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Percentage Increases and Decreases

Percentage Increases and Decreases. Tuesday, 07 October 2014. Objective. Learn how to carry out percentage increases and decrease. Percentage Increase and Decrease. £350. 10% ↓. 10% ↑. Find 10% and add it on. Find 10% and take it off. 0.10 x 350 = 35. 0.10 x 350 = 35. £385.

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Percentage Increases and Decreases

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  1. Percentage Increases and Decreases Tuesday, 07 October 2014

  2. Objective Learn how to carry out percentage increases and decrease.

  3. Percentage Increase and Decrease £350 10% ↓ 10% ↑ Find 10% and add it on. Find 10% and take it off. 0.10 x 350 = 35 0.10 x 350 = 35 £385 £315

  4. Percentage Increase and Decrease £350 10% ↓ 10% ↑ X 1.10 X 0.90 £315 £385

  5. 28.6 18 • Increase 26 by 10%. • Increase 15 by 20%. • Increase 120 by 11%. • Increase 500 by 5%. • Increase 42 by 8% 133.2 525 45.36 • Decrease 256 by 10%. • Decrease 165 by 20%. • Decrease 125 by 11%. • Decrease 510 by 5%. • Decrease 56 by 8% 230.4 132 111.25 484.5 51.52

  6. Practical Problems The next few problems are all practical problems where you have to read the question, pick out the key information and solve.

  7. Example The population of Somalia is 9.9 million. It is estimated to be increasing at the rate of 3% per year. Estimate the population next year.

  8. Example The population of Somalia is 9.9 million. It is estimated to be increasing at the rate of 3% per year. Estimate the population next year. This is a 3% increase:

  9. Example The population of Somalia is 9.9 million. It is estimated to be increasing at the rate of 3% per year. Estimate the population next year. This is a 3% increase: 1.03 x 9 900 000

  10. Example The population of Somalia is 9.9 million. It is estimated to be increasing at the rate of 3% per year. Estimate the population next year. This is a 3% increase: 1.03 x 9 900 000 = 10 197 000

  11. A new car costs £15 000. After one year the value of the car has decreased by 35%. Work out the value of the car after one year. • A meal in a restaurant costs £36. A service charge of 15% is added. Work out the cost of the meal including the service charge. • A statue is sold at auction for £800. Commission is charged to the buyer at 5% of the selling price. What is the total cost including the commission? • Gareth invests £950 for one year at 6% interest. What is the total value of the investment after one year? • Kai has $750. He spends 5% on clothes. How much does he have left? • Athie receives a gas bill for £70. VAT at 5% is added. How much is the total bill? • A computer costs £450 plus VAT at 17.5%. What is the total cost of the computer? • A man who weighed 14 stone lost 6% of this weight. Work out his new weight.

  12. A new car costs £15 000. After one year the value of the car has decreased by 35%. Work out the value of the car after one year. £9750 • A meal in a restaurant costs £36. A service charge of 15% is added. Work out the cost of the meal including the service charge. £41.40 • A statue is sold at auction for £800. Commission is charged to the buyer at 5% of the selling price. What is the total cost including the commission? £840 • Gareth invests £950 for one year at 6% interest. What is the total value of the investment after one year? £1007 • Kai has $750. He spends 5% on clothes. How much does he have left? $712.50 • Athie recieves a gas bill for £70. VAT at 5% is added. How much is the total bill? £73.50 • A computer costs £450 plus VAT at 17.5%. What is the total cost of the computer? £528.75 • A man who weighed 14 stone lost 6% of this weight. Work out his new weight. 13.16 stone

  13. Extra Problems • A school buys calculators for £5 and sells them for £6. Find the percentage profit. • A man buys a car for £3500 and sells it for £2625. Find his percentage loss. • During 1998, the rent on Karen’s flat increased from £80 to £90 per week. Find the percentage increase in her rent. In the same period, her wages increased from £250 to £280 per week. Comment on your answer. • During 1995 the population of a village decreased from 323 to 260. Find the percentage decrease in the population. • A rectangle has length 12cm, and width 8.5cm. The length is increased by 8.5% and the width by 13.5%. Find the percentage increase in the area of the shape. 20% 25% 12.5% & 12% 19.5% 6.1%

  14. A car worth £16 000 loses ¼ of its value every year. How much will the car be worth after 4 years? • The radioactive substance bismuth-210 decays at a rate of 12.9% each day. Starting with 1kg of bismuth-210, how much is left after 2 weeks? How many more days will it take until there are 100g left? B A

  15. Between 2000 and 2010 the world’s population increased from 6.1 billion to 6.9 billion. Use this information to make predictions about the world’s population may grow in each decade up to 2050. Are your predictions likely to be accurate? • A shop usually sells sports equipment at prices that include a mark up of 40% for profit. The manager decides to have a sale, but still wants to make at least 5% profit on the equipment sold. What is the maximum percentage by which the manager can reduce the usual prices of the equipment in the sale and still make 5% profit?

  16. Plenary Consider whether you were able to solve the grade A problem, the grade B problem or the functional maths problems. Write which grade you have worked at, and think about a target for improving your work.

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