Fractions
Fraction
1
2
1
4
1
10
1
5
1
3
2
3
1
8
3
4
1
20
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Decimal
Percentage
0.50
50%
0.25
25%
0.10
10%
0.20
20%
0.3333…
33.3…%
or 0.3
0.6666…
or 0.6
or 33.3%
66.6…%
or 66.6%
0.125
12.5%
0.75
75%
0.05
5%
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Page 1 of 7
Fractions
Fractions
A fraction is part
of a whole
Numerator
Denominator
3
6
=
3 boxes
out of
6 boxes
OR
1 column
out of
2 columns
1
2
2
6
=
Top number
Bottom number
2 boxes
out of
6 boxes
OR
1 row
out of
3 rows
1
3
Equivalent fractions
Equivalent fractions are the same size
When we make the
numbers smaller we are
cancelling down or
simplifying
Divide or multiply both
the ‘top’ and ‘bottom’
by the same number
3
4
=
6
2
8
6
Both multiplied by 2
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=
1
6
3
9
Both divided by 2
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=
2
3
Both divided by 3
Page 2 of 7
Fractions
Fractions
Adding and
Subtracting
Numerator
Denominator
Top number
Bottom number
We can only add or subtract when the
denominators (‘bottoms’) are the same
If possible simplify
your answer
5
8
+
1
8
6
=8=
3
4
The denominators stay the same
x both by 2
5 x 2 = 10
6 x 2 = 12
5
3
-4=
6
10
12
5
9
6
2
5
3
9
3
+ =
9
10
+
6
-1 =5
4
© www.teachitmaths.co.uk 2016
=
9
18
20
-
11
9
15
20
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=1
=5
9
x both by 3
3x3=9
4 x 3 = 12
=
12
1
12
2
9
3
20
Make
denominators
the same, and
try to simplify
Page 3 of 7
Fractions
Fractions
Multiplying
The rule:
Numerator
Denominator
Top number
Bottom number
Multiply the numerators
and multiply the denominators
5
8
2
3
4
5
x
x
x
1
2
3
5
=
16
6
=
8
3
24
12
=
10
=
3
12
6
=
25
50
=
1
4
OR: We can cancel down first: Any top with any bottom
42
3
5
10 5 25
x
=
1
2
4
3
2 x
=
or
5x
2
3
=
5
1
First change the mixed number
into an improper fraction
6
9
x
2
=
18
4
3
12
93 21 3
x
=
2
10
42 3 1 2
x
3
=
3
=1
=1
=3
12
1
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=1
1
2
2
Cancel
down first
1
3
(5 lots of two thirds = ten thirds =
© www.teachitmaths.co.uk 2016
6
3
1
3
)
Page 4 of 7
Fractions
Fractions
Dividing
The rule:
Numerator
Denominator
Top number
Bottom number
Keep the 1st fraction,
Turn the 2nd fraction upside down,
Multiply ‘tops’ and ‘bottoms’
3
1
÷ 2= 6
Ask yourself:
How many halves in 3?
(2 halves make a whole)
OR use the rule
3
÷
1
2
=
3
x
1
2
6
=1=6
1
Give 3 a denominator
(ALWAYS use 1)
3
5
7
÷8=
4
2 ÷
5
14
=15
3
5
x
3
x
3
5
2
=
=
7
14
=
10
10
8
24
35
Mixed number
becomes improper
3
÷ 10
28
3
=
Type equation here.
9
1
3
Remember you only
turn the 2nd fraction
upside down
Cancel down
before
multiplying
© www.teachitmaths.co.uk 2016
26885
28
9
1
Page 5 of 7
Fractions
Percentage
You need to know 2 methods for % questions:
Non calculator and Calculator
Calculator methods are
quick. Learn them and use
them in calculator tests
Finding a percentage of
Example: Find 6% of £32
Non calculator
Calculator
To find 10% ÷ by 10
0.06 x 3.20 = £1.92
10% = £3.20
5% = £1.60
1% = £0.32
6% = £1.92
Half of 10%
To find 1% ÷ by 100
Write 6% as a decimal
then multiply
Increasing or decreasing by a percentage
Example: Increase £32 by 6%
Non calculator
Find 6% (see above)
32 + 1.92 = £33.92
Write 106% as
a decimal then
multiply
Calculator
(100% + 6% = 106%)
1.06 x 32 = £33.92
Example: A mini hi-fi costs £190 but is reduced by 22%
in a sale. What is the sale price?
Non calculator
Find 22%
10% = £19
20% = £38
1% = £1.90
2% = £3.80
22% = £41.80
£190 – £41.80 = £148.20
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Write 78% as a
decimal then
multiply
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Calculator
(100% - 22% = 78%)
0.78 x 190 = £148.20
Page 6 of 7
Fractions
Percentage
Writing as a percentage
Example: Write 14 out of 20 as a %
Non calculator
𝟏𝟒
=
𝟐𝟎
Calculator
To write as a %
always create a
fraction first
𝟕𝟎
= 70%
𝟏𝟎𝟎
𝟏𝟒
𝟐𝟎
Use equivalent fraction rules
to make the denominator 100
x 100 = 70%
14 ÷ 20 x 100 =
Percentage profit or percentage loss
Example: Carol bought a CD for £5 then sold it for £8.
What was her percentage profit?
Non calculator
Profit = £3
𝟑
𝟓
=
𝟔𝟎
𝟏𝟎𝟎
Calculator
Find the profit,
create a fraction,
then make into %
Profit = £3
𝟑
= 60%
𝟓
x 100 = 60%
Reverse Percentage
Example: A TV was reduced by 15% in a sale. The sale price
was £748. What was the before sale price?
Calculator
100% - 15% = 85%


Find the % after the reduction
then find 100%
85% = £748
1% =
𝟕𝟒𝟖
𝟖𝟓
OR
= 8.8
𝟎.𝟖𝟓
= £880
Change the 85% to a decimal
 100% = 8.8 x 100 = £880
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𝟕𝟒𝟖
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