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4.2 Operations with Fractions

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

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: fractions of amounts, one quantity as a fraction of another, and fraction problems. 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

  • Find a fraction of an amount, including money, time and measures
  • Write one quantity as a fraction of another
  • Solve problems with several steps involving fractions
  • Find the whole amount when you know a fraction of it

Key words

  • Unit fraction: A fraction with numerator 1, e.g. 1/5.
  • Fraction of an amount: Divide by the denominator, then multiply by the numerator.
  • Bar model: A diagram of equal boxes that shows how a whole is split into parts.
  • Remainder: What is left after part of an amount has been used or taken away.

Finding a fraction of an amount

To find 1/5 of an amount, divide by 5. To find 3/5, find 1/5 and then multiply by 3. A bar model shows why this works.

Worked example: fractions of amounts

(a) 3/5 of 40: 40 ÷ 5 = 8, 8 × 3 = 24
(b) 5/8 of £24: £24 ÷ 8 = £3, £3 × 5 = £15
(c) 7/12 of 300 g: 300 ÷ 12 = 25, 25 × 7 = 175 g

Answer: (a) 24 (b) £15 (c) 175 g

Fractions of time and measures

Change to a smaller unit first if that makes the division easier: hours to minutes, kilograms to grams, metres to centimetres.

Worked example: time and mass

(a) 2/3 of 1 hour 30 minutes = 2/3 of 90 minutes: 90 ÷ 3 = 30, 30 × 2 = 60 minutes
(b) 3/4 of 2 kg = 3/4 of 2000 g: 2000 ÷ 4 = 500, 500 × 3 = 1500 g = 1.5 kg

Answer: (a) 60 minutes (1 hour) (b) 1.5 kg

One quantity as a fraction of another

Write the first quantity over the second, making sure both are in the same units. Then simplify.

Worked example: writing a fraction

(a) 45 minutes as a fraction of 2 hours. 2 hours = 120 minutes. 45/120 = 3/8
(b) 35p as a fraction of £2. £2 = 200p. 35/200 = 7/40
(c) In a class of 30, 18 walk to school. 18/30 = 3/5 walk.

Answer: (a) 3/8 (b) 7/40 (c) 3/5

Key fact: Same units first! 45 minutes out of 2 hours is not 45/2.

Problems with more than one step

Read carefully: is the fraction of the whole amount, or of what is left? Work one step at a time.

Worked example: fraction of the remainder

Kai has £120. He spends 1/4 of it on a game, then 1/3 of what is left on a ticket. How much does he have left?
Game: 120 ÷ 4 = £30. Left: 120 − 30 = £90.
Ticket: 90 ÷ 3 = £30. Left: 90 − 30 = £60.

Answer: £60

Finding the whole

If you know a fraction of an amount, find what one part is worth, then multiply by the denominator.

Worked example: working backwards

2/5 of a number is 18. Find the number.
2 parts = 18, so 1 part = 18 ÷ 2 = 9. 5 parts = 5 × 9 = 45.

Answer: 45

Common mistakes

  • Dividing by the numerator instead of the denominator.
  • Writing a fraction of two quantities in different units, e.g. 45/2 for 45 minutes out of 2 hours.
  • Taking the second fraction of the whole amount when the question says "of what is left".
  • Not simplifying the final fraction.

Revision questions

Try these, then check your answers below each one.

Question 1. Work out 3/8 of 64.

Answer: 24

Working: 64 ÷ 8 = 8, 8 × 3 = 24.

Question 2. Work out 2/5 of £45.

Answer: 18 pounds

Working: 45 ÷ 5 = 9, 9 × 2 = 18, so £18.

Question 3. Work out 3/4 of 2 hours. Give your answer in minutes.

Answer: 90 minutes

Working: 2 hours = 120 minutes. 120 ÷ 4 × 3 = 90 minutes.

Related lessons

Continue in the full course

This lesson is section 4.2 (EGCMF0402) 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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