Unit 10 Section 4 : Mixed Numbers and Improper Fractions

In all the fractions we have seen so far, the top number (numerator) has been smaller than the bottom number (denominator).

This means that these fractions are always less than one.

If we want to work with numbers greater than one, we need to use improper fractions or mixed numbers.

Improper fractions have a larger numerator than denominator.

The fraction
5
 can also be written as 1
1
. This is explained below:
4
4

We can also see that
7
 can be written as 3
1
.
2
2
The numbers 1
1
 and 3
1
 are called mixed numbers because they have a whole number part and a fraction part.
4
2

We can also convert mixed numbers back into improper fractions.

The mixed number 4
2
 can also be written as
14
. This is explained below:
3
3

 

You may find the following summary useful when answering questions in this section.

Example Question

Answer these questions using which ever method you find easiest.

Practice Questions
Work out the answer to each of these questions then click on the button marked Click on this button below to see the correct answer to see whether you are correct.
(a) What is
17
 as a mixed number?
6

(b) What is 4
5
 as an improper fraction?
8

 

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.

Question 1
Convert these improper fractions into mixed numbers.

(a)
9
 =
2
(b)
4
 =
3
(c)
5
 =
3
(d)
12
 =
5
(e)
18
 =
5
(f)
9
 =
7
(g)
11
 =
9
(h)
9
 =
4
(i)
8
 =
5
(j)
22
 =
9
(k)
6
 =
5
(l)
14
 =
5
(m)
13
 =
7
(n)
19
 =
7
(o)
20
 =
9

Question 2
Convert these mixed numbers into improper fractions.

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

You have now completed Unit 10 Section 4
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Produced by A.J.Reynolds January 2001