1. Percentages
23 May 2019
23/05/2019

2. Contents Converting between Fractions Decimals and Percentages
Finding a Percentage
Profit & Loss
Reverse Percentages
Writing as a Percentage
23/05/2019

3. Converting between F, D & P
Converting a percentage to a fraction
40% means 40 out of every 100
Don’t forget to cancel down, if possible

4. Converting between F, D & P
Converting a percentage to a decimal
67% means i.e  100
Remember  by 100 ?
So,
67% = 0.67 H T U 6 7

5. Converting between F, D & P
Converting a decimal to a percentage
Reverse the process i.e. X by 100 H T U 4 3
So, = 43%

6. Converting between F, D & P
Converting a fraction to a percentage
Convert to a decimal first then to a percentage i.e.
Then, change to a percentage, x by 100
So, = = 60%

7. Finding a Percentage - Without a Calculator Remember, 10% =
To find we  by 10
Also, 1% =
And, to find we  by 100

8. Finding a Percentage - Without a Calculator
Use these facts to find any percentage
i.e. Find 32% of £240
10% = £ and % = £2.40
So, 30% = 3 x £24 = £72
and 2% = 2 x £2.40 = £4.80
32% = £ = £76.80

9. Finding a Percentage - Without a Calculator
55% of 120 children at the theatre were boys, how many were boys ?
10% = and % = 1.2
So, 50% = 5 x 12 = 60
and 5% = 5 x 1.2 = 6
55% = = 66 boys
(5% can also be found by using ½ of 10%)

10. Finding a Percentage - With a Calculator
Change percentage to a decimal first
eg. Find 28% of 690
28% = and “of” means multiply
So 28% of 690 is
0.28 x 690
Type into your calculator
Answer = 193.2

11. Finding a Percentage - With a Calculator
Another example, find 17.5% of £250
So, x 250
Type into calculator
Answer = £43.75
Find 32.5% of 1200 …
0.325 x 1200 =
390

12. Profit & Loss 2 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 £1200
If it were sold for a 24% loss
Find 24% and then take it off the £1200

13. Actual Profit (or Loss)
Profit & Loss
Type 2 –
A car was bought for £1200 and later sold for £1500, what is the percentage profit ?
Use the format
To create a fraction
Cancel to simplest form and then change to a percentage
Actual Profit (or Loss)
Original Amount

14. Profit & Loss
A car was bought for £1200 and later sold for £1400, what is the percentage profit ?
Actual Profit
Original Amount

15. Profit & Loss
A cycle was bought for £600 and later sold for £450, what is the percentage loss ?
Actual Loss
Original Amount

16. Reverse Percentages The original amount is always 100%
A reduction of 20% means the new price is 80% of original
An increase of 15% means the new price is 115% of original
Use the calculator method to find original amount

17. Reverse Percentages
eg. 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
x 0.75
Price after
Sale £480
Price before
Sale ?
÷ 0.75

18. Reverse Percentages
eg. 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
x 1.10
New Price
£1.20
Price before
increase ?
÷ 1.10

19. Writing as a Percentage
One quantity as a percentage of another
eg. Aylish scored 32 out of 50 in a science test and 48 out of 80 in maths
Write as a fraction first, then cancel down
Science Maths
= 64%
= 60%

20. Writing as a Percentage
What percentage of cars are Green ?
22 out of 122 were green, so
Change to a decimal
Then convert to a percentage
Car Park Survey
Colour
Frequency
Green 22
Silver 43
Black 57
=18%

21. Session Summary Converting between Fractions Decimals and Percentages
Finding a Percentage
Profit & Loss
Reverse Percentages
Writing as a Percentage
Next week - Ratio
23/05/2019