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Percentages and Discounts

YEAR 8 ECHO MATHEMATICS

Contents

10/04/232

Converting between Fractions Decimals and Percentages

Finding a PercentageProfit & LossReverse Percentages Writing as a Percentage

Converting between F, D & P

Converting a percentage to a fraction40% means 40 out of every 100

Don’t forget to cancel down, if possible 10040

52

Converting between F, D & P

Converting a percentage to a decimal67% means i.e. 67 100

Remember by 100 ?10067

H T U

6 7101

1001

10001

So, 67% = 0.67

Converting between F, D & PConverting a decimal to a percentageReverse the process i.e. X by 100

H T U

0 4 3101

1001

10001

4 3

So, 0.43 = 43%

Converting between F, D & P

Converting a fraction to a percentageConvert to a decimal first then to a

percentage i.e.

Then, change to a percentage, x by 100 53 6.0

00.35

So, = 0.6 = 60%53

Finding a Percentage -

Remember, 10% =

To find we by 10

Also, 1% =

And, to find we by 100

101

10010

101

Without aCalculator

1001

1001

Finding a Percentage -Use these facts to find any percentagei.e. Find 32% of $24010% = $24 and 1% = $2.40So, 30% = 3 x $24 = $72and 2% = 2 x $2.40 = $4.80

32% = $72.00 + 4.80 = $76.80

Without aCalculator

Finding a Percentage -55% of 120 children at the theatre were boys,

how many were boys ?10% = 12 and 1% = 1.2So, 50% = 5 x 12 = 60and 5% = 5 x 1.2 = 6

55% = 60 + 6 = 66 boys(5% can also be found by using ½ of 10%)

Without aCalculator

Finding a Percentage -Change percentage to a decimal firsteg. Find 28% of 69028% = 0.28 and “of” means multiplySo 28% of 690 is 0.28 x 690Type into your calculatorAnswer = 193.2

With aCalculator

Finding a Percentage -Another example, find 17.5% of $250So, 0.175 x 250Type into calculatorAnswer = $43.75

Find 32.5% of 1200 …0.325 x 1200 =

With aCalculator

390

Profit & Loss2 types of question Type 1 - A car was bought for $1200 and was later

sold at a 15% profit, how much was it sold for ?

Find 15% and then add it on to $1200If it were sold for a 24% lossFind 24% and then take it off the $1200

Profit & LossType 2 – A car was bought for $1200 and later sold

for $1500, what is the percentage profit ?Use the formatTo create a fractionCancel to simplest form and then change to

a percentageActual Profit (or Loss)

Original Amount

Profit & Loss

A car was bought for $1200 and later sold for $1400, what is the percentage profit ?

%17

1666.0

00.1661

61

1200200 Actual Profit

Original Amount

Profit & Loss

A cycle was bought for $600 and later sold for $450, what is the percentage loss ?

%25

25.0

00.1441

41

600150 Actual Loss

Original Amount

Reverse PercentagesThe original amount is always 100%A reduction of 20% means the new price is

80% of originalAn increase of 15% means the new price is

115% of originalUse the calculator method to find original

amount

Reverse Percentageseg. In a 25% sale a sofa costs $480, how

much did it cost before the sale ?25% reduction means 75% of original i.e. 100% - 25% = 75%

So, $480 0.75 = $640

Price before Sale ?

Price after Sale $480

÷ 0.75

x 0.75

Reverse Percentageseg. Following a 10% increase petrol now

costs $1.20 per litre, how much did it cost before the increase ?

10% increase means 110% of original

So, $1.20 1.10 = $1.09 per litre

Price before increase ?

New Price $1.20

÷ 1.10

x 1.10

Writing as a Percentage

One quantity as a percentage of anothereg. Aylish scored 32 out of 50 in a science

test and 48 out of 80 in mathsWrite as a fraction first, then cancel downScience Maths

5032

8048

64.02516 6.05

3 = 64% = 60%

Writing as a Percentage

What percentage of cars are Green ?

22 out of 122 were green, so

Change to a decimalThen convert to a

percentage

Car Park Survey

Colour Frequency

Green 22

Silver 43

Black 57

12222 18.0122

22 =18%

Session Summary

10/04/2321

Converting between Fractions Decimals and Percentages

Finding a PercentageProfit & LossReverse PercentagesWriting as a Percentage

Next week - Ratio