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© Boardworks Ltd of 56 Percentages Stage 7 Chapter

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© Boardworks Ltd of 56 Objectives Solve percentage problems involving increasing and decreasing by using a multiplier

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© Boardworks Ltd of 56 Calculating percentages using fractions Remember, a percentage is a fraction out of % of 90, means 15 hundredths of 90 or × 90 = 15 × = 27 2 = Find 15% of 90

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© Boardworks Ltd of 56 Calculating percentages using decimals We can also calculate percentages using an equivalent decimal operator. 4% of 9 =0.04 × 9 = 4 × 9 ÷ 100 = 36 ÷ 100 = 0.36 What is 4% of 9?

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© Boardworks Ltd of 56 Complete the activity Calculating percentages

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© Boardworks Ltd of 56 Percentage increase There are two methods to increase an amount by a given percentage. The value of Franks house has gone up by 20% in three years. If the house was worth £ three years ago, how much is it worth now? Method 1 We can work out 20% of £ and then add this to the original amount. = 0.2 × £ = £ The amount of the increase = 20% of £ The new value = £ £ = £

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© Boardworks Ltd of 56 Percentage increase We can represent the original amount as 100% like this: 100% When we add on 20%, 20% we have 120% of the original amount. Finding 120% of the original amount is equivalent to finding 20% and adding it on. Method 2 If we dont need to know the actual value of the increase we can find the result in a single calculation.

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© Boardworks Ltd of 56 Percentage increase So, to increase £ by 20% we need to find 120% of £ % of £ = 1.2 × £ = £ In general, if you start with a given amount (100%) and you increase it by x %, then you will end up with (100 + x )% of the original amount. To convert (100 + x )% to a decimal multiplier we have to divide (100 + x ) by 100. This is usually done mentally.

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© Boardworks Ltd of 56 Here are some more examples using this method: Increase £50 by 60%. 160% × £50 =1.6 × £50 = £80 Increase £24 by 35% 135% × £24 =1.35 × £24 = £32.40 Percentage increase Increase £86 by 17.5% % × £86 =1.175 × £86 = £ Increase £300 by 2.5% % × £300 =1.025 × £300 = £307.50

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© Boardworks Ltd of 56 Percentage decrease There are two methods to decrease an amount by a given percentage. A CD walkman originally costing £75 is reduced by 30% in a sale. What is the sale price? Method 1 We can work out 30% of £75 and then subtract this from the original amount. = 0.3 × £75 = £ % of £75The amount taken off = The sale price = £75 – £22.50 = £52.50

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© Boardworks Ltd of 56 Percentage decrease 100% When we subtract 30% 30% we have 70% of the original amount. 70% Finding 70% of the original amount is equivalent to finding 30% and subtracting it. We can represent the original amount as 100% like this: Method 2 We can use this method to find the result of a percentage decrease in a single calculation.

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© Boardworks Ltd of 56 Percentage decrease So, to decrease £75 by 30% we need to find 70% of £75. 70% of £75 = 0.7 × £75 = £52.50 In general, if you start with a given amount (100%) and you decrease it by x %, then you will end up with (100 – x )% of the original amount. To convert (100 – x )% to a decimal multiplier we have to divide (100 – x ) by 100. This is usually done mentally.

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© Boardworks Ltd of 56 Here are some more examples using this method: Percentage decrease Decrease £320 by 3.5%. 96.5% × £320 =0.965 × £320 = £ Decrease £1570 by 95%. 5% × £1570 =0.05 × £1570 = £78.50 Decrease £65 by 20%. 80% × £65 =0.8 × £65 = £52 Decrease £56 by 34% 66% × £56 =0.66 × £56 = £36.96

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© Boardworks Ltd of 56 Complete the activity Percentage increase and decrease

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