11 Fractions and Percentages

Transcription

1 MEP Pupil Text Fractions and Percentages. Fractions, Decimals and Percentages Percentages can be converted to fractions because 'percentage' simply means 'per hundred'. They can also be converted very easily to decimals, which can be useful when using a calculator. Fractions and decimals can also be converted back to percentages. Worked Example Convert each of the following percentages to fractions. 0% (b) 0% (c) % 0 0 0% = (b) 0% = (c) % = = = = Worked Example Convert each of the following percentages to decimals. 0% (b) % (c) % 0% = 0 00 (b) % = 00 (c) % = 00 = 0. = 0. = 00. Worked Example Convert each of the following decimals to percentages. 0.0 (b) 0. (c) = Information 00 (b) 0. = 00 (c) 0.9 = 9 0 = % = % = 'Per cent' comes from the Latin, 'per centum', which means 'for each hundred'. = 90%

2 MEP Pupil Text Worked Example Convert each of the following fractions to percentages. 0 (b) (c) To convert fractions to percentages, multiply the fraction by 00%. This gives its value as a percentage. 0 = 00% (b) 0 = 00% (c) = 00% Exercises = 0% = % = %. Convert each of the following percentages to fractions, giving your answers in their simplest form. 0% (b) 0% (c) 90% (d) % (e) % (f) % (g) % (h) % (i) % (j) % (k) % (l) %. Convert each of the following percentages to decimals. % (b) 0% (c) % (d) 0% (e) % (f) % (g) % (h) % (i) % (j) % (k) % (l) %. Convert the following decimals to percentages. 0. (b) 0. (c) 0. (d) 0.0 (e) 0. (f) 0. (g) 0. (h) 0.0 (i) 0.0 (j) 0. (k) 0. (l) 0.. Convert the following fractions to percentages. (e) (i) 0 (b) (f) (j) (c) (g) (k) (d) (h) (l) 0

3 . MEP Pupil Text. Complete the equation (b) Change 0? = =? to a percentage. (MEG). Water is poured into this jug. Copy the diagram and show accurately the water level when the jug is three-quarters full. (b) What percentage of the jug is filled with water? (SEG). Plan of a garden Vegetable Patch Orchard Lawn Pond Not to scale In the garden the vegetable patch has an area of. m. The orchard has an area of. m. What is the total area of the vegetable patch and the orchard? Give your answer to the nearest square metre. (b) The garden has an area of 00 m. (i) The lawn is 0% of the garden. Calculate the area of the lawn. (ii) A pond in the garden has an area of 0 m. What percentage of the garden is taken up by the pond? (SEG). Fractions and Percentages of Quantities Percentages are often used to describe changes in quantities or prices. For example, '0% extra free' '0% discount' 'add % VAT' This section deals with finding fractions or percentages of quantities. Worked Example Find 0% of. This can be done by converting 0% to either a fraction or a decimal.

4 MEP Pupil Text Converting to a fraction Note that 0% = 0 00 = Therefore 0% of = Converting to a decimal =. 0. Note that 0% = 0. Therefore 0% of = 0. =. 0. Worked Example A shopkeeper decides to increase some prices by 0%. By how much would she increase the price of: a loaf of bread costing 90p (b) a packet of cereal costing.00? First note that 0% = 0. 0% of 90p = 0 = 9p. 90p So the cost of a loaf will be increased by 9p. (b) 0% of = 0 =. 00 or 0p. So the cost of a packet of cereal is increased by 0p. Worked Example A farmer decides to sell % of his 00 cows. How many cows does he sell? First note that % =. So he sells cows. % of 00 = =. 00

5 . MEP Pupil Text Worked Example Natasha invests 00 in a building society account. At the end of the year she receives % interest. How much interest does she receive? First convert % to a fraction. % = = 00 0 % of 00 = 0 = So she receives 0 interest. Exercises. Find 0% of 00 (b) 0% of (c) 0% of (d) % of 00 (e) 0% of 00 (f) 90% of 00 (g) % of (h) % of 00 (i) % of 000 (j) 0% of 0 kg (k) 0% of kg (l) 0% of 0 kg (m) % of 00 m (n) 0% of 0 m (o) % of 0. Find (d) of 0 (b) of 0 (c) of 90 of 0 (e) of 0 (f) of A firm decides to give 0% extra free in their packets of soap powder. How much extra soap powder would be given away free with packets which normally contain kg of powder (b). kg of powder?. A house costs A buyer is given a 0% discount. How much money does the buyer save?. John has invested 00 in a building society. He gets % interest each year. How much interest does he get in a year?. Karen bought an antique vase for 0. Two years later its value had increased by %. What was the new value of the vase?. Ahmed wants to buy a new carpet for his house. The cost of the carpet is 0. One day the carpet shop has a special offer of a % discount. How much money does he save by using this offer?

6 MEP Pupil Text. When Wendy walks to school she covers a distance of 00 m. One day she discovers a short cut which reduces this distance by 0%. How much shorter is the new route? 9. Chen earns 0 per week from his part-time job. He is given a % pay rise. How much extra does he earn each week? 0. Gareth weighed 90 kg. He went on a diet and tried to reduce his weight by 0%. How many kilograms did he try to lose?. Kim's mother decided to increase her pocket money by 0%. How much extra did Kim receive each week if previously she had been given.00 per week?. A new-born baby girl weighed kg. In the first three months her weight increased by 0%. How much weight had the baby gained?. Work out 0 of (b) 0% of (c) of metres. (LON). Calculate % of 00. (b) List these fractions in order of size, starting with the smallest., 9,, (MEG). A cake weighs 0 grams. 0% of the cake is sugar. Calculate the weight of sugar in the cake. (MEG). An athletics stadium has 000 seats. % of the seats are fitted with headphones to help people hear the announcements. How many headphones are there in the stadium? (NEAB). Jane wants to buy this car. The deposit is of the price of the car. 00 Jane's father gives her 0% of the price. Will this be enough for her deposit? You must explain your answer fully. Investigation The ancient Egyptians were the first to use fractions. However, they only used fractions with a numerator of one. Thus they wrote as 9 +, etc. What do you think the Egyptians would write for the fractions, 9 0, and?

7 MEP Pupil Text. Quantities as Percentages To answer questions such as, Is it better to score 0 out of 0 or 0 out of 0? it is helpful to express the scores as percentages. Worked Example Express '0 out of 0' and '0 out of 0' as percentages. Which is the better score? '0 out of 0' can be written as 0 0 and '0 out of 0' can be written as 0 0. Changing these fractions to percentages, = 00% and = 00% 0 = % = 0% So '0 out of 0' is the better score, since 0% is greater than %. Worked Example A pupil scores out of 0 in a test. Express this as a percentage. ' out of 0' can be written as. Changing this fraction to a percentage, 0 = 00% = 0%. 0 0 Worked Example Robyn and Rachel bought a set of CDs for 0. Robyn paid and Rachel paid 9. What percentage of the total cost did each girl pay? Robyn paid out of 0, which is 0 = 00% = %. 0 Rachel paid 9 out of 0, which is = 00% = %. 0 0

8 MEP Pupil Text Worked Example David earns 00 per week and saves 0 towards the cost of a new car. What percentage of his earnings does he save? He saves 0 out of 00, which is = 00% =. %. 00 Exercises. Express each of the following as percentages. out of 0 (b) out of (c) out of 0 (d) out of 0 (e) out of 0 (f) out of 0 (g) out of 0 (h) 9 out of 0 (i) out of 0 (j) 0 out of 00 (k) out of 00 (l) 0 out of 00 (m) out of 0 (n) out of 0 (o) out of 0. In a class of children there are 0 girls. What percentage of the class are girls and what percentage are boys?. The price of a bar of chocolate is p and includes p profit. Express the profit as a percentage of the price.. The value of a house is and the value of the contents is 00. Express the contents value as a percentage of the house value.. In the crowd at a football match there were 000 Manchester United supporters and 000 Tottenham supporters. What percentage of the crowd supported each team?. A school won a prize of 000. The staff spent 00 on a new computer and the rest on software. What percentage of the money was spent on software?. A book contained 0 black and white pictures and 0 colour pictures. What percentage of the pictures were in colour?. In a survey of 00 people it was found that people watched EastEnders regularly. Express this as a percentage. 9. James needs another 0 football stickers to complete his collection. There is a total of 00 stickers in the collection. What percentage of the collection does he have already? 0. A 00 ml bottle of shampoo contains 00 ml of free shampoo. What percentage is free?

9 . MEP Pupil Text. Adrian finds that in a delivery of 00 bricks there are 0 broken bricks. What percentage of the bricks are broken?. A glass of drink contains 0 ml of fruit juice and 00 ml of lemonade. What percentage of the drink is lemonade?. A recent survey shows that there are different types of fish in the world. People catch only 9000 different types. What percentage of the different types of fish do people catch? (NEAB). Georgina buys a bar of chocolate. The bar is divided into equal pieces. Georgina eats three pieces of chocolate. What fraction of the bar has she eaten? CHOCOLAT (b) (c) Later in the day Georgina eats of the pieces that are left. How many pieces of chocolate have been eaten altogether? What percentage of the bar has not been eaten? (SEG). More Complex Percentages Not all percentages can be expressed as simple fractions and often figures such as.% may need to be used. In these cases it is often better to work with decimals. Worked Example The cost of a hotel bill is 00. VAT at.% has to be added to this bill. Find the VAT and the total bill. Use.% = 0.. Then So the total bill is Worked Example.% of 00 = = =. Imran has. in his building society account which earns interest of.% per year. How much interest does he get and how much money does he have in his account after the first year?

10 MEP Pupil Text Writing.% as a decimal gives 0.0. So the account now contains Worked Example.% of. = =. 9. = 9. 9 (to the nearest penny) The cost of a large load of concrete blocks is plus VAT at.%. Find the total cost of the concrete blocks. The problem can be solved in one stage by finding.% of. This will give the original amount plus the VAT. Note that.% is. as a decimal. So.% of =. The total price is.0. =. 0. Worked Example Jessica's salary of 000 is to be increased by.%. Find her new salary. Her new salary is 0.% of her old salary. Her new salary is 00. Worked Example 0.% of 000 = = 00. A new car costs 999, but a special offer gives an.% discount. Find the discount price of the car. With an.% discount, 9.% of the original price must be paid. So 9.% of 999 = The discounted price is 9.. = 9. (to the nearest penny)

11 . MEP Pupil Text Exercises. Find each of the following, giving your answers to the nearest penny. % of 0 (b) % of (c).% of 0 (d).% of 0 (e).9% of (f).% of. (g) 0.% of 000 (h) 9.% of (i).% of.. Add.% VAT to. (b) Add.% interest to. (c) Increase a salary of 000 by.%. (d) Increase a price of 99 by.%. (e) Decrease 0 by %. (f) Find the price of a 0 television offer with a % discount. (g) Find the price of an 999 car after a % discount.. A portable CD player has a normal price of 0. In a sale its normal price is reduced by %. Find the sale price. (b) After the sale, normal prices are increased by.%. Find the new price of the CD player.. An ice cream firm sells ice-creams during one summer month. They expect sales to increase by % in the next month. How many ice-creams do they expect to sell?. Peter earns 9000 per year in his new job. He does not pay tax on the first 00 he earns and pays % tax on the rest. How much tax does he have to pay?. Richard and Debbie cancel their holiday at short notice. The travel agents refund % of the 0 they had paid. How much money do Richard and Debbie lose?. A chocolate manufacturer decides to introduce a range of King Size bars which are % larger than normal. A normal bar weighs 0 grams. What would a King Size bar weigh?. A midi-hifi costs plus VAT at %. Its price is increased by %. How much would you have to pay to buy the midi-hifi at the new price? 9. A company pays a Christmas bonus of 0 to each of its employees. This is taxed at %. One year they increase the bonus by %. How much does an employee take home? 0. A new gas supplier offers a 0% discount on the normal price and a further % discount if customers pay directly from their banks. For one household the gas bill is normally 00. Find out how much they have to pay after both discounts.

12 MEP Pupil Text. A mountain bike costs 0 plus VAT. VAT is charged at %. How much is the VAT? (SEG). CASH A discount of % off the marked price if you pay cash SUPER " TV TERMS A deposit of of the marked price then monthly payments of 9. each (b) Mr. Smith buys the television set for cash. How much discount is he allowed? Mr. Jones buys the set on terms. (i) How much must he pay as a deposit? (ii) Multiply 9 by without using a calculator. Show all your working. (iii) Work out the total price that Mr. Jones pays for his television set. (MEG). The usual price of a television set is 9 plus VAT at %. (i) Work out the exact value of % of 9. (ii) What is the usual price of this television set? GANNET STORE BARGAIN OFFER! You pay NO VAT! BERRIES' STORE SALE! OFF USUAL PRICES Gannet Store and Berries' Store are selling larger television sets at reduced prices. The usual price of these sets in both stores is ( 0 plus VAT). (b) (i) Calculate the difference between the reduced prices in the two stores. Show your working clearly. (ii) Which of the stores gives the bigger reduction? (MEG) Information Did you know that a gallon in the UK is 0% bigger than a gallon in the USA?

13 MEP Pupil Text. Percentage Increase and Decrease Percentage increases are calculated using actual increase Percentage increase = initial value 00% Similarly, percentage decreases are calculated using actual decrease Percentage decrease = initial value 00% Worked Example The population of a village increased from to during one year. Find the percentage increase. Worked Example Actual increase = Percentage increase = =. 00% =. % (to decimal places) When a beaker of sand is dried in a hot oven its mass reduces from 0 grams to 0 grams. Find the percentage reduction in its mass. Worked Example Actual reduction = 0 grams 0 grams = 0 grams. 0 Percentage reduction = 0 00% =.%. 9 % John buys calculators for each and then sells them to other students for.90. Find his percentage profit. Actual profit =. 90 = Percentage profit = 00% = %.

14 MEP Pupil Text Exercises. A baby weighed. kg and six weeks later her weight had increased to. kg. Find the percentage increase.. A factory produces video tapes at a cost of p and sells them for.0. Find the percentage profit.. A new car cost 00 and one year later it was sold for 999. Find the percentage reduction in the value of the car.. An investor bought some shares at a price of. each. The price of the shares dropped to.9. Find the percentage loss.. A supermarket offers a 0 discount to all customers spending 0 or more. Karen spends. and John spends.. Find the percentage saving for Karen and John.. After a special offer the price of baked beans was increased from p per tin to p per tin. Find the percentage increase in the price.. The size of a school increased so that it had 0 pupils instead of 0 and teachers instead of. Find the percentage increases in the number of teachers and pupils. Comment on your answers.. In a science experiment the length of a spring increased by cm to 0 cm. Find the percentage increase in the length of the spring. 9. The average cost of a local telephone call for one customer dropped by p to p. Find the percentage reduction in the average cost of a local call. 0. In a year, the value of a house increased from 000 to 000. Find the percentage increase in the value of the house and use this to estimate the value after another year.. A battery was tested and found to power a cassette player for hours. An improved version of the battery powered the cassette player for an extra 0 minutes. Find the percentage increase in the life of the batteries.. The value of a car depreciates as shown in the table. Vehicle Value New 000 After year After years 00 After years 000 During which year is the percentage decrease in the value of the car the greatest?

15 . MEP Pupil Text. Quality Garden Supplies SUMMER SALE! Save 0% on goods totalling 0 or more. (b) (c) Ken bought a ladder marked. How much did he save? Tom needs a new spade. He can buy spade A which is marked.9 or spade B which is marked.. (i) Calculate 0% of.. (ii) How much cheaper would it be for Tom to buy spade B than to buy spade A? Tom's wife suggests that he buys spade A, together with a plant costing.0 which she wants, so that he gets the 0% saving. If he buys the plant and spade A, express the saving as a percentage of the cost of spade A. (MEG). Super Ace Games System Normal Price 0 Sale Price off Work out the sale price of the Super Ace Games System. Mega Ace Games System Normal Price 0 Sale Price (b) Find the percentage reduction on the Mega Ace Games System in the sale. (LON). Jimmy paid 0 for a CD player. He sold it for 0. What was his loss as a percentage of the price he paid? (SEG) Just For Fun The growth rate of the human hair varies from person to person. On average, a human hair grows at a rate of 0. mm per day. If the length of a hair is cm, how long will it take the hair to grow to a length of cm?

16 MEP Pupil Text. Addition and Subtraction of Fractions Note The numerator is the top part of a fraction and the denominator is the bottom part of a fraction. When adding or subtracting fractions they must have the same denominator. Worked Example + =? As both fractions have the same denominator (), they can simply be added to give + = 9 =. Worked Example + =? As these fractions have different denominators, it is necessary to find the lowest common denominator, that is, the smallest number into which both denominators will divide exactly. In this case it is 0, since both and divide into 0 exactly. + = = + 0 Worked Example = 0 = 0 + =? In this example, is the lowest common denominator. 9

17 . MEP Pupil Text + = + = + = = = Worked Example =? Here is the lowest common denominator. = Exercises = =. Give the answers to the following, simplifying them as far as possible. + (b) + (c) + (d) (e) (f) 9 9 (g) 9 + (h) 9 + (i) + (j) 0 0 (k) 9 9 (l). Complete each of the following. + =? + (b)?? + = =? =? 0 0

18 MEP Pupil Text (c)? + = + (d) + = +? =? =? (e)?? + = + (f)?? + = =? =? 0. Find the answers to the following, simplifying them if possible. + (b) + (c) + (d) 0 + (e) + (f) + (g) + (h) 0 + (i) + (j) (k) (l) (m) (n) (o). A garden has an area of hectare. The owner buys an extra hectare of land to increase the size of the garden. What is the new size of the garden?. A large company makes a profit of million in one year and million the next year. Find the total profits for the two-year period. Not to scale. A hole of radius cm is drilled in the middle of a metal cm cm sheet of width cm. How far is it from the edge of the sheet to the hole?. A council decides to turn of a park into a dog-free zone. It later bans dogs from the play area which occupies of the park and which was originally outside 0 the dog-free zone. What fraction of the park is now open to dogs?. Mike has filled of the space on the hard disc in his computer with software. He wants to keep for extra software? of the disc free from software. What fraction of the disc is left

19 . MEP Pupil Text 9. In a school of the children eat school dinners, bring packed lunches and the rest go home. What fraction of the children go home for lunch? 0. A shopper buys kg of Golden Delicious apples and kg of Cox's apples. Find the total weight of the apples bought.. Multiplication and Division of Fractions Multiplication Consider finding of by starting with this rectangle. First select of the rectangle, as shown by the shaded area. Then select of the shaded area. This represents of of the original rectangle, that is, or of the original rectangle. Now of is the same as, so = =. When multiplying two fractions, the numerators (top parts) should be multiplied together to give the numerator of the result. Similarly, the two denominators should be multiplied together. In general terms, a b c = d a b c d Worked Example =? = =

20 MEP Pupil Text Worked Example =? = = 0 Worked Example =? Division = = 0 = 0 To understand how to divide with fractions, first consider how multiplication and division are related. 9 Take as an example, Then it is also true that =. =. So ' ' and ' ' are inverse operations. Note that =, so is the same as. Similarly, because is the same as, and, alternatively, =. = (check: = )

21 . MEP Pupil Text So is the same as. You can generalise these examples to give a is the same as a b and combining the two results gives is the same as b a b is the same as b a. For example, = =. (This result can be seen more easily from the diagram opposite.) Similarly, 0 = 0 = So to divide by a fraction, the fraction should be inverted, that is, turned upside down, and then multiplied. In general terms, a b c a = d b d c Worked Example =? = = =

22 MEP Pupil Text Exercises. Find each of the following, cancelling when possible. (d) (g) (b) 9 (e) 0 (h) (c) (f) (i) 0 9 (j) (k) (l) (m) (n) (o) (p) (q) (r). Find (d) (g) (b) (e) (h) (c) 9 (f) 0 (i) (j) (k) (l). Find the area of each rectangle below. (b) (c) (d) 0. In a garden, of it is used for growing vegetables and of this vegetable area for potatoes. What fraction of the garden is used for growing potatoes?

23 . MEP Pupil Text. In a school, of the children are boys and of these are colour-blind. 0 What fraction of the school are colour-blind boys?. A cube is made with sides of length cm. Find the volume and surface area of the cube. cm cm cm. A petrol can holds litres when full. How much petrol is in the can if it is full?. A car travels at 0 m.p.h. for hour. How far does the car travel? 9. Find the length of the unmarked side of this rectangle if its area is m. m 0. A recipe requires kg of sugar for a cake. How many cakes could be made with kg of sugar?. Alison cycles miles in hour. What is her speed?. It takes a factory hour to assemble a finished product. How many items could be assembled in an hour day?. Compound Interest and Depreciation When money is invested the interest is often compounded, which means that interest is given on the interest. Worked Example A person invests 00 in a building society account which pays % interest each year. Find the value of the investment after years. Interest of % will be added at the end of each year by multiplying by.0. So, value of account after year: = 0 value of account after years: 0. 0 =. value of account after years :.. 0 =. 9.

24 MEP Pupil Text Note that the amount of interest added increases each year. The final value could have been found in one calculation: Worked Example =. 9. When Gemma was born, her grandmother invested 00 in a building society for her. Find the value of this investment after years if the interest rate is % per year. Final value = = 0.. Problems with depreciation can be tackled in a similar way. Worked Example A car was bought for 000. Its value decreases by % each year. Find the value of the car after: year (b) years (c) 0 years. Decreasing the value by % leaves 9% of the original value. Value after one year = = 0 (b) Value after years = = 9. (c) Value after 0 years = = 0. Note You can see from these worked examples that the total amount in an account after n years, A n, with interest of r % is given by A n r = + 00 n A 0 where A 0 is the initial sum invested.

25 . MEP Pupil Text Exercises. Jane invests 00 in a bank account which earns interest at the rate of % per annum. Find the value of her investment after: year (b) years (c) years.. A sum of 000 is to be invested for 0 years. What is the final value of the investment if the annual interest rate is: % (b).% (c).%?. Which of the following investments would earn most interest? A B C 00 for years at % interest per annum, 00 for year at % interest per annum, 00 for years at % interest per annum. The value of a computer depreciates at a rate of % per annum. A new computer costs 00. What will the value of the computer be after: years (b) years (c) 0 years?. A car costs 9000 and depreciates at a rate of 0% per annum. Find the value of the car after years.. John invests 00 in a building society with interest of.% per annum. Karen invests 00 at the same rate. (b) How many years does it take for the value of Karen's investment to become greater than 00? How many years does it take for the value of John's investment to become greater than (i) 00 (ii) 900?. If the rate of inflation were to remain constant at %, find what the price of a jar of coffee, currently priced at., would be in years' time.. The population of a third world country is million and growing at.% per annum. (b) What size will the population be in years' time? In how many years' time will the population exceed 0 million? 9. The value of a car depreciates at % per annum. A man keeps a car for years and then sells it. If the car initially cost 000, find: (i) its value after years, (ii) the selling price as a percentage of the original value.

26 MEP Pupil Text (b) Repeat for a car which cost 000. (c) Comment on your answers. 0. A couple borrow 000 to furnish their new home. They have to pay interest of % on this amount. Find the amount of interest which would be charged at the end of the first year. (b) If they repay 00 at the end of each year, how much do they owe at the end of the third year of the loan?.9 Reverse Percentage Problems Sometimes it is necessary to reverse percentage problems. For example if the price of a television includes VAT, you might need to know how much of the price is the VAT. Worked Example The price of a computer is 0, including VAT at %. Find the actual cost of the computer and the amount of VAT which has to be paid. To add.% VAT to a price it should be multiplied by.. So to remove the VAT it should be divided by.. Original Price = 0. = 00. Worked Example VAT = 0 00 = 0. A customer is offered a 0% discount when buying a new bed. The discounted price is.0. Find the full price of the bed. To find the discounted price of the bed, the full price should be multiplied by 0.. So to find the full price, the discounted price should be divided by 0.. Worked Example Full price = = 9. Sharon invests some money in a building society at % interest per annum. After two years the value of her investment is Find the amount she invested. 9

27 .9 MEP Pupil Text To find the final value, the amount invested would be multiplied by. 0. To find the amount invested, divide the final value by. 0. Exercises Amount invested = = 0.. A foreign tourist can reclaim the VAT he has paid on the following items, the prices of which include VAT. Video Camera 9.0 Portable CD Player 0. Watch. FAX Machine 0.0 Find the total cost of the items without VAT at.%. (b) How much VAT can the tourist reclaim?. The price of a television is.0 including.% VAT. What would be the price with no VAT?. A gas bill of. includes VAT at %. Find the amount of VAT paid.. The end of year profits of a large company increased this year by % to Find the profits made last year.. A special bottle of washing up liquid contains ml of liquid. The bottle is marked '0% extra free'. How much liquid is there in a normal bottle?. In a sale the following items are offered at discount prices as listed. Item Sale Price Discount Television.00 0% Video Recorder. % Computer.0 % Calculator. % What were the prices of these items before the sale?. After one year, the value of a car has fallen by % to 0. What was the value of the car at the beginning of the year? 0

28 MEP Pupil Text. A sum is invested in a building society at % interest per annum and after years the value of the investment is.. How much was originally invested? 9. Jenny's pocket money is increased by % each year on her birthday. When she is years old, her pocket money is. per week. How much did she get per week when she was: years old (b) years old (c) 0 years old? 0. Jai buys a car, keeps it for years and then sells it for 00. If the value of the car has depreciated by % per year, how much did Jai originally pay for the car? Information Did you know that in 99 a Japanese mathematician (using a computer!) took just days to compute the value of π to over billion digits. Just For Fun The sum of School B. The sum of School C., and,, and of the enrolment of School A is exactly the enrolment of of the enrolment of School A is exactly the enrolment of What are the enrolments of these three schools, assuming that no school has more than 000 pupils? Information The Chinese represented negative numbers by indicating them in red and the Hindus denoted them by putting a circle or a dot over the numbers. The Chinese had knowledge of negative numbers as early as 00 BC and the Hindus as early as the th century. In Europe, as late as the th century, some scholars still regarded negative numbers as absurd. In, Cardano (0 0), an Italian scholar, called positive numbers 'true' and negative numbers 'fictitious' numbers.