Primary 5 maths · Fractions · About 12 minutes
Multiply mixed numbers by whole numbers
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 mixed numbers by whole numbers
Models used: number sentences, stories, tables.
Before you start
Multiply the wholes and the extra parts
Each bottle holds one and a half litres. We have three bottles.
Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.
Each bottle holds one and a half litres. We have three bottles.
The denominator determines one part’s size. The numerator tells us how many of those parts to take.
2/2 = 2/2 · 2/2 = 2/2 · 1/2 = 1/2 · 1/2 = 1/2 · 2/2 = 2/2 · 1/2 = 1/2: the same length, so the same amount.
Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.
The three whole litres make 3 litres. The three extra halves make one and a half litres.
3 × 1 + 3 × 1/2
The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.
2/2 = 2/2 · 2/2 = 2/2 · 2/2 = 2/2 · 2/2 = 2/2 · 2/2 = 2/2 · 2/2 = 2/2: the same length, so the same amount.
Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.
Join those amounts: four and a half litres altogether.
1 1/2 × 3 = 4 1/2
The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.
2/2 = 2/2 · 2/2 = 2/2 · 2/2 = 2/2 · 2/2 = 2/2 · 2/2 = 2/2 · 2/2 = 2/2: the same length, so the same amount.
What did the picture help us see?
Join those amounts: four and a half litres altogether.
Worked example: A new example, together
Find 6 1/4 × 6.
| Equal groups | In each group | Parts needed |
|---|---|---|
| 4 | 1.5 | 25 |
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 4 1.5 25 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 4, then take 25 of those parts.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 4 1.5 25 Find 6 1/4 × 6.
37 1/2
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 4, then take 25 of those parts.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 4 1.5 25 Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.
6 ÷ 4 × 25.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 4 1.5 25 Share into denominator-many parts, then select numerator-many. Read each value with the heading above its column.
The amount is 37 1/2.
Share into denominator-many parts, then select numerator-many Equal groups In each group Parts needed 4 1.5 25 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 6 equals 25/4.
We found 37 1/2. 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 4 1.5 25
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 mixed numbers 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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