percentages

• how do you find the percentage of a number?

  divide number by 100. multiply divided number by percentage
• what is 8% of 40?

  40 / 100 = 0.04

  0.04 x 8 = 3.2
• what is 160% of 18?

  18 / 100 = 0.18

  0.18 x 160 = 28.8
• how do you increase a number by a percentage?

  find new percentage by adding percentage increase to 100. divide number by 100. multiply number by percentage
• 8400 is increased by 5%. find the new number

  100% + 5% = 105%

  8400 / 100 = 84

  84 x 105 = 8820
• how do you decrease a number by a percentage?

  find new percentage by subtracting percentage decrease from 100%. divide number by 100. multiply new number by percentage.
• 8400 is decreased by 5%. find new number


  100% - 5% = 95%

  8400 / 100 = 84

  84 x 95 = 7980
• how do you find the percentage decrease if you have the new and original number?

  difference between original and new number divided by original number (original number aka higher number / difference between both numbers) times by 100.
• original number was 65 and was reduced to 55.25. what is the percentage decrease?

  65 - 55.25 = 9.75

  9.75 / 65 = 0.15

  0.15 x 100 = 15%
• what are reverse percentages?

  when you calculate the original price from the new price and percentage increase/ decrease rather than the other way round.
• how do you find the original number if you have the new number and percentage increase?

  finding new percentage by adding percentage increase to 100%. divide this percentage by 100. divide number by new percentage
• after a 12% pay rise jo’s salary was £28,560. what was her salary before this increase?

  100% + 12% = 112%

  112 / 100 = 1.12

  £28,560 / 1.12 = 25,500
• how do you find the original number if you have the new number and percentage decrease?

  find new percentage by subtracting percentage decrease from 100%. divide by 100. divide number by new percentage
• after a 45% reduction in a sale a shirt costs £22. what was its price before the sale?

  100% - 45% = 55%

  55% / 100 = 0.55

  £22 / 0.55 = £40
• a TV costs £752 including 17.5% VAT. how much of the cost is VAT? do you use normal or reverse percentages to calculate this?


  100% + 17.5% = 117.5%

  117.5% / 100 = 1.175

  £752 / 1.175 = £640

  £752 - £640 =£112

  reverse percentages.
• the average attendance at a football club fell by 7% in 2005. if 2030 fewer people went to matches in 2005, how many went in 2004?

  2030 = 7%

  2030 / 7 = 290 (1%)

  (to find 100%, the amount in 2004, multiply 1% by 100)

  290 x 100 = 29,000
• what is compound interest?

  the amount added onto a bank account each year based on the growing amount in the account
• which is the better investment over 10 years?

  1. £20,000 at 12% compound interest PA (per annum)
  2. £30,000 at 8% compound interest PA


  1)one year = £20,000 x 1.12 = £24,000

  ten years = £20,000 x (1.12)10 = £62,116.96

  interest = £62,116.96 - £20,000 = £42,116.96

  2)one year = £30,000 x 1.08 = £32,400

  ten years = £30,000 x (1.08)10 = £64,767.75

  interest = £64,767.75 - £30,000 = £34,767.75

  option 1 is a better investment.
• what is simple interest?

  the amount added onto a bank account each year based only on the original amount in the account
• every year jo gets 3% simple interest on her £200 savings. how much interest will she have after five years?

  £200 x 0.03 = £6

  £6 x 5 NOT (£6)5 = £30 interest.