1. PERCENTAGES Percentages Equivalence to decimals and fractions Percentage of Percentage Increase and decrease

2. Percentages Percentage means ‘out of 100’ It is basically a fraction 39% means 39 out of one hundred

3. Percentages 100% means 100 out of 100 The whole thing

4. Percentage as Fractions To change a percentage to a fraction place over 100 and simplify Dividing top and Bottom by 5

5. Fractions as Percentages 100= 100 x 1 100 = 50 x 2 100 = 25 x 4 100 = 20 x 5 100 = 10 x 10 LEARN THESE

6. Fractions as Percentages If you know the unitary fraction conversion the rest is just multiplying

7. Converting Fractions to Percentage To change a fraction to percentage Calculate the fraction of 100%

8. Quantities as percentages In a class of 20 students, 12 are men. What % of the students are a) menb) women? Ten chocolates in a box of twenty-five are soft centred. What % is this? The table shows the marks a student gets in his course assignments. Find his % mark for each assignment. What is 450g as a % of 900g? What % of £6 is 30p? Out of 75 people who take a driving test, 45 pass. What % is this? A new car is bought for £8000 and sold one year later for £7000. What is the % loss? Assignment 1234 Mark 18565266 Out of 307080120

9. Percentages as Decimals To write a percentage as a decimal: divide by 100 Move the decimal two places to the left 23% = 0.23 We can use this to find % of 100%=323.5cm 23% = 323.5 x 0.23 23% = 74.405cm

10. Finding 1% Divide by 100 Move the decimal 2 places to the left Find 1% of 323.50cm 100% = 323.50 1% = 323.50/100

11. Finding any Percentage If we know 1% we can calculate any percentage Just multiply Find 23% of 323.5cm This method works always. LEARN IT

12. Finding any Percentage 100% = 323.5 1% = 3.235 23% = 23 x 3.235 =74.405cm 23% of 323.5 = 23 x 323.5 100 = 74.405cm

13. Finding any Percentage Find percentage of the following quantity 1) 28% of 502) 16% of 2503) 15 % of 300 4) 7% of 4005) 31% of 7206) 16% of 240 7) 24% of 898) 52% of 639) 29% of 56 kg 10) 37% of 7 11) 69% 2m12) 12% of 170cm

14. Finding Percentages of- Short Cut - Knowing fraction If you know the fraction equivalent FIND THE FRACTION OF IT’S EASIER 75% of 500cm? LEARN EQUIVALENT FRACTION

15. Finding Percentages of To find percentage of amounts you can change them to fractions. Example What is 25% of £400? 25% =. So 25% of £400 is of £400 is £100. What is 75% of £400? 75% =. So, 75% of £400 is of £400 = 3 x £100 = £300 Find: 50% of £20025% of 40cm10% of $70 20% of $505% of £8075% of 60m 70% of 100kg40% of $5015% of £80

16. Finding Percentages of- Short Cut – Breaking the % Down Instead of calculating 23% directly Break 23% into 20% + 3% 23% of 323.5cm 100%=323.5 10%=32.35 20%=64.7 1%=3.235 3%=9.705 23%= 64.7+9.705 =74.405cm

17. VAT % VAT is now charged at 15%. What is 15% of £310? 100% = £310 10% = £165 (divide both by 10) 5% = £ 82.50 (divide both by 2) 15% = £165 + £82.50 = £247.50 (add)

18. Finding any Percentage Find percentage of the following quantity 1) 28% of 502) 16% of 2503) 15 % of 300 4) 7% of 4005) 31% of 7206) 16% of 240 7) 24% of 89 8) 52% of 63 9) 29% of 56 kg 10) 37% of 7 11) 69% 2m 12) 12% of 170cm

19. Percentage Increase METHOD 1 Calculate % Then add METHOD 2 Add % to 100% Calculate new % Used decimal to calculate %

20. Percentage Decrease METHOD 1 Calculate % Then subtract METHOD 2 Subtract % from 100% Calculate new %

21. % Increase/Decrease A stereo cost £320. In a sale it is reduced by 25%. What is the sale price? An antique clock cost £540. It’s price is increase by 18% in a year. What is it now worth? £6oo put in a bank. After a year the money has increased by 8%. How much is now in the bank? A second hand car costs £2400. The price falls by 45% when it is sold again. How much is it sold for? A season ticket for Bolton FC this season costs £410. It is to go up by 34% next season. How much will a season ticket cost next season? A shirt is slightly soiled so it is reduced by 30%. It was £40.50, how much is it to be sold for?

22. Reverse Questions 15% = £23.40 What is 49%?

23. Reverse Questions After 17% reduction a TV costs £217.46 What was the original price?

24. Compound Interest When money is invested or loaned out the money ‘earns’ an interest – a certain amount per £100 If it is invested for more than one year the interest builds up How much interest would £200 earn at 5% interest in three years?

25. Compound Interest END OF YEAR 1 5% of £200= £10 Total money = £200 + £10 = £210 END OF YEAR 2 5% of £210= £10.50 Total money = £210 + £10.50 = £220.50 END OF YEAR 3 5% of £220.50= £11.025 Total money = £220.50 + £11.025 = £231.525 Rounded £231.53

26. Percentage Point vs Percentage NEWS REPORT Interest rates have risen 1% This means that they have moved one % point If they were 4% they are now 5%