# 6.5 Self-Check

## Exercise 1: Enrolment

A group of 240 new students were asked about the main reasons they had decided to enrol in courses at a local university.

A third of the group wished to improve their career prospects, a quarter had enrolled for interest, and three-tenths had signed up for classes in order to help their children.

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

### Answer

(a) A third of 240 is .

So, 80 people enrolled for career reasons.

A quarter of 240 is .

So, 60 people enrolled for interest.

One-tenth of 240 is .

Three-tenths of 240 is .

Therefore, the total number of people who chose one of the three reasons is .

The number of people who expressed some other reason is .

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

### Answer

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

This fraction can then be reduced:

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

Alternatively, you could have worked out the fraction of students that gave some other reason as follows:

Then, to check your work, calculate this fraction with the original total of 240: .

## Exercise 2: Timing is Everything

A recipe specifies a cooking time of hours and suggests checking and basting two-thirds of the way through the cooking time. |

After how long should you check and baste your culinary creation?

### Answer

There are several ways you can do this calculation. For example, you could calculate two thirds of as follows:

So, the time is hours, or 1 hour and 40 minutes.

Alternatively, you might have converted the hours to minutes. Since there are 60 minutes in an hour and 30 minutes in half an hour, hours is the same as minutes, or 150 minutes.

minutes is the same as both 100 minutes, and 1 hour and 40 minutes.

## Exercise 3: Mowing Lawns

During the summer, you decide to mow lawns. It takes you an average of three-fourths of an hour to cut one client’s yard. |

If you decide to work a total of hours per day, how many lawns can you mow in that time?

### Answer

You must determine how many times goes into . The calculation is . Therefore, you could mow 11 lawns, if you work a full day.

## Exercise 4: More or Less Than 1?

Would the solutions to each of the following problems be more than 1, or less than 1?

Estimate your answers before you work them out accurately, either on paper or using your calculator.

(a)

### Answer

(a) Both these fractions are less than , so you would expect the answer to be less than 1. .

(b)

### Answer

(b) Since is less than , and a further fraction is subtracted, the answer will be less than 1. .

(c)

### Answer

(c) Since this calculation finds a third of a fraction that is less than 1, the answer will be less than 1. .

(d)

### Answer

(d) This calculation is equivalent to asking `How many quarters are there in a third?’, so you would expect an answer greater than 1. .

(e)

### Answer

(e) This calculation is equivalent to asking “How many quarters are there in 1?” so you should expect the answer 4. .

(f)

### Answer

(f) Since is less than , you would expect two lots of to be less than 1. .

6.4.4 Practice with Dividing Fractions