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Succeed with maths: part 1
Succeed with maths: part 1

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2.1 Calculating a result following a percentage increase or decrease

In this section you will concentrate on how to find out the result of a percentage increase and decrease. Like lots of things in maths, there’s more than one way of working this out. The way shown here is designed to make some of the later sections this week easier.

Let’s see how it works with a couple of examples.

A shop front with a coat on display. There is a sign which says 30% off.
Figure 2 Shop sale

A coat originally priced at £80 is now in the sale with 30% off. What is the new sale price?

The original price was £80. That corresponds to 100%. It now has 30% off, so that means you are left with 100% − 30% = 70%. Therefore, to find out how much the coat costs now, you need to find 70% of £80.

To do that, you need to multiply £80 by 70 divided by 100, so

pound 80 multiplication 70 divided by 100 equals pound 80 divided by one multiplication 70 divided by 100

which can be cancelled down to leave pound eight divided by one multiplication seven divided by one equals pound 56.

Now take a look at an example of a percentage increase.

In 2012, a house was sold for £180 000. Its value has now increased by 35%. What is it now worth?

The house started at £180 000 which corresponds to 100%. It’s worth 35% more so the price now corresponds to 135%.

To find its current price you need to find 135% of £180 000. To do that, you need to multiply £180 000 by135 divided by 100 so

prefix pound of 180000 multiplication 135 divided by 100 equals prefix pound of 180000 divided by one multiplication 135 divided by 100

which can be cancelled down to leave prefix pound of 1800 divided by one multiplication 135 divided by one equals prefix pound of 243000.

Now have a go yourself.

Activity 5 Percentage increases and decreases

  1. A type of chocolate used to come in 200g bars. The new bars are 15% smaller than the old ones. How big are the new bars?

Answer

The new chocolate bar is 100% – 15% = 85% the size of the old one. To work out the size of the new bar, you therefore need to find 85% of 200g.

equation sequence part 1 200 times normal g divided by one multiplication 85 divided by 100 equals part 2 two times normal g divided by one multiplication 85 divided by one equals part 3 170 times normal g
  1. In an old job I earnt £25 000 a year. In my new job I earn 10% more. What do I earn now?

Answer

The new pay is 100% + 10% = 110% of the old pay. So to work out the new pay, you need to find 110% of £25000.

equation sequence part 1 prefix pound of 25 000 divided by one multiplication 110 divided by 100 equals part 2 prefix pound of 250 divided by one multiplication 110 divided by one equals part 3 prefix pound of 27 500