Fraction Calculations 1
Addition and Subtraction of Fractions

In this section we consider how to add and subtract fractions. The key step in this process is to make sure that both fractions have the same denominator.

Worked Examples

1

Calculate:

(a)

+

Show me

As the denominator is the same in both fractions, we simply add the numbers on the top of the fraction to give

+ =
=

This addition is shown in the diagram below:
(b)

−

Show me

The denominator is the same in both fractions, so

− =
=
=

This is shown in the diagram below:
2

Calculate:

(a)

+

Show me

These fractions do not have the same denominator, so the first step is to change them so that they do. In this case, we can use 20 as the common denominator.

+ = +
=
=

This is illustrated in the diagram below:
(b)

−

Show me

The denominator is not the same in both fractions, so

− = −
=
=

This is illustrated in the diagram below:
3

Calculate:

(a)

+

Show me

1 + 3 = 4

+ = +
=
=
So + =
(b)

−

Show me
− = −
= −
=
=
=

Note: It is usually easier to convert the mixed numbers into improper fractions.
(c)

+

Show me
+ = +
= +
=
=
=

Exercises

Calculate:

(a)
+ =
(b)
+ = =
(c)
+ =
(d)
+ = =
(e)
+ =
(f)
+ =
(g)
+ = =
(h)
− = =
(i)
− =
(j)
− = =
(k)
− =
(l)
− =
(m)
− =
(n)
− =
(o)
− =

Fill in the missing numbers:

(a)
+ = + =
(b)
+ = + =
(c)
+ = + =
(d)
− = − =
(e)
− = − =

Calculate:

(a)
+ =
(b)
+ =
(c)
+ =
(d)
+ =
(e)
+ =
(f)
+ = =
(g)
+ =
(h)
+ =
(i)
+ = =
(j)
+ =
(k)
− = =
(l)
− =
(m)
− =
(n)
− =
(o)
− =

A birthday cake is divided into 12 equal parts. Andrew eats of the cake and Tim eats of the cake.

(a)

What fraction of the cake is left?

=
(b)

How many pieces of cake are left?

A garden has an area of hectare. The owner buys an extra of a hectare of land.

(a)

What is the area of the garden now?

ha
(b)

How much more land would the owner need to have a garden with an area of 2 hectares?

ha

Steve and Sheila buy a computer. Steve fills of the hard disk with his programs. Sheila fills of the hard disk with her programs.

(a)

What fraction of the hard disk is full?

(b)

What fraction of the hard disk is empty?

(c)

Steve deletes one of his programs that takes up of the hard disk. What fraction of the hard disk do his programs fill now?

If of all men in the UK own cars, and of all men in the UK own more than one car, what fraction of men in the UK:

(a)

do not own a car,

(b)

own only one car?

Calculate:

(a)
+ or
(b)
+ or
(c)
+ or
(d)
+ or
(e)
−
(f)
− or
(g)
−
(h)
+ or
(i)
− or
(j)
− or
(k)
− or
(l)
− or

Ron wins £ million. He gives £ million to his daughter and £ million to his wife. How much does he have left?

£ million

An old-fashioned gardener measures the height of a plant as inches. A week later the height is measured as inches. How much did the plant grow during the week?

or inches