2. Contents
Converting
between Fractions Decimals
and Percentages
Finding a Percentage
Profit & Loss
Reverse Percentages
Writing as a Percentage
02/11/14
2
3. Converting between F, D & P
Converting
a percentage to a fraction
40% means 40 out of every 100
40
100
Don’t
=
2
5
forget to cancel down, if possible
4. Converting between F, D & P
Converting
a percentage to a decimal
67% means 67 i.e. 67 ÷ 100
100
Remember
H
T
6
÷ by 100 ?
1
U
10
7
So,
67% = 0.67
1
100
1
1000
5. Converting between F, D & P
Converting
a decimal to a percentage
Reverse the process i.e. X by 100
1
1
1
H
T
U
10
100
1000
0
4
So, 0.43 = 43%
3
6. Converting between F, D & P
Converting
a fraction to a percentage
Convert to a decimal first then to a
percentage i.e. 3
0 .6
5 = 5 3.00
Then,
change to a percentage, x by 100
So, 3 = 0.6 = 60%
5
7. Without a
Finding a Percentage - Calculator
Remember,
To
1
find
10
10
10% =
100
=
1
10
we ÷ by 10
Also,
1
1% =
100
And,
1
to find 100 we
÷ by 100
8. Without a
Finding a Percentage - Calculator
Use
these facts to find any percentage
i.e. Find 32% of £240
10% = £24
and
1% = £2.40
So, 30% = 3 x £24 = £72
and 2% = 2 x £2.40 = £4.80
32%
= £72.00 + 4.80 = £76.80
9. Without a
Finding a Percentage - Calculator
55%
of 120 children at the theatre were
boys, how many were boys ?
10% = 12
and
1% = 1.2
So, 50% = 5 x 12 = 60
and 5% = 5 x 1.2 = 6
55%
= 60 + 6 = 66 boys
(5% can also be found by using ½ of 10%)
10. With a
Finding a Percentage - Calculator
Change
percentage to a decimal first
eg. Find 28% of 690
28% = 0.28 and “of” means multiply
So 28% of 690 is
0.28 x 690
Type into your calculator
Answer = 193.2
11. With a
Finding a Percentage - Calculator
Another
example, find 17.5% of £250
So, 0.175 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. Profit & Loss
Type
2–
A car was bought for £1200 and later
sold for £1500, what is the percentage
profit ?
Actual Profit (or Loss)
Use the format
Original Amount
To create a fraction
Cancel to simplest form and then
change to a percentage
14. Profit & Loss
A
car was bought for £1200 and later
sold for £1400, what is the percentage
profit ?
Actual Profit
Original Amount
1
6
=
=
200
1200
=
0.1666
6 1.00 = 17%
1
6
15. Profit & Loss
A
cycle was bought for £600 and later
sold for £450, what is the percentage
loss ?
Actual Loss
Original Amount
1
4
=
=
150
600
=
0.25
4 1.00 = 25%
1
4
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%
Price before
Sale ?
So,
x 0.75
÷ 0.75
£480 ÷ 0.75 = £640
Price after
Sale £480
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
Price before
increase ?
So,
x 1.10
÷ 1.10
New Price
£1.20
£1.20 ÷ 1.10 = £1.09 per litre
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 32
Maths 48
50
16
= 25 = 0.64
= 64%
80
3
= 5 = 0.6
= 60%
20. Writing as a Percentage
What
percentage of cars
are Green ?
22 out of 122 were
green, so 22
122
Change
to a decimal
Then convert to a
percentage
Car Park Survey
Colour
Frequency
Green
22
Silver
43
Black
57
22
122
= 0.18
=18%
21. Session Summary
Converting
between Fractions Decimals
and Percentages
Finding a Percentage
Profit & Loss
Reverse Percentages
Writing as a Percentage
Next
02/11/14
week - Ratio
21
