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Percentages 17/10/2015 1 17 October 2015

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Contents Converting between Fractions Decimals and Percentages Finding a Percentage Profit & Loss Reverse Percentages Writing as a Percentage 17/10/2015 2

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Converting between F, D & P Converting a percentage to a fraction 40% means 40 out of every 100 Don’t forget to cancel down, if possible

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Converting between F, D & P Converting a percentage to a decimal 67% means i.e. 67 100 Remember by 100 ? HTU 67 6 7 So, 67% = 0.67

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Converting between F, D & P Converting a decimal to a percentage Reverse the process i.e. X by 100 HTU 043 4 3 So, 0.43 = 43%

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Converting between F, D & P Converting a fraction to a percentage Convert to a decimal first then to a percentage i.e. Then, change to a percentage, x by 100 So, = 0.6 = 60%

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Finding a Percentage - Remember, 10% = To find we by 10 Also, 1% = And, to find we by 100 Without a Calculator

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Finding a Percentage - Use these facts to find any percentage i.e. Find 32% of $240 10% = $24 and 1% = $2.40 So, 30% = 3 x $24 = $72 and 2% = 2 x $2.40 = $4.80 32% = $72.00 + 4.80 = $76.80 Without a Calculator

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Finding a Percentage - 55% of 120 children at the theatre were boys, how many were boys ? 10% = 12 and 1% = 1.2 So, 50% = 5 x 12 = 60 and 5% = 5 x 1.2 = 6 55% = 60 + 6 = 66 boys (5% can also be found by using ½ of 10%) Without a Calculator

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Finding a Percentage - Change percentage to a decimal first eg. Find 28% of 690 28% = 0.28 and “of” means multiply So 28% of 690 is 0.28 x 690 Type into your calculator Answer = 193.2 With a Calculator

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Finding a Percentage - Another example, find 17.5% of $250 So, 0.175 x 250 Type into calculator Answer = $43.75 Find 32.5% of 1200 … 0.325 x 1200 = With a Calculator 390

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Profit & Loss 2 types of question Type 1 - A car was bought for $1200 and was later sold at a 15% profit, how much was it sold for ? Find 15% and then add it on to $1200 If it were sold for a 24% loss Find 24% and then take it off the $1200

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Profit & Loss Type 2 – A car was bought for $1200 and later sold for $1500, what is the percentage profit ? Use the format To create a fraction Cancel to simplest form and then change to a percentage Actual Profit (or Loss) Original Amount

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Profit & Loss A car was bought for $1200 and later sold for $1400, what is the percentage profit ? Actual Profit Original Amount

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Profit & Loss A cycle was bought for $600 and later sold for $450, what is the percentage loss ? Actual Loss Original Amount

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Reverse Percentages The original amount is always 100% A reduction of 20% means the new price is 80% of original An increase of 15% means the new price is 115% of original Use the calculator method to find original amount

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Reverse Percentages eg. In a 25% sale a sofa costs $480, how much did it cost before the sale ? 25% reduction means 75% of original i.e. 100% - 25% = 75% So, £480 0.75 = $640 Price before Sale ? Price after Sale £480 ÷ 0.75 x 0.75

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Reverse Percentages eg. Following a 10% increase petrol now costs $1.20 per litre, how much did it cost before the increase ? 10% increase means 110% of original So, $1.20 1.10 = $1.09 per litre Price before increase ? New Price $1.20 ÷ 1.10 x 1.10

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Writing as a Percentage One quantity as a percentage of another eg. Aylish scored 32 out of 50 in a science test and 48 out of 80 in maths Write as a fraction first, then cancel down ScienceMaths = 64%= 60%

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Writing as a Percentage What percentage of cars are Green ? 22 out of 122 were green, so Change to a decimal Then convert to a percentage Car Park Survey ColourFrequency Green22 Silver43 Black57 =18%

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Session Summary Converting between Fractions Decimals and Percentages Finding a Percentage Profit & Loss Reverse Percentages Writing as a Percentage Next week - Ratio 17/10/2015 21

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