# 7.4 Self-Check

In this unit, you might have found some portions easier than others. It’s not uncommon to get stuck on difficult problems.

The more you practice, the more your skills improve. It will help to work through the exercises for each section provided below.

## Exercise 1: Signing Up

160 people joined a new Fitness Center on the first day it opened. They were asked about the main reasons they had decided to join the center.

A quarter of the group wanted to take advantage of the discounted payment for those joining on the first day, three-eighths were advised to join by their physician and one-fifth were motivated by watching the Olympics.

(a) How many people had some other reason for joining?

### Answer

(a) A quarter of 160 is .

So, 40 people joined on the first day to take advantage of the discount.

One-eighth of 160 is 20, so three-eighths of 160 is .

So, 60 people were advised to join the center by their physician.

One-fifth of 160 is .

So, 32 people were motivated by watching the Olympics.

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

The number of people who gave some other reason was .

(b) What fraction of the people who joined gave some other reason for joining the center?

### Answer

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

This fraction can then be reduced by dividing each term by 4:

So, of the people joining gave some other reason.

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

Check by calculating

(You could also have used your calculator to work out these fractions.)

## Exercise 2: A Party Cake

A recipe for an iced cake requires pounds of icing.

Two-thirds of the icing is to go on the sides of the cake, with one-third on the top. How much icing should be reserved for the sides of the cake? Give your answer in ounces.

### Answer

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

There are 16 ounces in a pound, so pounds is

So, 24 ounces should be reserved for the sides of the cake.

Alternatively, you might have converted the pounds to ounces. As there are 16 ounces in one pound, there are = = 36 ounces in pounds.

## Exercise 3: Stacking Shelves

A Walmart employee is a shelf stacker. His time for stacking shelves is 50 minutes for an average set of shelves. If he is at work for 9 hours, and he has a 40 minute break in that time, how many sets of shelves will he be able to fill?

### Answer

You need to calculate first how many hours he is working, and then divide that by how long it takes him to complete one set of shelves.

Alternatively, you could convert the 9 hours to minutes: minutes. So he is in the store for 540 minutes.

He has a break of 40 minutes, leaving his working time minutes.

It takes him 50 minutes to stack a set of shelves, so the number of shelves he can stack is sets of shelves.

## Exercise 4: Egyptian Fractions

Unit fractions are fractions which have a numerator of 1, for example and .

The Ancient Egyptians used only the fraction and unit fractions.

For example, could be written as + + .

(a) Can you express and as the sum of unit fractions? How did you work these out?

### Answer

One way to work these out is to use a diagram split into quarters or eighths, with the required fraction shaded.

Alternatively, you can think about the problem practically: means '3 divided by 4'. So imagine three bars of chocolate being shared equally among four people. If you broke all the bars in half and gave one half to each person, there would still be two half bars left. These could be broken in half again, and a quarter given to each person. So each person would get a half and a quarter.

You can check by using the calculator.

The calculator can be accessed on the left-hand side bar under Toolkit.

(b) What is the answer when you add the unit fractions , and ?

### Answer

(b) .

Did this answer surprise you?

(c) (More challenging) The number 60 was very important to the Ancient Egyptians (in a similar way to how the number 10 is important in the modern world). Can you use fractions with the denominator of 60 to find a sum of unit fractions which represent the fraction ?

### Answer

(c) This is one answer:

You can check this answer and the one you got by using the calculator.

The calculator can be accessed on the left-hand side bar under Toolkit.

You might find it interesting to look at Egyptian Fractions on the internet.

7.3.1 Fraction Origami