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Published byLaurence Freeman Modified over 7 years ago

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Getting sick of powerpoints yet?

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Now it is time for calculators If you haven’t got one it may get difficult

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Writing a fraction as a percentage We saw that 7 = 35 = 35% 20 100 With more difficult fractions this is not so simple eg. 23 35

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23 as a percentage 35 Write the fraction as a decimal 23= 23 ÷ 35 = 0.657142857….. 35 Multiply by 100 0.657142857 x 100 = 65.7% (to 1 d.p.)

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18 as a percentage 70 18 = 18 ÷ 70 = 0.2571……. 70 0.2571 x 100 = 25.7% (to 1 d.p.)

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Now for finding a percentage of an amount

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Two slightly different approaches

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Method 1 1.Find 1% by dividing by 100 2.Multiply this by the percentage you want to find Find 32% of 450 1% of 450 = 4.5 (450÷100) 32% of 450 = 32 x 4.5 = 144

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Try this one – 27% of 46 1% of 46 = 46 ÷ 100 = 0.46 27% of 46 = 27 x 0.46 = 12.42

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Method 2 1.Change the percentage you want to find into a decimal 2.Multiply your ‘amount’ and ‘decimal percentage’ together Find 62% of 93 62% = 0.62 62% of 93 = 0.62 x 93 = 57.66

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Try this one – 87% of 58 87% = 0.87 87% of 58 = 0.87 x 58 = 50.46

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The second method is important for questions involving ‘compound interest’

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Compound interest is paid at regular intervals (usually yearly)… You earn interest on your total amount (original amount plus any interest you have already received)

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Need to write the percentage as a decimal If you are paid 8% interest, you will end up with 108% of your starting amount. 108% as a decimal is 1.08 Instead of finding 8% and adding it on, you can find 108% by multiplying by 1.08

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The value of a £52000 house goes up 4% - find the new value House is now worth 104% of what it was originally 104% = 1.04 (104 ÷ 100) New value = £52000 x 1.04 = £54080

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A teacher gets a 2.5% pay rise. If he was paid £18500 originally, what is his new salary? Salary is now 102.5% of what it started at 102.5% = 1.025 (102.5 ÷ 100) New salary = £18500 x 1.025 = £18962.50

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We can use these ‘multipliers’ when a value decreases too.

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The value of a car falls 14% from its value of £9800. Find the new value Car is now worth 86% (100 – 14) of its original value. 86% = 0.86 (86 ÷ 100) New value = £9800 x 0.86 = £8428

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Find the multipliers which correspond to these percentage increases/decreases 8% decrease 0.92 7% increase 1.07 14% increase 1.14 36% decrease 0.64 17.5% increase 1.175 3.5% decrease 0.965

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Compound interest for yearly savings n = number of years Savings = original savings x (percentage) percentage must be written as multiplier eg. 6% interest = 1.06 n

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If you put £500 in a bank for 4 years and were paid 3% interest per year –how much would you have? Savings = original savings x (percentage) Percentage = 3% so multiplier = 1.03 No. of years, n = 4 Savings = £500 x 1.03 = £562.75 n 4

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If you put £100 in a bank for 24 years and were paid 4% interest per year –how much would you have? Savings = original savings x (percentage) Percentage = 4% so multiplier = 1.04 No. of years, n = 24 Savings = £100 x 1.04 = £256.33 n 24

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Also works for decreases

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A car loses 12% of its value each year. What is it worth after 7 years if it cost £12000 when new? 12% decrease = 0.88 Value = £12000 x 0.88 = £4904.11 7

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Percentage Increase And decrease

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Really easy.. % increase (decrease) = increase (decrease) x 100% original value

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A house was bought for £46000 and is now worth £82000. Find the percentage increase in the value of the house. Increase = 82000 – 46000 = £36000 Percentage = 36000 x 100% increase 46000 = 78.2%

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