perfect revision resource for GCSE students

1. Fractions & Percentages
30/11/17 1
30 November 2017

2. Contents
Fractions – the Language of
Equivalent Fractions and Cancelling
Fractions
Top Heavy Fractions and Mixed Numbers
Ordering Fractions
Finding a Fraction
30/11/17 2

3. What are Fractions ?
Parts of a whole
Eg.
Numerator
Denominator
Unit Fractions
30/11/17 3
7
6
4
3
3
2
2
1
3
2
2
1
3
1
4
1
5
1
50
1

4. Fractions
What do they mean …
We have 1 of those parts
The whole is split into 2 parts
We have 3 of those parts
The whole is split into 4 parts
30/11/17 4
2
1
4
3

5. Equivalent Fractions
30/11/17 5
4
2
2
1
=
164
3
= 12
4
2
2
1
= 16
12
4
3
=
x 2
x 2
x 4
x 4

6. Equivalent Fractions
6
328
5
= 21
12
7
=
x 4
x 4
x 3
x 3
20
36

7. Cancelling Fractions
 Reducing fractions to their simplest form
 Equivalent fractions using the smallest
numbers
 Reduce to simplest form
 Find HCF of 5 and 10
 So divide both numerator & denominator by 5
30/11/17 7
10
5
5
2
1
10
5
=
÷ 5
÷ 5

8. Cancelling Fractions
 Cancel
 HCF = 3 HCF = 4
 So,
30/11/17
15
12
36
16
5
4
15
12
=
÷ 3
÷ 3
9
4
36
16
=
÷ 4
÷ 4

9. Top Heavy Fractions & Mixed Numbers
Convert into a mixed number
1 + 1 + =
12 ÷ 5 = 2 with left over
30/11/17 9
3
7
3
1
2
5
12
5
2
5
2
2
5
2

10. Top Heavy Fractions & Mixed Numbers
Convert into a mixed number
26 ÷ 3 = 8, with left over, so
Convert into a top heavy fraction
How many fifths
30/11/17 10
3
26
3
2
5
3
3
5
18
3
2
8

11. Top Heavy Fractions & Mixed Numbers
Convert into a top heavy fraction
So = =
Try
 = =
30/11/17 11
5
3
3
5
3)5x3( +
5
3
3 5
18
3
1
3 7
3
5
3
1)3(3x +
7
3x7)5( +
3
10
7
38

12. Ordering Fractions
Easy !!
But what about …..
Convert to equivalent fractions with
same denominator first
Find LCM of 5, 8 and 20 (denominators)
30/11/17 12
5
1
5
4
5
2
5
3
5
3
8
5
20
11
40

13. Ordering Fractions
Now put them in order …
So, then answer the question
30/11/17 13
40
24
5
3
= 40
25
8
5
= 40
22
20
11
=
40
24
40
25
40
22
5
3
8
5
20
11

14. Finding a Fraction
What is of £50 ?
What about of £100 ?
To find ÷ 5
To find ÷ 25
How would we find
30/11/17 14
2
1
4
1
502
1004
5
1
25
1
157
1 yes,
÷ 157

15. Finding a Fraction
What about of £125 ?
Find first –
Then, x by 2
So, of £125 is £50
30/11/17 15
5
2
5
1 25
1255
25
x 2
50
5
2

16. Contents - Percentages
What are Percentages ?
Converting between Fractions and
Percentages
Finding a Percentage
30/11/17 16

17. What are Percentages ?
They are just like fractions
The whole is always split into 100 parts
So 35% means 35 out of the 100 parts
30/11/17 17
100
35

18. 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
100
40
5
2
=

19. Converting between F, D & P
Converting a fraction to a percentage
You need to find the equivalent fraction
which has 100 as the denominator
 ___
 1005
3 =
x 20
x 20
60 So 60%

20. Finding a Percentage -
Remember, 10% =
To find we ÷ by 10
10
1
100
10
=
10
1
Without a
Calculator

21. Finding a Percentage -
Use this info to find any percentage
i.e. Find 30% of £240
10% = £24
So, 30% = 3 x £24 = £72
30% = £72.00
Without a
Calculator

22. Finding a Percentage -
45% of 120 children at the theatre were
boys, how many were boys ?
10% = 12 so 5% = 6 (half of 10%)
So, 40% = 4 x 12 = 48
and 5% = 6
45% = 48 + 6 = 54 boys
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Calculator