The document provides an overview of key concepts for understanding fractions including: finding fractions of amounts by dividing the amount by the denominator and multiplying by the numerator; equivalent fractions and cancelling fractions down; mixed numbers and converting between mixed numbers and improper fractions; converting fractions to percentages by writing the fraction with a denominator of 100. It includes examples and practice problems for each concept.

1. Fraction Revision

2. Things you need to know about
fractions...
Finding Fractions of
Amounts
Equivalent Fractions
and cancelling
down
Top Heavy Fractions
and Mixed Numbers
Adding and
Subtracting
Fractions
Multiplying
Fractions
Dividing Fractions
Fractions and
Decimals
Fractions and
Percentages
Ordering Fractions
Click this to get back here
Things you
should know
These are
REALLY
important

3. Finding Fractions of Amounts
3
5
If you are asked for of an amount
Find by dividing by 5 and then find by
multiplying by 3.
To find of 60:
60 ÷ 5 = 12
12 x 3 = 36
1
5
3
5
3
5
3
5
of 60 is 36

4. Finding Fractions of Amounts
2
7
If you are asked for of an amount
Find by dividing by 7 and then find by
multiplying by 2.
To find of 35:
35 ÷ 7 = 5
5 x 2 = 10
1
7
2
7
2
7
2
7
of 35 is 10

5. Finding Fractions of Amounts
5
9
If you are asked for of an amount
Find by dividing by 9 and then find by
multiplying by 5.
To find of 63:
63 ÷ 9 = 7
5 x 7 = 35
1
9
5
9
5
9
5
9
of 63 is 35

6. Finding Fractions of Amounts
A quick way to remember what to do
is:
“Divide by the bottom, times by the
top”

7. Fractions of Amounts
10 multiple choice questions,
work out your answer then click
to see if you were right

8. 30
15
40
6
What is..
1
2
of 60
A) B)
C) D)

9. 15
20
12
4
What is..
1
4
of 60
A) B)
C) D)

10. 12
6 9
8
What is..
1
3
of 36
A) B)
C) D)

11. 14 16
18
12
What is..
1
4
of 56
A) B)
C) D)

12. 33
13 11
21
What is..
3
6
of 66
A) B)
C) D)

13. 75
66.6666
25
80
What is..
3
4
of 100
A) B)
C) D)

14. 60
20
15
35
What is..
3
5
of 100
A) B)
C) D)

15. 25
45 50
80
What is..
1
8
of 200
A) B)
C) D)

16. 140
80
120
100
What is..
20
40
Of 280
A) B)
C) D)

17. 70 49
74
81
What is..
7
9
of 90
A) B)
C) D)

19. Multiplying Fractions
To multiply simply times the numbers at the top, then times
the numbers at the bottom, you may have to simplify
3
4
5
8
x =
15
32
2
7
5
6
x =
10
42
3
5
7
9
x =
21
45
=
= 7
15
5
21

20. Simplify before multiplying
6
7
5
6
x = 1x5
7x1
1
1
=
5
7
4
5
3
8
x = 1x3
5x2
1
2
=
3
10
4
9
6
7
x = 4x2
3x7
3
2
=
8
21
This will help
with division
too, do it
after the
keep, change
flip bit

22. Dividing Fractions
To divide remember KEEP, CHANGE, FLIP
-KEEP the first fraction
-CHANGE the multiply sign to divide
-FLIP the second fraction
3
4
5
8
÷ =
24
20
3
4
x 8
5
= =1 4
20
or 1
1
5
1
2
7
8
÷ =
8
14
1
2
x 8
7
= =
4
7
4
7
3
4
÷ =
16
21
4
7
x 4
3
=

25. Three friends each have 12 sweets
Abbie puts hers into 4 piles
and eats 2 of them
Abbie has had
2/4
Libby puts hers into 2 piles
and eats 1 of them
Libby has had
1/2
Chrissy puts hers into 6
piles and eats 3 of them
Chrissy has had
3/6
They all eat 6 sweets
2/4, ½ and 3/6 look different but these
fractions are all the same, they are
EQUIVALENT

26. Are these fractions EQUIVALENT?
8
24
12
36
1
3
1
3
÷8
÷12
Simplify the
fractions
Look for the
biggest number
that goes into the
top and bottom
of the fractions
Divide by the
number
These fractions
are equivalent

27. Are these fractions EQUIVALENT?
8
10
12
16
4
5
3
4
÷2
÷4
Simplify the
fractions
Look for the
biggest number
that goes into the
top and bottom
of the fractions
Divide by the
number
These fractions
are NOT
equivalent

28. Are these fractions EQUIVALENT?
9
12
21
28
3
4
3
4
÷3
÷7
Simplify the
fractions
Look for the
biggest number
that goes into the
top and bottom
of the fractions
Divide by the
number
These fractions
are equivalent

29. What number goes here?
15
20
32
40
3
4
4
5
÷5
÷8

30. What number goes here?
2
3
1
5
8
24
9
45
X8
X9

31. Equivalent Fractions
10 multiple choice questions.
Work out your answer then click
to see if you were right

32. A) B)
C) D)
1
2
2
8
3
9
4
8
4
10
Which fraction is equivalent to....

33. A) B)
C) D)
1
3
4
12
3
9
4
8
5
20
Which fraction is equivalent to....

34. A) B)
C) D)
1
4
7
21
5
16
3
10
4
16
Which fraction is equivalent to....

35. A) B)
C) D)
1
10
4
44
3
30
Which fraction is equivalent to....
4
44
4
44

36. A) B)
C) D)
3
4
15
20
Which fraction is equivalent to....
18
20
12
20
16
20

37. A) B)
C) D)
2
5
6
15
Which fraction is equivalent to....
6
25
8
22
12
35

38. A) B)
C) D)
5
6
30
36
Which fraction is equivalent to....
15
24
35
36
10
18

39. A) B)
C) D)
4
9
16
36
Which fraction is equivalent to....
12
54
16
81
8
27

40. A) B)
C) D)
5
7
30
42
Which fraction is equivalent to....
10
21
35
35
15
28

41. A) B)
C) D)
9
11
63
77
Which fraction is equivalent to....
27
22
63
88
45
44

42. Cancelling fractions down
It is often best to have the numbers possible
when we write fractions
Instead of we would have
We have cancelled the fractions down, by dividing top and
bottom numbers by the same number (in this case 4)
12
20
3
5

43. 15
35
24
36
55
66
=
=
=
3
7
2
3
5
6
Divide by 5
Divide by 12
Divide by 11

44. Cancelling fractions down
If we pick the biggest number possible to divide
by we only have to cancel down once.
We must always check that there are no more
numbers which go into the top and bottom
number
When there are no more numbers which go into
the top and bottom of the fraction, the
fraction is FULLY SIMPLIFIED or CANCELLED
DOWN FULLY

45. Cancelling Fractions
10 multiple choice
questions

46. A) B)
C) D)
12
15
4
5
3
5
3
4
2
5
Cancel completely

47. A) B)
C) D)
4
8
2
8
1
3
1
2
1
4
Cancel completely

48. A) B)
C) D)
7
21
1
3
3
7
1
8
1
7
Cancel completely

49. A) B)
C) D)
15
25
4
5
3
4
5
6
3
5
Cancel completely

50. A) B)
C) D)
28
32
7
14
7
8
4
6
14
16
Cancel completely

51. A) B)
C) D)
27
36
3
4
3
5
5
7
6
8
Cancel completely

52. A) B)
C) D)
24
60
2
5
3
8
2
7
1
5
Cancel completely

53. A) B)
C) D)
55
66
5
6
8
9
6
7
4
6
Cancel completely

54. A) B)
C) D)
48
64
3
4
4
6
3
5
2
3
Cancel completely

55. A) B)
C) D)
56
72
7
9
1
2
2
5
6
7
Cancel completely

57. Mixed numbers and top heavy
fractions
When you see a fraction with a large number in front of it,
this is a MIXED NUMBER.
2
2
3 This mean, 2 and 2 thirds
When we have a fraction where the number at the top
(NUMERATOR) is bigger than the number at the bottom
(DENOMINATOR) we have a TOP HEAVY FRACTION
5
3
8
4
9
2

58. Mixed numbers and top heavy
fractions
You need to be able to:
• turn MIXED NUMBERS into TOP
HEAVY FRACTIONS
•turn TOP HEAVY FRACTIONS into
MIXED NUMBERS

59. Top heavy fractions to mixed numbers
14
3
How many 3’s go into 14? 4
What is the remainder? 2
So we can make 4 wholes and we have 2 thirds
left over:
4
2
3
14
3
=

60. Top heavy fractions to mixed numbers
19
5
How many 5’s go into 19? 3
What is the remainder? 4
So we can make 3 wholes and we have 4 fifths
left over:
3
4
5
19
5
=

61. Top heavy fractions to mixed numbers
31
10
How many 10’s go into 31? 3
What is the remainder? 1
So we can make 3 wholes and we have 1 tenth
left over:
3
1
10
31
10
=

62. Mixed Numbers to Top heavy fractions
To turn the mixed numbers into top heavy fractions:
3
1
10
31
10
=
Multiply these numbers together=
Add on the number at the top=
30
31 (this will be the top number)
The number at the bottom will stay the same

63. Mixed Numbers to Top heavy fractions
To turn the mixed numbers into top heavy fractions:
5
3
4
23
4
=
Multiply these numbers together=
Add on the number at the top=
20
23 (this will be the top number)
The number at the bottom will stay the same

64. Mixed Numbers to Top heavy fractions
To turn the mixed numbers into top heavy fractions:
6
2
5
32
10
=
Multiply these numbers together=
Add on the number at the top=
30
32 (this will be the top number)
The number at the bottom will stay the same

65. Top heavy fractions
10 multiple choice
questions

66. 8
3
22
3
7
3
4
3
A) B)
C) D)
22
3 =

67. 19
5
17
5
12
5
34
5
A) B)
C) D)
34
5 =

68. 9
2
8
2
4
2
12
2
A) B)
C) D)
41
2 =

69. 53
5
13
4
50
5
35
5
A) B)
C) D)
103
5 =

70. 19
3
18
3
9
3
6
3
A) B)
C) D)
61
3 =

71. 3
1
9
2
A) B)
C) D)
10
3 =
1
3
1
3
1
3
9
3

72. 7
8
9
6
A) B)
C) D)
57
8 =
1
8
2
8
3
8
1
8

73. 3
4
4
3
A) B)
C) D)
15
4 =
3
4
1
4
1
4
3
4

74. 2 1
2
10
A) B)
C) D)
21
10 =
1
2
11
10
11
20
1
10

75. 5
4 5
6
A) B)
C) D)
26
5 =
1
5
6
5
1
5
1
5

77. Fractions and Percentages
• Think of percentages as fractions with 100 as
the denominator so,
17 % =
32 % =
88 % =
17
100
32
100
88
100

78. Fractions and Percentages
• Some fractions can be simplified
25 % =
55 % =
30 % =
25
100
55
100
30
100
1
4
11
20
3
10
=
=
=

79. Fractions and Percentages
To turn a fraction into a percentage you need to use what you know about equivalent
fractions. Turn your fraction into an equivalent fraction over 100.
12
20
60
100
x5
60%

80. Fractions and Percentages
To turn a fraction into a percentage you need to use what you know about equivalent
fractions. Turn your fraction into an equivalent fraction over 100.
7
10
70
100
x10
70%

81. Fractions and Percentages
Sometimes you need to simplify the fraction first.
14
35
40
100
x20
40%
2
5
=

82. Fractions and Percentages
Sometimes you need to simplify the fraction first.
26
40
65
100
x5
65%
13
20
=

83. 60% 70% 8% 27% 80%
1
4
33
100
51
100
4
5
1
5
Practise Questions, click to show answers

84. Fractions to Percentages
10 multiple choice questions,
work out your answer then click
to see if you were right

85. 50%
20%
40%
100%
A) B)
C) D)
Convert this fraction to a percentage
1
2

86. 25%
40%
2%
4%
A) B)
C) D)
Convert this fraction to a percentage
1
4

87. 10% 100%
20%
1%
A) B)
C) D)
Convert this fraction to a percentage
1
10

88. 20%
2% 15%
5%
A) B)
C) D)
Convert this fraction to a percentage
1
5

89. 75%
80% 12%
45%
A) B)
C) D)
Convert this fraction to a percentage
3
4

90. 21%
0.21% 2.1%
210%
A) B)
C) D)
Convert this fraction to a percentage
21
100

91. 40%
4%
10%
44%
A) B)
C) D)
Convert this fraction to a percentage
4
10

92. 60%
6%
80%
15%
A) B)
C) D)
Convert this fraction to a percentage
3
5

93. 1%
100%
0.110%
0.1%
A) B)
C) D)
Convert this fraction to a percentage
1
100

94. 33.333333.. % 13%
11%
3%
A) B)
C) D)
Convert this fraction to a percentage
1
3

96. Adding and Subtracting
Fractions
Two rulers add three rulers is:
Four pens add five pens is: 9 pens
5 rulers
Two pens add Five rulers is:
We can’t so this until we have a name
that describes both groups
7 Pieces of equipment
When we add fractions we need them to have the same name

97. Adding and Subtracting
Fractions
2
7
3
7
5
7
+ =
2
9
4
9
6
9
+ =
1
11
3
11
4
11
+ =

98. Adding and Subtracting
Fractions
2
7
3
7
5
7
+ =
2
9
4
9
6
9
+ =
5
11
3
11
2
11
- =

99. Adding and Subtracting
Fractions
We need to make sure the denominator of both fractions is the
same before we add or subtract
2
5
3
10
7
10
+ =
10
3
10
+ =
4
We need a number in the 5
and 10 times table to
use as our bottom
number- 10?

100. Adding and Subtracting
Fractions
We need to make sure the denominator of both fractions is the
same before we add or subtract
1
3
5
12
9
12
+ =
12
5
12
+ =
4
We need a number in the 3
and 12 times table to
use as our bottom
number- 12?

101. Adding and Subtracting
Fractions
We need to make sure the denominator of both fractions is the
same before we add or subtract
2
5
3
6
27
30
+ =
30 30
+ =
12
We need a number in the 5
and 6 times table to use
as our bottom number-
30?
15

102. Adding and Subtracting
Fractions
We need to make sure the denominator of both fractions is the
same before we add or subtract
7
8
2
3
5
24
- =
24 24
- =
21
We need a number in the 8
and 3 times table to use
as our bottom number-
24?
16

103. Adding and Subtracting Fractions
a) 7/8
b) 8/12
c) 7/9
d) 7/10
e) 2/3
a) 11/12
b) 7/10
c) 8/15
d) 16/12 or 1 ¼
e) 11/24
a) 1 7/12
b) 1 5/56
c) 29/30
d) 29/52
e) 1 1/10
a) 5/8
b) 5/12
c) 1/3
d) 2/5
e) 1/2
a) 7/20
b) 8/21
c) 23/36
d) 9/22
e) 71/126
Click for
answers

105. Fractions and Decimals
To turn fractions into decimals and decimals into
fractions we need to remember column names
000.000
Hundreds
Tens
Units
Tenths
Hundredths
Thousandths

106. Decimals to Fractions
0.03 is 3 hundredths 3
100
Tenths
Hundredths
0.5 is 5 tenths 5
10
Tenths

107. Decimals to Fractions
0.12 is 12 hundredths 12
100
Tenths
Hundredths
0.01 is 1 hundredth 1
100
Tenths
Hundredths

108. Decimals to Fractions
0.032 is 32 thousandths 32
1000
Tenths
Hundredths
Thousandths
0.154 is 154 thousandths 154
1000
Tenths
Hundredths
Thousandths
Don’t forget you may
have to simplify

109. Fractions to Decimals
7
10
64
100
152
1000
=
=
=
0.7
0.64
0.152
3
100
= 0.03
53
1000
=0.053 2
1000
=0.002
000.000
Hundreds
Tens
Units
Tenths
Hundredths
Thousandths

110. Fractions to Decimals
You can also turn fractions into decimals
by dividing the top number by the bottom
number either with a calculator or any
other method you may know

112. Ordering Fractions
To order fractions you need to know
all about equivalent fractions

113. It’s difficult to order fractions when
they have different denominators
1
2
1
4
3
5
3
10
11
20
What number is in the 2,4,5,10 and
20 times table, we need a common
multiple
20?

114. Make all fractions have 20 as a
denominator
1
2
1
4
3
5
3
10
11
20
Now order them
10
20
5
20
15
20
6
20
11
20
5
20
6
20
10
20
11
20
15
20

115. What denominator do we need now?
1
3
4
6
2
5
5
12
5
6
Now order them
20
60
40
60
24
60
25
60
50
60
20
60
24
60
25
60
40
60
50
60

116. Ordering Fractions- click for answers
ANSWERS
1. 1/4 3/8 ½ and 4/8 3/4
2. 2/5 ½ 3/5 and 6/10 2/29
3. 1/3 5/12 1/1 4/6 3/4
4. 1/4 1/2 2/3 5/6 7/8
5. 1/4 2/5 1/2 6/10 3/4
6. 1/3 4/9 1/2 2/3 5/6
7. 2/6 1/4 5/12 2/3 7/9
8. 2/7 2/4 5/8 11/14 3/2

118. Fraction Percentage Decimal
1/2 50% 0.5
1/4 25% 0.25
3/4 75% 0.75
1/5 20% 0.2
1/10 10% 0.1
1/100 1% 0.01
Things you should know
The top number of a fraction is the
NUMERATOR
The bottom number of a fraction is the
DENOMINATOR