Taking your first steps into higher education
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Taking your first steps into higher education

3.1 Using fractions and percentages

One way of better understanding the impact of the Browns’ water savings is to express them as fractions and percentages.

Using the example of the Browns’ first water saving measure, not using water outside the house, we can calculate that as a fraction. A fraction should be expressed as a numerator (the saving) and a denominator (the total water used):

20 divided by 400

In this case the units cancel each other out:

two divided by 40

Fractions can be simplified when the numerator and denominator have a common factor in them. If both the numerator and denominator have common factors, then we can cancel these factors out. In this case the common factor is 2. It is therefore possible to simplify the fraction by cancelling the 2 from both the numerator and denominator of the fraction. Cancelling is equivalent to dividing both the numerator and denominator by the same number.

As a result the Browns’ saving expressed as a fraction is:

one divided by 20

This fraction can also be expressed as a percentage. To do this it is useful to understand that the fraction one divided by 20 is the same as the division sum 1 ÷ 20.

The percentage can therefore be calculated as follows:

one divided by 20 multiplication 100 equals five percent
one divided by 20 multiplication 100

The Browns’ water savings could also have been calculated directly:

20 divided by 400

Activity 6 Fractions and percentages

Timing: Allow approximately 10 minutes

What saving would result from their strategy to reduce their water use for baths and showers to two-thirds of the normal use?

You can calculate the reduced daily amount of water used for baths and showers as follows:

This will be two divided by three multiplication nine six litres equals 64 litres.

The saving is therefore nine six litres minus 64 litres equals 32 litres.

An alternative way to get to this answer is to recognise that if the water use is reduced to two divided by three of its normal value, the saving must be one divided by three of the normal value.

Copy Table 3 into your notebook and enter your answers there.

Question 1

Now express the water saving as a fraction and a percentage of the family’s initial total average daily water use.

Question 2

Now consider the savings from their third strategy. What fraction of their normal use for flushing the toilet will be saved, and what is this saving as a percentage of the normal use for flushing the toilet?

What total daily saving results from their strategy of reducing their water use for flushing the toilet? Express your answer in litres and as a fraction and a percentage of the initial total daily water use.

Table 3 The Browns’ water savings relative to initial total use

Use of water Fraction Percentage
outside use5%
bath/shower
flushing toilet

Comment

Question 1

As a fraction this saving is 32 divided by 400 or two divided by 25 and as a percentage two divided by 25 multiplication 100 percent equals eight percent.

Question 2

By putting a 1-litre ‘save-a-flush’ bag in the cistern, the amount of water used per flush is reduced from the normal 10 litres to 9 litres, a saving of 1 litre.

This saving as a fraction is one divided by 10 and as a percentage one divided by 10 multiplication 100 percent equals 10 percent

  • The daily saving will be one divided by 10 of the daily use for flushing the toilet, so this is one divided by 10 postfix multiplication 120 litres equals 12 litres.

This saving can again be expressed as a fraction of the total daily use as 12 divided by 400 or three divided by 100 and as a percentage three divided by 100 multiplication 100 percent equals three percent.

Table 3 The Browns’ water savings relative to initial total use (complete)

Use of water Fraction Percentage
outside use 5%
bath/shower 8%
flushing toilet 3%

Activity 7 Comparing fractions and percentages

Timing: Allow approximately 2 minutes

Which of the two ways (fractions and percentages) used in the table above to express the relative savings makes them easiest to compare?

Comment

The completed table shows that the savings are much easier to compare when expressed as percentages. The savings on water for toilet flushing is lowest – 3% of the total use – followed by outside use (5%), and the largest saving, of 8%, is for baths and showers. The savings are not so easy to compare when expressed as fractions. For example, can you tell from a quick glance which of one divided by 20, two divided by 25 and three divided by 100 is the largest and which is the smallest? 

If you would like to find out more about using fractions and percentages you could take a look at the free badged open course Succeed with maths – Part 1 [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

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