Everyday maths 2 (Wales)
Everyday maths 2 (Wales)

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Everyday maths 2 (Wales)

8.2 Expressing one number as a percentage of another

Sometimes you need to write one number as a percentage of another. You have already practised writing one number as a fraction of another; this just takes it a bit further.

Example 1: What percentage are women?

A class is made up of 21 women and 14 men, what percentage of the class are women?

To work this out, you start by expressing the numbers as a fraction. You then multiply by 100 to express as a percentage.

The formula is:

  • a times m times o times u times n times t postfix times italic italic times italic w times e postfix times italic italic n times e times e times d divided by t times o times t times a times l × 100

In this case, 21 out of a total of 35 people are women so the sum we do would be:

  • 21 divided by 35 × 100

The fraction line is also a divide line, so if you were doing this on a calculator you would do:

  • 21 ÷ 35 × 100 = 60%

How would you work this out without a calculator?

There are different ways you can make the calculation. Two methods are shown below.

Method 1

  • 21 multiplication times 100 divided by 35

You start by multiplying the top number in the fraction by 100. The bottom number will stay the same:

  • equation left hand side 21 postfix times multiplication 100 divided by 35 equals right hand side 2100 divided by 35

Now you need to cancel the fraction down as much as possible:

  • 2100 divided by 35 ÷ top and bottom by 5 = 420 divided by seven, then, ÷ top and bottom by 7 = 60 divided by one

Anything over 1 is a whole number so the answer is 60.

So 60% of the class are women.

Note: When using this method, if you cancel as far as possible and you do not end up with an answer over 1, you will need to divide the top number by the bottom number to work out the final answer, e.g. the fraction 15 divided by four cannot cancel any further, so:

  • 15 ÷ 4 = 3.75

Method 2

The other method involves expressing the fraction as a decimal first and then converting it to a percentage. This means that you multiply by 100 at the very end of the calculation.

A local attraction sold 150 tickets last bank holiday, 102 of which were full price. What percentage of the tickets sold were at the concessionary price?

Work out the number of concessionary tickets sold:

  • 150 – 102 = 48

Write the number of concessionary tickets sold as a fraction of the total number sold:

  • 48 divided by 150

Cancel down your fraction:

  • 48 divided by 150 ÷ top and bottom by 6 = eight divided by 25

Once you cannot cancel any further, you need to divide the top number by the bottom number to express as a decimal:

  • 8 ÷ 25 = 0.32

Described image
Figure 10 Expressed as a decimal: 8 divided by 25

Finally, multiply the decimal answer by 100 to express as a percentage:

  • 0.32 × 100 = 32%

So 32% of the tickets were sold at the concessionary price.

Activity 19: Expressing one number as a percentage of another

Use whichever method you prefer to calculate the answers to the following. Give answers to two d.p. where appropriate.

Hint: make sure your units are the same first.

  1. What percentage:

    • a.of 1 kg is 200 g?

    • b.of an hour is 48 minutes?

    • c.of £6 is 30p?

Answer

  1.  

    • a.1 kg = 1000 g

      200 divided by 1000 × 100 = 20%

    • b.1 hour = 60 minutes

      48 divided by 60 × 100 = 80%

    • c.£1 = 100 p

      30 divided by 600 × 100 = 5%

  1. Bea swam 50 laps of a 25 m swimming pool in a charity swim. A mile is almost 1600 m. What percentage of a mile did Bea swim?

Answer

  1. 50 × 25 = 1250 m

    1250 divided by 1600 × 100 = 78.13% (to two d.p.)

  1. A student gets the following results in the end of year tests:

Table 8

 MathsEnglishScienceArt
Mark achieved64147256
Possible total mark802012070
  • Calculate her percentage mark for each subject.

Answer

Maths: 64 divided by 80 × 100 = 80%

  

English: 14 divided by 20 × 100 = 70%

  

Science: 72 divided by 120 × 100 = 60%

  

Art: 56 divided by 70 × 100 = 80%

  1. Susan is planting her flower beds. She plants 13 yellow flowers, 18 white flowers and 9 red ones. What percentage of her flowers will not be white?

Answer

  1. Number not white = 13 + 9 = 22

    Total number she is planting = 13 + 18 + 9 = 40

    22 divided by 40 × 100 = 55%

    55% of the flowers will not be white.

  1. A building society charges £84 interest on a loan of £1200 over a year. What percentage interest is this?

Answer

  1. 84 divided by 1200 × 100 = 7%

    The interest rate is 7%.

Next you will look at percentage change. This can be useful for working out the percentage profit (or loss) or finding out by what percentage an item has increased or decreased in value.

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