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Everyday maths 1
Everyday maths 1

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6 Equivalencies between fractions, decimals and percentages

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Figure _unit2.6.1 Figure 25 Looking at equivalencies

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.

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

Extract _unit2.6.1

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.

Case study _unit2.6.1 Example: Mine’s a half

What is 50% of £200?

Method

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

Extract _unit2.6.2

50% of £200 = one divided by two 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 _unit2.6.1 Activity 17: Looking for equivalencies

  1. What is 20% of £600?
  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. How much would you pay for a new kitchen worth £8,000 in the sale?
  5. You buy an antique necklace for £3,000. After ten years, its value increases by 20%. How much is it now worth?

Answer

  1. 20% is the same as one divided by five.

    • 600 ÷ 5 = 120

    So 20% of £600 is £120.

  2. 0.25 is the same as one divided by four. There are 1,000 m in 1 km.

    • 1,000 ÷ 4 = 250

    So walking 0.25 km is the same as 250 divided by 1,000 m, simplified to 25 divided by 100, or one divided by four of a kilometre.

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

    So house prices have increased by 50% in the last five years.

  4. 50% is the same as one divided by two.

    • 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
  5. 20% is the same as one divided by five.

    • 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.