1
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