Rules of fractions
Fractions
You can’t escape these basic rules for fractions – they’ll come up time and time again. So you
need to learn them, and practise them.
First, remember that the denominator (the bottom part) of a fraction can never equal zero. So
0
5
5
=0 but 0 is undefined (it has no answer)
Another quick rule is to remember that to get the reciprocal of a fraction, turn it upside down.
The reciprocal of a whole number is 1 over that number. For example,
the reciprocal of
2
11
is
the reciprocal of 7 is
11
2
1
7
Mixed to improper
A number such as 2 53 is a mixed fraction, and a number such as
7
is an improper fraction,
4
where the top number (numerator) is bigger than the bottom number (denominator).
To change the mixed fraction A bc to an Improper Fraction, use this rule :
𝑏
𝐴𝑐 =
𝐴𝑐+𝑏
𝑐
where 𝐴 means 𝐴 x 𝑐
For example,
4
5
2 =
(2×5)+4
5
=
14
5
Improper to mixed
To change
d
to the mixed fraction A bc , first see how many times c goes into d.
c
This will be your number A. The remainder will be b. The number c does not change.
For example,
23
7
2
= 37
using the fact that 7 into 23 is 3 remainder 2. The denominator 7 does not change.
Remember to cancel down when necessary:
14
4
© www.teachitmaths.co.uk 2016
2
1
= 34 = 32
27126
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Rules of fractions
Multiplying
Multiplying fractions is easy – just multiply straight across the top and straight across the
bottom:
3
7
2
6
x 5 = 35
2
5
and
3
6
x 4 = 20 =
3
10
Dividing
Dividing has one additional step: turn the second fraction “upside down” and then multiply :
3
10
4
5
÷
3
5
= 10 x 4 =
15
40
3
=8
Note that you could have cancelled before multiplying:
3
10
÷
5
4
=
3
2
1
4
x
=
3
8
Adding and subtracting
Here’s a rule that works for all numbers :
𝑎
𝑏
±
𝑐
𝑑
=
𝑎𝑑±𝑏𝑐
𝑏𝑑
For example,
2
3
+
4
5
=
(2×5) +(4×3)
3×5
=
12
15
7
= 113
1
5
and
4
−5 =
(1×7)−(3×5)
5×7
=
−8
35
8
= − 35
It’s not always necessary to use this rule however. For example:
When the bottom numbers are the same, just add the top numbers:
3
11
2
5
11
6
4
+4=4
+ 11 =
Or find a common denominator first:
3
2
© www.teachitmaths.co.uk 2016
3
+4=
27126
3
9
Page 2 of 2