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Succeed with maths: part 1
Succeed with maths: part 1

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7 What percentage is it?

You probably agree that comparing percentages can be easier than comparing fractions. So it is useful to know when you have a certain quantity, how to write it as a percentage of another, usually larger, number.

For example, in a test if you got 42 out of 70 , what percentage did you get?

Person taking an exam on a table.

Whenever you have numbers for a part of a total and the total, you can calculate the percentage by first expressing the numbers as a fraction. So the number for the total marks is the fraction’s denominator and the number for marks received is the numerator. You can then turn this fraction successfully into a percentage.

So in this example, the fraction is 42 divided by 70. Remember that to turn a fraction into a percentage you first multiply by 100 per cent and then simplify, as shown below:

42 divided by 70 multiplication 100 percent equals 42 divided by 70 sub seven multiplication 100 super 10 divided by one percent equals 42 super six divided by seven sub one multiplication 10 divided by one percent equation sequence part 1 equals part 2 six multiplication 10 divided by one multiplication one equals part 3 60 percent

(Note: you also could have simplified 42 divided by 70 to three divided by five first and then turned it into a percentage.)

These calculations show us that in the test you scored 60 per cent.

The calculation 42 ÷ 70 × 100 can be performed even more quickly with a calculator, as can the other percentage calculations, but it is good to get practice on paper to cement your understanding of percentages.

Have a go yourself in the next activity.

Activity 3 What percentage?

Timing: Allow approximately 10 minutes

As before, you may wish to do your working out on paper then put your answers in the boxes provided.

  • a.In a group of 250 children, 75 said that they would prefer to visit the zoo and 25 the cinema. What percentage of children preferred to visit the zoo?
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Start by writing the numbers as a fraction.

75 divided by 250

Now simplify the fraction by dividing the top and bottom by 25, to give:

three divided by 10

Now multiply by 100% to convert to a percentage

three divided by 10 multiplication 100 percent equals 300 divided by 10 percent equals 30 percent

So, 30% of the children preferred to go to the zoo.

  • b.There are 159 important habitats for conservation recognised by the European Habitats Directive. Scotland reportedly has 65 of these habitats (Scottish Executive, 2004). What percentage of the total recognised habitats does Scotland have? Give your answer to one decimal place.
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The two numbers shown as a fraction are: 65 divided by 159

You may remember from your study of fractions that a good way to start looking at ways to simplify is to start by seeing if 2, 5 or 10 will divide into both the numerator and the denominator. Looking at the numerator here, you can divide it by 5 to give 13. So you could use either of these numbers to try and simplify the fraction. Unfortunately, if you try and divide 159 by 5 or 13, you don’t get a whole number – this means that you can’t simplify it, so you’ll have to move straight on to multiplying by 100 per cent to work out the percentage.

The percentage is 65 divided by 159 multiplication 100 percent equals 6500 divided by 159 percent equals 40.9 percent (to 1 decimal place). So, Scotland has around 41 per cent of the recognised important habitats.

You’ve covered a lot of the important foundations of percentages this week – understanding these will be a great help when you are faced with new situations that involve them.