6 Equivalencies between fractions, decimals and percentages

Fractions, decimals and percentages are different ways of saying the same thing. It’s an important skill to learn about the relationships (or ‘equivalencies’) between fractions, decimals and percentages to make sure you are getting the better deal.

Figure 31 Looking at equivalencies

Here are some common equivalencies. Try to memorise them – you will come across them a lot in everyday situations:

Extract

10% = one divided by 10 = 0.1

20% = one divided by five = 0.2

25% = one divided by four = 0.25

50% = one divided by two = 0.5

75% = three divided by four = 0.75

100% = 1 = 1.0

Look at the following example. If you can identify equivalences, they’ll make it easier to make simple calculations.

Example: Mine’s a half

What is 50% of £200?

Method

Since 50% is the same as one divided by two, so:

Extract

50% of £200 = one divided by two of £200 = £100

Refer to the common equivalencies above (if you need to) to help you with the following activity. Remember to check your answers once you have completed the questions.

Activity 36: Looking for equivalencies

  1. What is 0.75 as a fraction?

  2. If you walked 0.25 km each day, what fraction of a kilometer have you walked?

  3. House prices have increased by one divided by two in the last five years. What is this increase as a percentage?

  4. A DIY shop is holding a ‘50% off’ sale on kitchens. What is this discount as a fraction?

  5. You buy an antique necklace for £3 000. After ten years, its value increases by 20%. What is this increase as a decimal?

  6. A headline reads ‘Number of Ulster Scots speakers predicted to drop by 10%’. What is this decrease as a fraction?

  7. What percentage of an hour is 15 minutes?

Answer

  1. 0.75 as a fraction is three divided by four.

  2. 0.25 is the same as one divided by four, so you will have walked one divided by four of a kilometre.

  3. one divided by two is the same as 50%, so the increase is 50%.

  4. 50% is the same as one divided by two, so the discount as a fraction is one divided by two.

  5. 20% is the same as 0.2, so the increase as a decimal is 0.2.

  6. 10% is the same as one divided by 10, so according to the headline, the number is predicted to drop by one divided by 10.

  7. Think of this as a fraction first: 15 minutes is a quarter (one divided by four) of an hour. one divided by four is the same as 25%, so 15 minutes is 25% of an hour.

If you find that you are struggling to understand how to convert, please look at the following resource:

Transcript (opens in new window)

Summary

Knowing the common equivalencies between fractions, decimals and percentages is important when trying to compare discounts when shopping or choosing a tariff when paying your bills.

OpenLearn - Everyday maths 1 (Northern Ireland)
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