Primary 5 maths · Fractions · About 12 minutes
Multiply fractions by fractions
Identify the amount that acts as the whole, then one part, then the selected parts.
Start the interactive lesson →Practise: Fraction multiplication lab
What you will learn
- Multiply fractions by fractions
Models used: number sentences, stories, tables.
Before you start
A part of a part
The orange part is three quarters of a sheet.
The whole rectangle has 3 equal rows and 4 equal columns. We are finding 2/3 of 3/4.
The orange part is three quarters of a sheet.
Start with the fraction after “of”. This shaded part is the amount we are taking a share of.
The whole rectangle has 3 equal rows and 4 equal columns. We are finding 2/3 of 3/4.
We only want two thirds of that orange part. Split it into three equal rows and keep two.
Taking a fraction of an amount means sharing that amount into equal parts, then choosing some of them. Only the overlap belongs to both selections.
The whole rectangle has 3 equal rows and 4 equal columns. We are finding 2/3 of 3/4.
The overlap covers 6 of 12 equal pieces. That is half of the original sheet.
2/3 × 3/4 = 6/12 = 1/2
The overlap counts the parts we kept. Count it against every equal part in the original whole, not just the originally shaded part.
What did the picture help us see?
The overlap covers 6 of 12 equal pieces. That is half of the original sheet.
Worked example: A new example, together
Find 7/5 × 6/4.
| First fraction | Multiply by |
|---|---|
| 7/5 | 6/4 |
An improper fraction contains at least one whole. 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.
An improper fraction contains at least one whole First fraction Multiply by 7/5 6/4 An improper fraction contains at least one whole. Read each value with the heading above its column.
A fraction of an amount means divide by 5, then take 7 of those parts.
An improper fraction contains at least one whole First fraction Multiply by 7/5 6/4 Find 7/5 × 6/4.
21/10
An improper fraction contains at least one whole. Read each value with the heading above its column.
Multiply numerators and denominators: (7 × 6)/(5 × 4).
An improper fraction contains at least one whole First fraction Multiply by 7/5 6/4 An improper fraction contains at least one whole. Read each value with the heading above its column.
The amount is 21/10.
An improper fraction contains at least one whole First fraction Multiply by 7/5 6/4 An improper fraction contains at least one whole. Read each value with the heading above its column.
Check the result against the question we started with.
The selected amount divided by 1.5 equals 7/5.
We found 21/10. A fraction of a amount scales that quantity by the fraction.
An improper fraction contains at least one whole First fraction Multiply by 7/5 6/4
Common mistakes to discuss
- Expecting a larger answer. Taking a fraction of a fraction gives less than either one. 1/2 × 3/4 = 3/8, which is smaller than 3/4.
Check your understanding
- Multiply fractions by fractions
- 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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