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.
Here are some common equivalencies. Try to memorise them – you will come across them a lot in everyday situations:
Extract
10% = 
= 0.1
20% = 
= 0.2
25% = 
= 0.25
50% = 
= 0.5
75% = 
= 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 , so:
Extract
50% of £200 = of £200 = £100
Use the example above to help you with the following activity. Remember to check your answers once you have completed the questions.
Activity 17: Looking for equivalencies
- What is 20% of £600?
- If you walked 0.25 km each day, what fraction of a kilometer have you walked?
- House prices have increased by in the last five years. What is this increase as a percentage?
- A DIY shop is holding a ‘50% off’ sale on kitchens. How much would you pay for a new kitchen worth £8,000 in the sale?
- You buy an antique necklace for £3,000. After ten years, its value increases by 20%. How much is it now worth?
Answer
20% is the same as
.- 600 ÷ 5 = 120
So 20% of £600 is £120.
0.25 is the same as
. There are 1,000 m in 1 km.- 1,000 ÷ 4 = 250
So walking 0.25 km is the same as
m, simplified to 
, or of a kilometre.- is the same as 50%.
So house prices have increased by 50% in the last five years.
50% is the same as
.- 8,000 ÷ 2 = 4,000
The discount is £4,000, so the cost of a new kitchen worth £8,000 in the sale is:
- £8,000 – £4,000 = £4,000
20% is the same as
. - 3,000 ÷ 5 = 600
The new value of necklace is:
- £3,000 + £600 = £3,600
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.
Summary
In this section you have learned about common equivalencies between fractions, decimals and percentages.
OpenLearn - Everyday maths 1
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