting them all.
Keep two of those groups. Two groups of four make eight.
2/3 of 12 = 8
4 + 4 = 2 × 4 = 8
What did the picture help us see?
Keep two of those groups. Two groups of four make eight.
Worked example: A new example, together
Find 13/8 × 5.
| Equal groups | In each group | Parts needed |
|---|---|---|
| 8 | 0.625 | 13 |
Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.
Identify the amount that acts as the whole, then one part, then the selected parts.
A fraction of a amount scales that quantity by the fraction.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 8 0.625 13 Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.
A fraction of an amount means divide by 8, then take 13 of those parts.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 8 0.625 13 Find 13/8 × 5.
65/8
Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.
5 ÷ 8 × 13.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 8 0.625 13 Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.
The amount is 65/8.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 8 0.625 13 Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.
Check the result against the question we started with.
The selected amount divided by 5 equals 13/8.
We found 65/8. A fraction of a amount scales that quantity by the fraction.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 8 0.625 13
Common mistakes to discuss
- Multiplying the denominator as well. Only the number of parts grows. 3 × 2/5 = 6/5, because the fifths stay fifths.
Check your understanding
- Multiply proper and improper fractions by whole numbers
- explain fraction multiplication as selecting a share of an amount
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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