Getting sick of powerpoints yet

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Getting sick of powerpoints yet?
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Now it is time for calculators

• If you havent 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 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

• Find 1 by dividing by 100
• Multiply this by the percentage you want to find

• Find 32 of 450
• 1 of 450 4.5
• (450100)
• 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

• Change the percentage you want to find into a
  decimal
• 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?
n

• Savings original savings x (percentage)
• Percentage 3 so multiplier 1.03
• No. of years, n 4
• Savings 500 x 1.03
• 562.75

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?
n

• Savings original savings x (percentage)
• Percentage 4 so multiplier 1.04
• No. of years, n 24
• Savings 100 x 1.04
• 256.33

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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

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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