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4.3 Multiplying Fractions

GCSE Maths Foundation · Edexcel · Chapter 4: Fractions and percentages

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: multiplying fractions by whole numbers, by other fractions, and with mixed numbers. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Multiply a fraction by a whole number
  • Multiply two fractions and simplify the answer
  • Cancel common factors before multiplying
  • Multiply mixed numbers and solve problems such as areas

Key words

  • Product: The answer when you multiply.
  • Cancel: Divide a numerator and a denominator by a common factor before multiplying.
  • Improper fraction: A fraction bigger than 1, e.g. 7/2. Change mixed numbers to these before multiplying.
  • "of": In fractions, "of" means multiply: 2/3 of 3/4 = 2/3 × 3/4.

A fraction times a whole number

Multiply the numerator by the whole number and keep the denominator. Think of it as repeated adding: 4 × 2/3 = 2/3 + 2/3 + 2/3 + 2/3.

Worked example: whole number × fraction

4 × 2/3 = 8/3 = 2 2/3
6 × 5/12 = 30/12 = 5/2 = 2 1/2

Answer: 2 2/3 and 2 1/2

Multiplying two fractions

Multiply the numerators together and multiply the denominators together. Then simplify. You do not need a common denominator.

Worked example: fraction × fraction

2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2
3/5 × 2/7 = 6/35 (already in its simplest form)

Answer: 1/2 and 6/35

Key fact: When you multiply by a fraction less than 1, the answer is smaller than the number you started with.

Cancelling first

Look for a numerator and a denominator (in either fraction) with a common factor. Divide both by it before you multiply. The numbers stay small and the answer is already simplified.

Worked example: cancelling

4/9 × 3/8: 4 and 8 share 4 → 1 and 2; 3 and 9 share 3 → 1 and 3.
So 4/9 × 3/8 = 1/3 × 1/2 = 1/6

Answer: 1/6

Mixed numbers and problems

Change mixed numbers to improper fractions first. Multiply, then change the answer back to a mixed number.

Worked example: mixed numbers

1 1/2 × 2 2/3 = 3/2 × 8/3 = 24/6 = 4

Answer: 4

Worked example: area of a rectangle

A rug is 2 1/4 m long and 1 1/3 m wide. Find its area.
9/4 × 4/3 = 36/12 = 3

Answer: 3 m²

Common mistakes

  • Multiplying both the numerator and the denominator by the whole number (4 × 2/3 is not 8/12).
  • Finding a common denominator first: you do not need one when multiplying.
  • Multiplying mixed numbers part by part: 1 1/2 × 2 2/3 is not 2 2/6.
  • Forgetting to simplify, or to change an improper answer back to a mixed number.

Revision questions

Try these, then check your answers below each one.

Question 1. Work out 3 × 2/7. (Type your answer like 2/5.)

Answer: 6/7

Working: 3 × 2/7 = 6/7.

Question 2. Work out 2/5 × 3/4 in its simplest form. (Type your answer like 2/5.)

Answer: 3/10

Working: 6/20 = 3/10.

Question 3. Work out 5/6 × 3/10 in its simplest form. (Type your answer like 2/5.)

Answer: 1/4

Working: 15/60 = 1/4.

Related lessons

Continue in the full course

This lesson is section 4.3 (EGCMF0403) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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