Ratio and PercentagesRatio and Percentages

Percentage/Decimal/FractionPercentage/Decimal/Fraction

• These are different ways of saying how much of something you have

• E.g. 100% = 1.0 = 1• 50%= 0.5 = ½• What is 25%?• 0.25 and ¼• What is 10%?• 0.1 and 1/10

Percentage/Decimal/FractionPercentage/Decimal/Fraction

• What is 1/3?• 33.3% and 0.33• What is 2/3?• 66.67% and 0.67• What is 150%?• 1 ½ and 1.5• What is 7%?• 0.07 and 7/100

Simplifying FractionsSimplifying Fractions

• Fractions should always be simplified• E.g. 2/4 is ½• What are these:• 10/100?• 1/10• 2/100?• 1/5• 4/6?• 2/3

Try theseTry these

• Change these percentages to fractions:• 70%• 5%• 15%• 2%• 12 ½ %• 6 ¼ %• 66 2/3 %

AnswersAnswers

• 7/10

• 5/100 which is 1/20

• 15/100 which is 3/20

• 2/100 which is 1/50

• 1/8

• 1/16

• 2/3

Converting Fractions to Converting Fractions to PercentagesPercentages

• To convert a fraction into a percentage there are two ways:

1. Type the fraction into your calculator and multiply by 100

2. Divide the top part of the fraction by the bottom part and multiply by 100 e.g.

• ½ is ½ x 100 = 50%• ¼ is • 25%

Try theseTry these

• Convert these fractions to percentages:

• 71/80

• 4/5

• 56/60

• 16/40

• 23/28

• 112/125

AnswersAnswers

• 88.75%

• 80%

• 93.3%

• 40%

• 82.1%

• 89..6%

SalesSales

• Often sales are 25% off or 50% off

• This means you can work out what the sale price is

• E.g. If a football costs £12 and there is 25% off

• You type in 12 x 25% on your calculator

• This is £3

• The football is £12-3 = £9

Work out these:Work out these:

• What are the prices of these if there is a 25% off sale;

• A £6 football pump• £7 tennis balls• £20 fishing rod• If there is 10% off these;• £108 tent• £12 airbed• £16 gas cooker

AnswersAnswers

• £4.50

• £5.25

• £15

• £97.20

• £10.80

• £14.40

Working out the % of somethingWorking out the % of something

• If you are asked to find the percentage of something e.g. 12% of 300g

• Type 300 x 12% into the calculator• 36g• There is another method • 300 ÷ 100 gives you 1%, then multiply your

answer by 12• 300 ÷ 100 = 3g• 3g x 12 = 36g

Try theseTry these

• Find 18% of 250cm

• Find 8% of 600cm

• Find 45% of 120g

• Find 34% of 350m

• Find 12.5% of £150

• Find 15% of £450

• Find 9.75% of £420

AnswersAnswers

• 45cm

• 48cm

• 54g

• 14m

• £18.75

• £67.50

• £39.90

RatioRatio

• Ratio is when you want to split something unevenly between several people

• E.g. You have 10 sweets and 2 friends and yourself to share them with

• You want the most and then your best friend gets the next most

• You could split them 5 to you: 3 to your best friend: 2 to the other friend

• The ratio is 5:3:2

Simplifying ratiosSimplifying ratios

• Ratios are really fractions and they need to be simplified

• 20:5• Both can be divided by 5 so it becomes• 4:1• 6:4:2?• All can be divided by 2• 3:2:1

Try theseTry these

• Simplify these ratios;

• 10:5:20

• 5:5

• 7:7:14

• 12:6:6

• 9:3:6:3

• 24:16:8:80

AnswersAnswers

• 2:1:4

• 1:1

• 1:1:2

• 2:1:1

• 3:1:2:1

• 3:2:1:10

Ratios with nRatios with n

• If you are asked to convert ratios into the form 1:n you must divide the first number down to 1 and divide the other side by this same number

• E.g.

• 7:14

• Both sides are divided by 7

• So the answer is 1:2

Try theseTry these

• Convert these to the form 1:n• 4:5• 2:3• 3:7.5• 7:2• 16:11• Convert these to the form n:1• 3:4• 2:3• 10:20

AnswersAnswers

• 1:1.25• 1:1.5• 1:2.5• 1:0.29• 1:0.69• 0.75:1• 0.67:1• 0.5:1

Using ratiosUsing ratios

• If you want to split £21 in the ratio 2:1:4• How much does everybody get?• Ratios are like fractions so what do all these

parts add up to?• 2+1+4= 7• This means that they get 2/7:1/7:4/7• 1/7 of £21 is £3• 2/7 of £21 is £6• And 4/7 of £21 is £12• This is £6:£3:£12

Work out theseWork out these

• £27 – 8:10

• £3 – 4:4:2

• £34 – 7:10

• £4.40 – 2:8:10

• 70p – 18:9:3

AnswersAnswers

• £12 : £15

• £1.20 : £1.20 : £0.60

• £14 : £20

• £0.44 : £1.76 : £2.20

• 42p : 21p : 7p