6.5 Self-Check

Exercise symbolExercise 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?

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Answer

(a) A third of 240 is 240 division three equals 80.

So, 80 people enrolled for career reasons.

A quarter of 240 is 240 division four equals 60.

So, 60 people enrolled for interest.

One-tenth of 240 is 240 division 10 equals 24.

Three-tenths of 240 is 24 multiplication three equals 72.

Therefore, the total number of people who chose one of the three reasons is sum with, 3 , summands 80 plus 60 plus 72 equals 212.

The number of people who expressed some other reason is 240 minus 212 equals 28.

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

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Answer

Take your solution from part (a), and express it as a fraction. You should now have 28 divided by 240.

This fraction can then be reduced:

So, seven divided by 60 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:

equation left hand side one minus one divided by three minus one divided by four minus three divided by 10 equals right hand side equation left hand side 60 divided by 60 minus 20 divided by 60 minus 15 divided by 60 minus 18 divided by 60 equals right hand side seven divided by 60

Then, to check your work, calculate this fraction with the original total of 240: equation sequence seven divided by 60 multiplication 240 equals seven divided by 60 times one multiplication 240 super four divided by one equals 28.

Exercise symbol Exercise 2: Timing is Everything

Woman cooking

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?

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Answer

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

equation sequence two divided by three multiplication equals two super one divided by three multiplication five divided by two super one equals five divided by three equals full stop

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 two multiplication 60 plus 30 minutes, or 150 minutes.

two divided by three multiplication 150 minutes is the same as both 100 minutes, and 1 hour and 40 minutes.

Exercise symbolExercise 3: Mowing Lawns

Man mowing lawn

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?

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Answer

You must determine how many times three divided by four goes into . The calculation is equation sequence three divided by four equals 33 divided by four division three divided by four equals 33 times 11 divided by four times one multiplication four super one divided by three sub one equals 11. Therefore, you could mow 11 lawns, if you work a full day.

Exercise symbolExercise 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.

Number 1

(a) one divided by three plus one divided by four

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Answer

(a) Both these fractions are less than one divided by two, so you would expect the answer to be less than 1. equation sequence one divided by three plus one divided by four equals four divided by 12 plus three divided by 12 equals seven divided by 12.

(b) one divided by three minus one divided by four

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Answer

(b) Since one divided by three is less than one divided by two, and a further fraction is subtracted, the answer will be less than 1. equation sequence one divided by three minus one divided by four equals four divided by 12 minus three divided by 12 equals one divided by 12.

(c) one divided by three multiplication one divided by four

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Answer

(c) Since this calculation finds a third of a fraction that is less than 1, the answer will be less than 1. equation sequence one divided by three minus one divided by four equals four divided by 12 minus three divided by 12 equals one divided by 12.

(d) one divided by three division one divided by four

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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. equation sequence one divided by three division one divided by four equals one divided by three multiplication four divided by one equals four divided by three equals.

(e) one division one divided by four

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Answer

(e) This calculation is equivalent to asking “How many quarters are there in 1?” so you should expect the answer 4. equation sequence one division one divided by four equals one multiplication four divided by one equals four divided by one equals four.

(f) two multiplication one divided by four

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Answer

(f) Since one divided by four is less than one divided by two, you would expect two lots of one divided by four to be less than 1. equation sequence two multiplication one divided by four equals two super one divided by one multiplication one divided by four squared equals one divided by two.

6.4.4 Practice with Dividing Fractions

6.6 Quiz Time