1 of 56. Percentages

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1 1 of 56 Percentages

2 2 of 56 Convert a percentage to a decimal

3 Copy into your notes 3 of 56 Converting a Percentage to a Decimals Before we use percentages in calculation we need to learn how to convert a percentage into a decimal Percentage 100 Decimal E.g. 1) Convert 56% to a decimal E.g. 2) Convert 6% to a decimal = = 0.06

convert a percentage into a decimal Percentage 100 Decimal E.g. 1) Convert 56% to a decimal E.

4 4 of 56 Your Turn: Convert the following percentages to decimals 1) 76% 2) 25% 3) 92% 4) 8% 5) 6.8% 6) 12.4%

5 5 of 56 Percentage of (percentage of)

6 6 of 56 Copy into your notes Percentage of To work out a percentage of an amount, write the percentage as a decimal and multiply. For example, What is 38% of $65? So key in: 38% = = The calculator will display the answer as We write the answer as $24.70

For example, What is 38% of $65? So key in: 38% = 0.38 0.

7 7 of 56 Calculating percentages

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9 9 of 56 Answers

10 10 of 56 Percentage Increase/Decrease (how to increase or decrease by a percentage)

11 Copy into your notes Percentage increase The value of Frank s house has gone up by 20% in three years. If the house was worth $ three years ago, how much is it worth now? There are two methods to increase an amount by a given percentage. Method 1 (ACHIEVED METHOD) We can work out 20% of $ and then add this to the original amount. The amount of the increase = 20% of $ = 0.2 $ = $ The new value = $ $ = $ of 56

There are two methods to increase an amount by a given percentage.

12 12 of 56 Copy into your notes Percentage increase Method 2 (MERIT METHOD) If we don t need to know the actual value of the increase we can find the result in a single calculation. We can represent the original amount as 100% like this: 100% 20% When we add on 20%, we have 120% of the original amount. Finding 120% of the original amount is equivalent to finding 20% and adding it on.

We can represent the original amount as 100% like this: 100% 20% When we add on 20%, we have

13 13 of 56 Copy into your notes Percentage increase 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.

2 $150 000 = $180 000 In general, if you start with a given amount (100%)

14 14 of 56 Percentage increase Here are some more examples using this method: Increase $50 by 60%. 160% $50 = 1.6 $50 = $80 Increase $86 by 17.5% % $86 = $86 = $ Increase $24 by 35% 135% $24 = 1.35 $24 = $32.40 Increase $300 by 2.5% % $300 = $300 = $307.50

6 $50 = $80 Increase $86 by 17.5%. 117.5% $86 = 1.175 $86 = $101.

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16 16 of 56 Answers

17 17 of 56 Percentage decrease Speakers originally costing $75 are reduced by 30% in a sale. What is the sale price? There are two methods to decrease an amount by a given percentage. Method 1 (Achieved Method) We can work out 30% of $75 and then subtract this from the original amount. The amount taken off = 30% of $75 = 0.3 $75 = $22.50 The sale price = $75 $22.50 = $52.50

Method 1 (Achieved Method) We can work out 30% of $75 and then subtract this from the

18 18 of 56 Copy into your notes Percentage decrease Method 2 (Merit Method) We can use this method to find the result of a percentage decrease in a single calculation. We can represent the original amount as 100% like this: 70% 100% 30% When we subtract 30% we have 70% of the original amount. Finding 70% of the original amount is equivalent to finding 30% and subtracting it.

We can represent the original amount as 100% like this: 70% 100% 30% When we subtract 30% we

19 19 of 56 Copy into your notes 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.

50 In general, if you start with a given amount (100%) and you

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

8 $65 = $52 Decrease $320 by 3.5%. 96.5% $320 = 0.965 $320 = $308.

21 Percentage increase and decrease 21 of 56

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23 23 of 56 Answers

24 24 of 56 Worded percentage increase/decrease questions

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26 26 of 56 Answers

27 27 of 56 Reverse Percentages (reverse percentage)

28 28 of 56 Reverse percentages Sometimes, we are given the result of a given percentage increase or decrease and we have to find the original amount. I bought some jeans in a sale. They had 15% off and I only paid $25.50 for them. What is the original price of the jeans? We can solve this using inverse operations. Let p be the original price of the jeans. p 0.85 = $25.50 so p = $ = $30

29 of 56 Copy into your notes Reverse percentages Sometimes, we are given the result of a given percentage increase or decrease and we have to find the original amount.

29 29 of 56 Copy into your notes Reverse percentages Sometimes, we are given the result of a given percentage increase or decrease and we have to find the original amount. I bought some jeans in a sale. They had 15% off and I only paid $25.50 for them. What is the original price of the jeans? We can show this using a diagram: Price before discount. 0.85% 0.85% Price after discount.

30 30 of 56 Reverse percentages

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33 33 of 56 Answers

34 34 of 56 GST

35 Copy into your notes GST GST: Goods and Services Tax GST at 15% is a tax applied by the government on all goods and services bought and sold in NZ Item pre GST = cost or GST exclusive or GST not included Price before GST + GST = Price including GST or GST inclusive GST Exclusive + GST = GST Inclusive 35 of 56 35

36 Copy into your notes x 1.15 GST exclusive GST inclusive of 56 Take care: if finding just the GST, multiply by 0.15

37 37 of 56 Your Turn: fill the blanks in the table Item Cost exclusive GST GST inclusive T shirt $18? $20.70 Car $4000? Purse? $25 $21.74 $ $4600 I-pod? $300 TV $450? $67.50 Book $45? $6.75 Coke? 9c? 60c 69c

4 Percentages Chapter notes

4 Percentages Chapter notes GCSE Specification concepts and skills Find a percentage of a quantity (N o): 4. Use percentages to solve problems (N m): 4., 4.2, 4., 4.4 Use percentages in real-life situations: