Percentages

Percentages

• 1.
  Percentages
• 2.
  Percentages • Aims To look at percentages and the different methods for calculating them. • Objectives To be able to quickly find common percentages such as 50%, 25% and 10%. To understand the method for calculating a percentage.
• 3.
  Per cent •The term per cent literally translates to per hundred. • We can think of a single per cent as being the same as a 1 100 th. • Many other commonly used percentages can be thought of as simple fractions.
• 4.
  Per cent =Fraction • 50% = 1 2 • 25% = 1 4 • 20% = 1 5 • 10% = 1 10 • 5% = 1 20 • This means to work out these percentages we can simply multiply by the fraction or divide by the inverse value. • So 50% is half and we can divide the original number by 2 to work it out. For 20% we would divide by 5.
• 5.
  Per cent •Because a single per cent is a hundredth then if we have to calculate a whole percentage we can simply work out a hundredth and multiply this by the percentage. • eg • Find 12% of 87 • 1% of 87 is equal to 87÷100 or 0.87 • 0.87 x 12 = 10.44 • So 12% of 87 is 10.44
• 6.
  Per cent •Some times working with small decimals can be tricky. Because of the nature of the sum for calculating percentages, we can alter it so that we multiply by the percentage first and then divide by 100. • eg • Find 12% of 87 • 87 x 12 = 1,044 • 1044 ÷ 100 = 10.44 • So 12% of 87 is 10.44
• 7.
  Practice Questions 17% of 100  20% of 80  25% of 16  50% of 18  40% of 12  35% of 20  20% of 45  25% of 36  120% of 10  150% of 18  125% of 40  700% of 2  133% of 15  12.5% of 72  20% of 105  120% of 105
• 8.
  Practice Questions 17% of 100  20% of 80  25% of 16  50% of 18  40% of 12  35% of 20  20% of 45  25% of 36  17  16  4  9  4.8  7  9  9  120% of 10  150% of 18  125% of 40  700% of 2  133% of 15  12.5% of 72  20% of 105  120% of 105  12  27  50  14  19.95  9  21  126
• 9.
  Finding Per cent • Some times rather than finding the value of a percentage you will want to find the percentage of a value in relation to another. To do this we reverse the sum used to work out a percentage value. • eg • Find 54 as a percentage of 63 • 54÷63 = 0.8571 • 0.8571 x 100 = 85.7%
• 10.
  Finding Per cent • Much like when using a percentage to find a value, when trying to find a percentage of a value we can change the order of the sum to avoid as many decimals as possible. • eg • Find 54 as a percentage of 63 • 54 x 100 = 5400 • 5400 ÷ 63 = 85.7%
• 11.
  Practice Questions 34 from 100  20 from 80  12 from 16  3 from 18  3 from 12  5 from 20  5 from 45  4 from 32  18 from 10  45 from 18  45 from 40  5 from 2  22.5 from 15  45 from 72  5 from 105  147 from 105
• 12.
  Practice Questions 34 from 100  20 from 80  12 from 16  3 from 18  3 from 12  5 from 20  5 from 45  4 from 32  34%  25%  75%  c.16.7%  25%  25%  c.11.1%  12.5%  18 from 10  45 from 18  45 from 40  5 from 2  22.5 from 15  45 from 72  5 from 105  147 from 105  180%  250%  112.5%  250%  150%  62.5%  c.4.8%  140%
• 13.
  • You areout walking and see that the gradient of the hill you are walking up is 18%. If you have walked 5 miles according to your GPS then how much higher are you than when you started? • You are told that the profit margins are being squeezed at local car dealerships to an average of 15%. If the average car sales at £6000 then how much profit would a dealer normally expect?
• 14.
  • You areout walking and see that the gradient of the hill you are walking up is 18%. If you have walked 5 miles according to your GPS then how much higher are you than when you started? • 5 miles x 0.18 = 0.9 miles • You are told that the profit margins are being squeezed at local car dealerships to an average of 15%. If the average car sales at £6000 then how much profit would a dealer normally expect? • £6000 / 100 x 15 = £900
• 15.
  • Income taxin Russia is a flat 18%. If we imagine income tax in the UK is 0% upto £10,000 and 22% upto £40,000 then would you be better off after tax if you earned £38,000 in Russia or the UK? • You purchase a coffee while attending a meeting for your company. You get receipt which states the amount includes VAT. How much VAT can your company expect to claim back if the coffee cost £1.50?
• 16.
  • Income taxin Russia is a flat 18%. If we imagine income tax in the UK is 0% upto £10,000 and 22% upto £40,000 then would you be better off after tax if you earned £38,000 in Russia or the UK? • £38,000 x 0.18 = £6840, £28,000 x 0.22 = £6160 You would be better off in the UK • You purchase a coffee while attending a meeting for your company. You get receipt which states the amount includes VAT. How much VAT can your company expect to claim back if the coffee cost £1.50? • £1.50 / 120 x 20 = £0.25 or 25p