Unit 20 Section 2 : Adding and Subtracting Fractions

In this section we look at how to add and subtract fractions.

Two fractions can only be added or subtracted if they have the same denominator

For example, it is possible to add
3
 and
1
 because both fractions have 5 as the denominator.
5
5
In this case, we simply add the numerators to find the answer: 
3
  + 
1
  = 
4
5
5
5

If fractions do not have the same denominator, you need to find equivalent fractions which do

For example, it is not possible to add
3
 and
1
 without changing each fraction so that they have the same bottom number.
5
4
We can use equivalent fractions to rewrite each fraction with 20 as the denominator: 
3
  = 
12
  and 
1
  = 
5
5
20
4
20
Now we can see that 
3
  + 
1
  = 
12
  + 
5
  = 
17
5
4
20
20
20

Example Questions
Examples of questions involving adding and subtracting fractions are given below.
After each example there are practice questions for you to try.
In each case, work out the what you think the answer is, then click Click on this button below to see the correct answer to see whether you are correct.

Example 1

Practice Questions

Example 2

Practice Questions

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

When answering fraction questions, fill in all the boxes before checking your answer, like this:

Question 1
Work out the answers to these additions and subtractions:

(a)
3
 +
1
 =
7
7
(b)
1
 +
7
 =
9
9
(c)
1
 +
3
 =
5
5
(d)
2
 +
4
 =
7
7
(e)
7
 -
5
 =
9
9
(f)
8
 -
3
 =
11
11
(g)
4
 -
2
 =
15
15
(h)
6
 -
3
 =
13
13
(i)
4
 -
3
 =
7
7
(j)
6
 -
2
 =
25
25

Question 2
Fill in the missing numbers in the fraction additions below.

(a)
1
 +
1
=
 +
=
2
5
10
10
10
(b)
4
 +
2
=
 +
=
5
3
15
15
15
(c)
1
 +
4
=
 +
=
6
5
30
30
30
(d)
4
 -
1
=
 -
=
7
3
21
21
21
(e)
5
 -
2
=
 -
=
6
3
6
6
6

Question 3
Work out the answers to these additions and subtractions and fill them in below.
You will need to use pen and paper to do your working.

(a)
1
 +
1
 =
3
2
(b)
3
 +
2
 =
4
3
(c)
1
 +
1
 =
5
4
(d)
3
 +
2
 =
5
3
(e)
5
 +
1
 =
8
4
(f)
4
 +
2
 =
5
7
(g)
1
 +
2
 =
7
3
(h)
6
 +
2
 =
7
3
(i)
7
 -
3
 =
8
4
(j)
8
 -
3
 =
9
4
(k)
3
 -
1
 =
7
3
(l)
4
 -
3
 =
5
4

Question 4
A birthday cake is divided into 12 equal pieces.
Andrew eats
3
 of the cake and Timothy eats
1
 of the cake.
12
12
(a) What fraction of the cake is left?

(b) How many pieces of cake are left? pieces

Question 5
Steve and Sheila buy a computer.
Steve fills
2
 of the hard disk with his programs and Sheila fills
1
 of the hard disk with her programs.
5
3
(a) What fraction of the hard disk is full?

(b) What fraction of the hard disk is empty?

Question 6
9
 of all men in the UK own at least one car, and
2
 of all men in the UK own more than one car.
10
3
(a) What fraction of men in the UK do not own a car?

(b) What fraction of men in the UK own only one car?

You have now completed Unit 20 Section 2
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Produced by A.J.Reynolds January 2001