EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Percentages
Fractions, ratio and percentages · Lesson 4 of 5
Last Lesson and Before
Answer each one, then check.
1. What is 10% of 80?
8
2. Write 0.35 as a percentage.
35%
3. Write ¾ as a percentage.
75%
4. Work out 1.2 × 50.
60
Learning Objectives
1. Find a percentage of an amount, with and without a calculator.
2. Increase and decrease by a percentage using a multiplier.
3. Write one quantity as a percentage of another and find a percentage change.
4. Find the original amount after a percentage change (reverse percentages).
5. Work out simple and compound interest and depreciation.
Percentages of Amounts
Per cent means "out of 100".
▸ Without a calculator. Build from 10%, 5% and 1%: 35% of £180 = 30% + 5% = £54 + £9 = £63.
▸ With a calculator. Use the decimal: 35% of 180 = 0.35 × 180 = 63.
▸ As a fraction of the whole. 15 out of 60 is 15/60 × 100 = 25%.
Multipliers
A multiplier does a percentage change in one step.
▸ Increase by 15%. 100% + 15% = 115%, so multiply by 1.15.
▸ Decrease by 15%. 100% − 15% = 85%, so multiply by 0.85.
▸ More examples. Increase by 3%: × 1.03. Decrease by 40%: × 0.6. Increase by 100%: × 2.
▸ Why use them. They work for every amount and every percentage, and they make repeated changes easy.
Percentage Increase with a Multiplier
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Increase £240 by 15%. |
1. The multiplier
100% + 15% = 115% = 1.15
2. Multiply
240 × 1.15 = 276
Answer: £276
Percentage Change
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The price of a jacket rises from £60 to £75. Find the percentage increase. |
1. Find the change
75 − 60 = 15
2. Divide by the ORIGINAL amount
15/60 = 0.25
3. Convert to a percentage
0.25 × 100 = 25%
Answer: 25% increase
Reverse Percentages
When you know the amount AFTER a percentage change, divide by the multiplier to get back to the original.
▸ The trap. After a 20% increase to £90, the original is NOT £90 minus 20% of £90.
▸ The method. £90 is 120% of the original, so the original is 90 ÷ 1.2 = £75.
▸ Check. 75 × 1.2 = 90.
A Reverse Percentage
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In a sale, prices are reduced by 30%. A coat costs £56 in the sale. What was its original price? |
1. The sale price is 70% of the original
multiplier 0.7
2. Divide by the multiplier
56 ÷ 0.7 = 80
3. Check
80 × 0.7 = 56
Answer: £80
Simple and Compound Interest
Interest is money added to savings (or a loan) each year.
▸ Simple interest. The same amount each year, worked out on the original sum: 3% of £2000 is £60 a year.
▸ Compound interest. Interest is added to the total, so next year's interest is on a bigger amount.
▸ The formula. Amount = original × multiplier^(years).
▸ Depreciation. The same idea for losing value: a car losing 12% a year is × 0.88 each year.
Compound Interest
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£2000 is invested at 3% compound interest per year. How much is it worth after 4 years? |
1. The multiplier for one year
1.03
2. Four years: multiply by 1.03 four times
2000 × 1.03⁴
3. Work it out
2251.017…
Answer: £2251.02
Simple or Compound?
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SIMPLE INTEREST ON £2000 AT 3% |
COMPOUND INTEREST ON £2000 AT 3% |
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▸ Year 1: £60 ▸ Year 2: £60 ▸ Year 3: £60 ▸ Year 4: £60 ▸ Total after 4 years: £2240 |
▸ Year 1: £60 ▸ Year 2: £61.80 ▸ Year 3: £63.65 ▸ Year 4: £65.56 ▸ Total after 4 years: £2251.02 |
Key Terms
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Percentage A number out of 100. |
Multiplier The number you multiply by to make a percentage change, e.g. 1.15 for a 15% increase. |
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Percentage change change/original × 100. |
Reverse percentage Finding the original amount from the amount after a change. |
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Simple interest Interest worked out on the original amount only. |
Compound interest Interest added to the total, so later interest is on a bigger amount. |
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Depreciation A loss in value over time. |
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Your Task: The Best Deal
12 minutes
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(a) A shop increases a £50 price by 20%, then reduces the new price by 20%. What is the final price? (b) Bank A pays 4% simple interest. Bank B pays 3.8% compound interest. Which gives more on £1000 after 5 years? (c) A phone costs £252 after a 16% discount. What did it cost before? 1. Write each multiplier. 2. Multiply, or divide for a reverse percentage. 3. Check your answer makes sense. |
A good answer shows: (a) 50 × 1.2 × 0.8 = £48 - not £50. (b) A: 1000 + 5 × 40 = £1200. B: 1000 × 1.038⁵ = £1205.03. Bank B. (c) 252 ÷ 0.84 = £300.
Can I...?
☐ Find a percentage of an amount without a calculator.
☐ Write a percentage as a multiplier.
☐ Increase or decrease by a percentage.
☐ Write one amount as a percentage of another.
☐ Work out a percentage change.
☐ Find the original amount (reverse percentage).
☐ Work out compound interest.
☐ Work out depreciation.
Summary
✓ Increase by p%: multiply by 1 + p/100. Decrease: multiply by 1 − p/100.
✓ Percentage change = change ÷ original × 100.
✓ Reverse percentage: divide by the multiplier.
✓ Compound interest: original × multiplier to the power of the number of years.
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EXAM FOCUS After a 15% decrease, the price of a TV is £391. What was the price before the decrease? (3 marks) In a reverse percentage question, the amount you are given is NOT 100%. Divide by the multiplier - never take the percentage off the new amount. |