1. Getting sick of powerpoints yet?

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

3. 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

4. 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.)

5. 18 as a percentage 70 18 = 18 ÷ 70 = 0.2571……. 70 0.2571 x 100 = 25.7% (to 1 d.p.)

6. Now for finding a percentage of an amount

7. Two slightly different approaches

8. 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

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

10. 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

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

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

13. 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)

14. 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

15. 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

16. 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

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

18. 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

19. 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

20. 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

21. 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

22. 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

23. Also works for decreases

24. 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

25. Percentage Increase And decrease

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

27. 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%