Multiplying fractions

Primary 6 Fractions study guide: the whole chapter, step by step

About this subtopic

Cancel any common factor, so that the answer is in its simplest form. A fraction of a fraction is a multiplication, every time. In the lesson. A fraction of a fraction is a multiplication, every time.

Lesson video, with the working

Multiplying fractions

3 min 00 s

The film teaches 1 question. The question shows first; its working is written as the film explains it.

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Today's question

Work out 1/2 of 1/3. Work out 3/4 × 2/5. Give the answer in its simplest form.

  1. =3/10

Ans: {3|10}

How to solve it
  1. The word of means multiply, so one half of one third is one half times one third.
  2. Multiply the tops and multiply the bottoms: 1 times 1 on top and 2 times 3 on the bottom gives one sixth.
  3. Look across for a common factor. In two thirds times one quarter, the top 2 and the bottom 4 share a factor of 2.
  4. Divide both by it: write 1 above the 2 and 2 below the 4. Then multiply what is left.
  5. Three quarters times two fifths: cancel the 4 and the 2, then 3 times 1 over 2 times 5 is three tenths.

Cancel any common factor, so that the answer is in its simplest form. A fraction of a fraction is a multiplication, every time.

Practice questions with worked solutions

Questions 1 and 5 are free to try. The other 3 open in the free trial, each with its full working.

Basic

1Free23

Intermediate

4

More questions

5Free

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3 more questions, each with its full working.Answers checked, progress kept, wrong ones come back in revision. No card needed.

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Question 1 of 5 · Basic · free to tryFind 6 × 7/4 without using a calculator. Give your answer as a mixed number…Find 6 × 7/4 without using a…

Find 6 × 7/4 without using a calculator. Give your answer as a mixed number in simplest form.

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Video solution · 1 min 8 s

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Working

  1. product = 6 × 7/4 = 3 × 7/2
  2. product = 3 × 7/2 = 21/2
  3. 21/2 = 10 1/2

Answer: 10 1/2

Question 5 of 5 · Unbanded · free to tryA chocolate bar has 24 equal squares. How many squares make up 2/3 of 1/4 of…A chocolate bar has 24 equal…

A chocolate bar has 24 equal squares. How many squares make up 2/3 of 1/4 of the bar?

squares

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Video solution · 1 min 26 s

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Working

  1. 2/3 × 1/4 = 1/6 (simplest form)
  2. 6 units = 24
  3. 1 unit = 24 ÷ 6 = 4

Answer: 4 squares

For parents

How do you solve multiplying fractions questions in P6?

Multiplying a fraction by a fraction was taught a year earlier and is used throughout Primary 6, in fraction of a remainder questions and in percentages.

What your child learns here

Multiplying a fraction by a fraction was taught a year earlier and is used throughout Primary 6, in fraction of a remainder questions and in percentages. This page revises it as 'a fraction of a fraction', so the rule has a picture behind it.

  • Understand 'of' between two fractions as multiplication.
  • Multiply a proper fraction by a proper or improper fraction, and two improper fractions.
  • Cancel a common factor between a top number and a bottom number before multiplying.
  • Give the answer in its simplest form.
Does the answer make sense?

Multiplying by a fraction less than 1 must give less than the number you started with, and multiplying by an improper fraction must give more. So your child's answer to 9 times four sevenths must land below 9, while two improper fractions multiplied together give more than either of them.

How to practise these questions

Basic questions train multiplying a fraction by a fraction, and reading a fraction of a fraction as the product of the two. Intermediate questions raise the difficulty with two improper fractions, where cancelling first keeps the numbers manageable. If multiplying fractions stalls, read the written step-by-step solution together.

Questions parents ask

Is multiplying fractions in the P6 syllabus? Multiplying a proper fraction by a proper or improper fraction, and multiplying two improper fractions, are taught the year before Primary 6. The Primary 6 fraction outcomes, dividing with fractions, build directly on them.

Why does 'of' mean multiply in fractions? Because finding one half of something is the same as multiplying it by one half. One half of one third is one sixth, and one half times one third is also one sixth.

Do you need a common denominator to multiply fractions? No. A common denominator is needed for adding and subtracting. For multiplying, multiply the top numbers together and the bottom numbers together, cancelling first if you can.