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4.8 Calculating Percentages 2

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

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: one amount as a percentage of another, percentage change and reverse percentages. 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

  • Write one amount as a percentage of another
  • Work out a percentage increase or decrease
  • Find the original amount after a percentage change (reverse percentages)
  • Choose between multipliers and the unitary method to solve problems

Key words

  • Original amount: The amount before any change. It is always 100%.
  • Percentage change: The change as a percentage of the original amount.
  • Reverse percentage: Working backwards from the new amount to find the original amount.
  • Unitary method: Find the value of 1% (one unit), then multiply to get the percentage you need.

One amount as a percentage of another

Write the first amount as a fraction of the second (same units!), then multiply by 100.

Worked example: percentages of a total

(a) Sam scored 18 out of 24. 18 ÷ 24 × 100 = 75%
(b) 45p as a percentage of £3. £3 = 300p. 45 ÷ 300 × 100 = 15%

Answer: (a) 75% (b) 15%

Percentage increase and decrease

Find the actual change first. Then divide by the original amount and multiply by 100.

Formula: Percentage change = (change ÷ original amount) × 100

Worked example: increase and decrease

Increase: £40 → £46. Change = £6. 6 ÷ 40 × 100 = 15% increase.
Decrease: 250 → 210. Change = 40. 40 ÷ 250 × 100 = 16% decrease.

Answer: 15% increase and 16% decrease

Reverse percentages

If you know the amount after a percentage change, work out what percentage it is of the original. Then divide by the multiplier, or find 1% and then 100%.

Worked example: after an increase

After a 20% increase a price is £66. Find the original price.
Multiplier: 66 ÷ 1.2 = £55.
Unitary: 120% = £66, so 1% = 66 ÷ 120 = 0.55, and 100% = £55.

Answer: £55

Worked example: after a decrease

In a 30% off sale a coat costs £42. What was the price before the sale?
The sale price is 70% of the original. 42 ÷ 0.7 = £60.

Answer: £60

Watch out: Do not find 20% of the new amount and take it off: 20% of £66 is £13.20, and £66 − £13.20 = £52.80 is wrong.

Solving problems

Decide what you know: the original amount, the new amount, or the percentage. Then choose the method.

  • original and %; You want new amount; Method original × multiplier
  • original and new; You want % change; Method change ÷ original × 100
  • new and %; You want original; Method new ÷ multiplier

Worked example: percentage profit

A shop buys mugs for £4 each and sells them for £6.50. Find the percentage profit.
Profit = £2.50. 2.50 ÷ 4 × 100 = 62.5%

Answer: 62.5% profit

Common mistakes

  • Dividing by the new amount instead of the original amount in a percentage change.
  • Reverse percentages: taking the percentage of the new amount instead of dividing by the multiplier.
  • Comparing amounts in different units, e.g. 45p as a percentage of £3 written as 45 ÷ 3.
  • Thinking a 20% rise followed by a 20% fall gets you back to the start.

Revision questions

Try these, then check your answers below each one.

Question 1. Write 18 as a percentage of 72.

Answer: 25 %

Working: 18 ÷ 72 × 100 = 25%.

Question 2. A price rises from £60 to £75. Work out the percentage increase.

Answer: 25 %

Working: Change = 15. 15 ÷ 60 × 100 = 25%.

Question 3. A value falls from 400 to 340. Work out the percentage decrease.

Answer: 15 %

Working: Change = 60. 60 ÷ 400 × 100 = 15%.

Related lessons

Continue in the full course

This lesson is section 4.8 (EGCMF0408) 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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