Primary 5 Foundation maths · Fractions · About 12 minutes
Multiply a proper or improper fraction by a whole number
Identify the amount that acts as the whole, then one part, then the selected parts.
Start the interactive lesson →Open practice activity
What you will learn
- Multiply a proper or improper fraction by a whole number
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.
The denominator determines one part’s size. The numerator tells us how many of those parts to take.
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 14/12 × 2.
| Equal groups | In each group | Parts needed |
|---|---|---|
| 12 | 0.166667 | 14 |
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 12 0.166667 14 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 12, then take 14 of those parts.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 12 0.166667 14 Find 14/12 × 2.
7/3
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 12, then take 14 of those parts.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 12 0.166667 14 Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.
2 ÷ 12 × 14.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 12 0.166667 14 Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.
The amount is 7/3.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 12 0.166667 14 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 2 equals 14/12.
We found 7/3. 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 12 0.166667 14
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 a proper or improper fraction by a whole number
- 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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