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Percentages.pptx
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Percentages
Fractions, ratio and percentages
Lesson 4 of 5
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Last Lesson and Before
Fractions, ratio and percentages
Lesson 4 of 5
Answer each one, then check.
1
What is 10% of 80?
2
Write 0.35 as a percentage.
3
Write ¾ as a percentage.
4
Work out 1.2 × 50.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Last Lesson and Before - Answers
Fractions, ratio and percentages
Lesson 4 of 5
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
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Learning Objectives
Fractions, ratio and percentages
Lesson 4 of 5
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.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Percentages of Amounts
Fractions, ratio and percentages
Lesson 4 of 5
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%.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Multipliers
Fractions, ratio and percentages
Lesson 4 of 5
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.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Percentage Increase with a Multiplier
Fractions, ratio and percentages
Lesson 4 of 5
Increase £240 by 15%.
1
The multiplier
100% + 15% = 115% = 1.15
2
Multiply
240 × 1.15 = 276
ANSWER
£276
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Percentage Change
Fractions, ratio and percentages
Lesson 4 of 5
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
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Reverse Percentages
Fractions, ratio and percentages
Lesson 4 of 5
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.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
A Reverse Percentage
Fractions, ratio and percentages
Lesson 4 of 5
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
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Simple and Compound Interest
Fractions, ratio and percentages
Lesson 4 of 5
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.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Compound Interest
Fractions, ratio and percentages
Lesson 4 of 5
£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
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Simple or Compound?
Fractions, ratio and percentages
Lesson 4 of 5
SIMPLE INTEREST ON £2000 AT 3%
• Year 1: £60
• Year 2: £60
• Year 3: £60
• Year 4: £60
• Total after 4 years: £2240
COMPOUND INTEREST ON £2000 AT 3%
• Year 1: £60
• Year 2: £61.80
• Year 3: £63.65
• Year 4: £65.56
• Total after 4 years: £2251.02
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Key Terms
Fractions, ratio and percentages
Lesson 4 of 5
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.
Percentage change
change/original × 100.
Reverse percentage
Finding the original amount from the amount after a change.
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.
Depreciation
A loss in value over time.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Fractions, ratio and percentages
Lesson 4 of 5
YOUR TASK
The Best Deal
12 minutes
(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.
WHAT 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.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can I...?
Fractions, ratio and percentages
Lesson 4 of 5
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.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Summary & Exam Focus
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.
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.
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