Percentages.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Percentages

Fractions, ratio and percentages

Lesson 4 of 5

openrevise.com

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.

openrevise.com

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

openrevise.com

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.

openrevise.com

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%.

openrevise.com

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.

openrevise.com

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

openrevise.com

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

openrevise.com

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.

openrevise.com

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

openrevise.com

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.

openrevise.com

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

openrevise.com

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

openrevise.com

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.

openrevise.com

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.

openrevise.com

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.

openrevise.com

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.

openrevise.com