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18.1 Multiplying and Dividing Fractions

GCSE Maths Foundation · Edexcel · Chapter 18: Fractions, Indices and Standard Form

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: multiplying fractions, fractions of amounts, dividing by a fraction and working 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 fractions and simplify, cancelling common factors first
  • Multiply a fraction by a whole number and find a fraction of an amount
  • Divide by a fraction using its reciprocal
  • Multiply and divide mixed numbers and solve problems in context

Key words

  • Numerator: The top number of a fraction. In 3/8 it is 3.
  • Denominator: The bottom number of a fraction. In 3/8 it is 8.
  • Reciprocal: The fraction turned upside down. The reciprocal of 2/5 is 5/2, and of 7 is 1/7. A number × its reciprocal = 1.
  • Improper fraction: A fraction where the numerator is bigger than the denominator, such as 11/4.
  • Mixed number: A whole number and a fraction, such as 2 3/4 (= 11/4).
  • Simplest form: A fraction that cannot be cancelled any further, such as 2/3 instead of 8/12.

Multiplying fractions

Multiply the numerators together and multiply the denominators together. Then simplify.

Worked example: multiply then simplify

2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2

Answer: 1/2

Worked example: cancel first

5/8 × 4/15. Cancel 5 with 15 (÷5) and 4 with 8 (÷4) before multiplying:
= 1/2 × 1/3 = 1/6

Answer: 1/6

Tip: You may cancel a numerator with any denominator when multiplying. It keeps the numbers small.

Whole numbers and fractions of amounts

Write a whole number as a fraction over 1. “Of” means multiply.

Worked example: fraction of an amount

3/5 of 40 kg: 40 ÷ 5 = 8, then 8 × 3 = 24

Answer: 24 kg

Worked example: whole number × fraction

4 × 2/7 = 4/1 × 2/7 = 8/7 = 1 1/7

Answer: 1 1/7

Dividing by a fraction

Dividing by a fraction is the same as multiplying by its reciprocal. Remember: keep the first fraction, change ÷ to ×, flip the second fraction.

Worked example: fraction ÷ fraction

3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8

Answer: 1 7/8

Worked example: whole number ÷ fraction

How many 3/4-hour lessons fit into 6 hours?
6 ÷ 3/4 = 6/1 × 4/3 = 24/3 = 8

Answer: 8 lessons

Worked example: fraction ÷ whole number

2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6

Answer: 1/6

Check: Dividing by a fraction less than 1 gives a bigger answer: there are 8 three-quarters in 6.

Mixed numbers

Always change mixed numbers to improper fractions first. Multiply the whole number by the denominator and add the numerator: 2 1/2 = (2 × 2 + 1)/2 = 5/2.

Worked example: multiplying

2 1/2 × 1 3/5 = 5/2 × 8/5 = 40/10 = 4

Answer: 4

Worked example: dividing

3 1/3 ÷ 1 1/4 = 10/3 ÷ 5/4 = 10/3 × 4/5 = 40/15 = 8/3 = 2 2/3

Answer: 2 2/3

Problems in context

Worked example: area of a rug

A rug is 2 3/4 m long and 1 1/3 m wide. Find its area.
11/4 × 4/3 = 44/12 = 11/3 = 3 2/3

Answer: 3 2/3 m²

Worked example: bags of rice

How many 3/8 kg bags can be filled from 4 1/2 kg of rice?
9/2 ÷ 3/8 = 9/2 × 8/3 = 72/6 = 12

Answer: 12 bags

Common mistakes

  • Flipping the first fraction instead of the second when dividing.
  • Multiplying mixed numbers in parts: 2 1/2 × 1 1/3 is not 2 × 1 plus 1/2 × 1/3.
  • Finding a common denominator when multiplying. That is only needed for adding and subtracting.
  • Not giving the answer in its simplest form, or leaving an improper fraction when a mixed number is asked for.
  • Forgetting that a whole number n is n/1 when you flip it: the reciprocal of 4 is 1/4.

Revision questions

Try these, then check your answers below each one.

Question 1. Work out 3/4 × 2/9. Give your answer in its simplest form.

Answer: 1/6

Working: (3 × 2)/(4 × 9) = 6/36 = 1/6.

Question 2. Work out 2/7 of 63.

Answer: 18

Working: 63 ÷ 7 = 9, 9 × 2 = 18.

Question 3. Work out 5/6 ÷ 2/3. Give your answer as a mixed number.

Answer: 1 1/4

Working: 5/6 × 3/2 = 15/12 = 5/4 = 11/4.

Related lessons

Continue in the full course

This lesson is section 18.1 (EGCMF1801) 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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