# 5 Fractions – bringing it all together

This is the final activity for this week, it brings everything you’ve learned about fractions together, and gives you a bit more practice.

## Activity _unit4.5.1 Activity 7 Reasons for enrolment

A group of 240 new students were asked about the main reasons they had decided to enrol on courses at The Open University.

Of the 240 students, 80 wished to improve their career prospects, 60 had enrolled for interest and 72 had signed up for a course in order to help their children.

(a) Write a fraction for each of these groups, remembering to show them in the simplest form.

### Answer

(a) There are 240 in the whole group, giving the denominator needed for all the fractions before simplification.

Career prospects: 80 of 240 students is .

Divide the top and bottom by 10, and then by 8, to give .

Interest: 60 of 240 students is .

Divide the top and bottom by 10, and then by 6, to give .

To help their children: 72 of 240 students is .

Divide the top and bottom by 12, and then by 2, to give .

(b) How many students expressed some other reason for enrolling?

### Answer

(b) The total number of people who chose one of the three reasons is 80 + 60 + 72 = 212.

So, the number of people who expressed some other reason for enrolling is 240 − 212 = 28.

(c) What fraction of the students surveyed expressed some other reason for registering for courses?

### Answer

(c) Take your solution from part (b) and express it as a fraction. You should now have .

This fraction can then be simplified:

So, of the group gave some other reason for enrolling on Open University courses. (You could also have used your calculator to work out these fractions.)