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 →Related practice: Fraction bakery
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.
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.
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.
Try this lesson →Related Primary 5 Foundation lessons
- Represent fractions of a whole or setRepresent fractions of a whole or set · About 12 minutes
- Generate equivalent fractions and simplifyGenerate equivalent fractions and simplify · About 12 minutes
- Compare fractions with denominators up to 12Compare fractions with denominators up to 12 · About 12 minutes
- Convert between mixed numbers and improper fractionsConvert between mixed numbers and improper fractions · About 12 minutes
- Add and subtract fractions with denominators up to 12 without a calculatorAdd and subtract fractions with denominators up to 12 without a calculator · About 12 minutes
- Add and subtract mixed numbersAdd and subtract mixed numbers · About 12 minutes