Everyday maths 1
Everyday maths 1

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Everyday maths 1

5 Percentages

Described image
Figure 20 Looking at percentages

Like fractions and decimals, you’ll see plenty of references to percentages in your everyday life. For example:

Described image
Figure 21 Examples of percentages

This section will help you to:

  • order and compare percentages
  • work out percentages in different ways
  • understand how percentages increase and decrease
  • recognise common equivalencies between percentages, fractions and decimals.

So what is a percentage?

  • It’s a number out of 100.
  • 40% means ‘40 out of every 100’.
  • The symbol for percentage is %.
  • 100% means 100 out of 100. You could also say this as the fraction 100 divided by 100.

You may have seen examples of percentages on clothes labels. ‘100% wool’ means that the garment is made entirely of wool and nothing else. ‘50% wool’ means that the garment is half made of wool, half made of other materials.

The following example shows how to work out the percentage discount.

Example: How can you calculate percentage reductions?

An online shop offers a 10% discount on a television that usually costs £400. How much discount do you get?

There are different ways that percentages can be worked out. The method that you choose really depends on the numbers that you are working with.

Here are two methods for solving this problem:

Method 1

A percentage is a number out of 100, so 10% means ‘10 out of 100’. This could also be put as 10 divided by 100, or 10 hundredths.

Just like fractions, we start with finding 1%.

If we first work out one divided by 100 of £400, we can then work out of 10 divided by 100 of £400. To find one divided by 100 of £400:

400 ÷ 100 = 4

So 10/100 of £400 is:

4 × 10 = 40

The discount is £40.

If you think of 10% as a large fraction, 10 divided by 100, you use the rule of dividing by the denominator (the bottom number in a fraction) and multiplying by the numerator (the top number).

There is an alternative method for finding the answer.

Method 2

A percentage is a number out of 100, so 10% is 10 divided by 100, which is the same as saying one divided by 10.

If we want to find out 10% of £400, that’s the same as finding out one divided by 10 of £400:

400 ÷ 10 = 40

This gives us the answer £40.

Which method do you prefer?

  • Method 1 will always work.
  • Method 2 can be used to work out percentages in your head if the numbers are suitable.

If you want to use Method 2, here are some common percentages given in fraction form:

10% = one divided by 10

25% = one divided by four

50% = one divided by two

75% = three divided by four

If you want to know what 20% of a number is, work out 10% and multiply the answer by 2.

Similarly, if you want to know what 30% is, work out 10% and multiply the answer by 3.

If you need to know 5%, work out 10% and then halve the answer.

Use the example above to help you with the following activities. Remember to check your answers once you have completed the questions.

Activity 14: A holiday discount

You need to pay a 20% deposit on a holiday that costs £800. How much is the deposit?

Answer

Method 1

In order to identify how much the deposit is, you need to find out what 20% (20 divided by 100) of £800 is. To do this, first you need to find out one divided by 100 of £800:

  • 800 ÷ 100 = 8

So 20 divided by 100 of £800 is:

  • 8 × 20 = 160

The deposit is £160.

Method 2

In order to calulate 10%, or one divided by 10, you need to divide the number by 10:

  • 800 ÷ 10 = 80

You now have 10% and you need 20%. Therefore you need to multiply your 10% by 2:

  • 80 × 2 = 160

The deposit is £160.

Activity 15: Comparing discounts

The same diamond ring is being sold at different prices, and with different percentage discounts, in two different shops.

Described image
Figure 22 Comparing percentage discounts

Which shop offers the better deal?

Please check your answers before you move on.

Answer

In order to identify Shop A’s discount, you need to find out what 25% (25 divided by 100) of £500 is. To do this, first you need to find out one divided by 100 of £500:

  • 500 ÷ 100 = 5

So 25 divided by 100 of £500 is:

  • 5 × 25 = 125

The discount is £125, so you would have to pay:

  • £500 – £125 = £375

In order to identify Shop B’s discount, you need to find out what 10% (10 divided by 100) of £400 is. To do this, first you need to find out one divided by 100 of £400:

  • 400 ÷ 100 = 4

So 10 divided by 100 of £400 is:

  • 4 × 10 = 40

The discount is £40, so you would have to pay:

  • £400 – £40 = £360

So Shop B offers the best deal.

FSM_1

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has nearly 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus