11 Fractions and Percentages

Transcription

1 MEP Practice Book SA Fractions and Percentages. Fractions, Decimals and Percentages. Express each of the following percentages as a fraction in its lowest terms. 0% % % (d) 0% (e) 60% (f) 0% (g) % (h) 6 % (i) % (j) 6 %. Express each of the following percentages as a decimal. 0% % 6% (d) 0% (e) 0% (f) 0% (g) % (h) % (i) % (j) 0 %. Express each of the following fractions as a percentage. (d) 0 (e) (f) (g) (h) 6 (i) (j). Express each of the following decimals as a percentage (d) 0. (e) 0. (f) 0.00 (g) 0. (h) 0.6. Write the following percentages as (i) fractions (ii) decimals. 6% % % (d) % (e) 0% (f) % (g) % (h) % 6

2 MEP Practice Book SA 6. of this shape is shaded. What percentage of the shape is shaded? What percentage of the shape is not shaded? (LON). Copy and complete the table. Express the fractions in their lowest terms. Percentage Fraction Decimal % 0 0% 0. % (d) % (e) 6 % (f) 6 % (g) 00% (h) %. Write as a percentage. Write % as a fraction.. Which two of these fractions are equivalent to? Write 0% as a decimal. Write 0 as a decimal.

3 . MEP Practice Book SA 0. Copy and complete the table below. Fraction Decimal Percentage % %. Write % as a decimal. Write as a percentage. Write 60% as a fraction. Give your fraction in its simplest form. (d) Write million in figures. (e) % of the students in a school are female. What percentage of students are male? (Edexcel). Which of these fractions is closest to? You must show your working Fractions and Percentages of Quantities. Calculate each of the following: 0% of 0 6% of 00 % of 00 (d) 0% of 00 (e) 6% of (f).% of (g) 0% of (h) % of (i) 6% of 0 (j) 0.% of 000. Find the value of each of the following: % of % of 6.0 % of 0 (d) 0 % of 00 g (e) % of 60 (f) % of km

4 MEP Practice Book SA (g) 66 % of 000 (h) 6 % of 0 (i) 0% of 0 m (j) 00% of. In a town of people, 6% own terrace houses. How many people own terrace houses?. Ali scored 0% in a Mathematics test. If the total possible mark is 0, how many marks did he get?. A couple are inviting 60 friends to their wedding reception. They expect 0% to accept the invitation. How many will this be? 6. A 0% service charge is added to the cost of food ordered in a restaurant. If the food costs 6.0, what would be the total charge including the service charge?. A used-car dealer sells a car at 0% of its cost. If a car costs 000, how much will he sell the car for?. Mrs. Warren earns 60 a month. S he spends 0% of it on petrol, 60% on household expenditure and food, 0% on clothing and saves the rest. How much does she spend on household expenditure and food? How much altogether does she spend on petrol and clothing? How much does she save each month?. 60 boys and 0 girls sat for an examination. 6% of the boys and % of the girls passed. Find the number of boys who passed. Find the number of girls who passed. What percentage of the total number of boys and girls in the examination passed? 0. This chart shows how a council spends its total income. Education Social Police Fire Others Service Services Service Service % % 0% % 6% What percentage is spent on Social Services? The council has a total income of 60 million. How much does the council spend on the Fire Service? (SEG)

5 . MEP Practice Book SA. The cost of some building materials is 6.0 plus VAT. VAT is charged at.% How much VAT is charged? What is the total cost? (SEG). An estate agent charges commission on the sale price of a house. Calculate the commission charged on a house sold for Work out 0 (SEG) (Edexcel). Tom works hours each week. He earns per hour. Tom saves of his earnings each week. How many weeks does it take Tom to save 0? You must show all your working. Find 0% of 6.0 of 00. Quantities as Percentages. In a class of 0 pupils, failed the physical fitness test. What percentage of the class failed the test?. 0 people attended a concert. There were 0 children. What percentage of the people were children?. In a survey, 0 people were interviewed. of them owned cars. What percentage of the people interviewed owned cars? What percentage did not own cars?. Mr Smith bought a basket of 0 plants. of the plants were spoilt. What percentage of the plants were not spoilt?. During an election, 6 out of 000 people for Candidate A. What percentage of the people did not vote for Candidate A? 0

6 MEP Practice Book SA 6. On a certain day, aeroplanes arrived at the airport. of them were on time. What percentage of them were not on time?. To prepare 0 ml of lemonade, Meiling adds 0 ml of syrup to water. What percentage of the lemonade is syrup?. An alloy consists of. kg of zinc and kg of tin. What percentage of the alloy is made up of tin?. The following shows the marks obtained by a pupil in an examination: English - out of 0 French - out of Mathematics - out of 60 Science - out of 0 Geography - out of 0 Express each mark as a percentage of its total. In terms of percentage, for which subject did the pupil score (i) the highest, (ii) the lowest? 0. The following table shows how 00 people travel to work. Mode of Transport Number of People Walk Cycle 6 Train 0 Car x Bus 0 Calculate the value of x. Find the percentage of people who travel by each mode of transport.. A circle of radius cm is increased in area by %. Find the radius of the new circle and give the answer correct to the nearest cm.. Express 00 cm as a percentage of m.. 00 people voted in an election. The table shows the four candidates and the votes received by two of them. Allgood Betterdon Carewell Didright 0

7 . MEP Practice Book SA What percentage of the votes did Allgood receive? Carewell received twice as many votes as Didright. How many votes did Carewell receive?. More Complex Percentages. In a constituency, there are 000 eligible voters. In a particular election, the following results were obtained Candidate Percentage of votes A % B % C % Find the actual number of votes for each candidate, given that % of eligible voters did not vote.. A factory has 600 workers and the percentages of workers absent from work from Monday to Friday in a certain week are given in the table. Find the number of workers who turn up for work on each day. Day Percentage of absentees Monday % Tuesday.% Wednesday 0% Thursday % Friday %. The Smith family's expenses for a particular month is given as follows: Item Expenditure Rent 6 Food Clothing Travel 6 Miscellaneous Calculate each expenditure as a percentage of the total expenditure.

8 MEP Practice Book SA. Kathy earned in. Her tax allowance was. She did not pay tax on this amount of her income. On a further 0 of her income she did not pay tax, because she paid this amount into a pension scheme. She paid tax on the rest of her income. How much of her income was taxable? She paid tax at % on the first 00 of her taxable income. She paid tax at 0% on the rest of her taxable income. Calculate the total amount of tax that she paid in. (SEG). A shopkeeper buys a washing machine for 0. Find the sale price if the shop keeper is to make a profit of % % % (d) % (e) %. 6. A supermarket sells brands of detergent, A, B, C and D. On a particular day, % of the total number of boxes sold was brand A and % was brand C. Find the ratio of the number of boxes of brand A sold to the total number of boxes sold. Give your answer as a fraction. Given that 60 boxes of brand A were sold, calculate the number of boxes of brand C that were sold. Given that the number of boxes of brand D sold is one third the number of boxes of brand B that were sold, what percentage of the detergent sold was brand D?. Find the discount, the actual amount of money paid, in the following cases. (i) A watch is priced in a catalogue at but the dealer offers a % discount to the purchaser. (ii) Luggage which has a catalogue price of but is sold at a discount of 0% during a sale. (iii) A cabinet which has a marked price of 00 but is sold at a discount of % to a customer who pays for it in cash. (iv) A sofa-bed priced at 00 but is sold at a discount of 6% to a customer who arranges for its delivery. (v) An air ionizer, with a marked price of 600, is offered for sale at a discount of % to a customer who pays in cash.. Andy sells CDs. He sells each CD for.0 plus VAT at %. He sells 60 CDs. Work out how much money Andy gets. (Edexcel)

9 . MEP Practice Book SA. A dish contains 000 bacteria. The number of bacteria increases by 6% per hour. How many bacteria will be in the dish after hours? 0. Jane earns 00 per year. After her pay rise she earns per year. What was her percentage pay rise?. Percentage Increase and Decrease. Ten years ago, a town had a population of 0. Now, the population of the town is 6. Find the percentage increase in the population of the town.. The ABC Dress Company determines the selling price of its dresses by adding % to the cost. Calculate the selling price of a garment that costs.. A dealer sells cloth at.0 a metre, which he bought at 0 for 0 metres. Find the percentage profit or loss.. A carpenter made a dozen chairs at a cost of 0. She sold each of them for 0. Find her percentage gain.. A trader mixes kg of butter which costs per kg with kg of butter which costs 6 per kg. He sells the mixture at. per 0 g. Find his percentage gain. 6. Calculate the percentage decrease for each of the following, correct to the nearest %. From to 00. From. to 0.. From 6 kg to 0 kg. From 00 km to 0 km.. Calculate the percentage increase for each of the following correct to the nearest %. From 0 to. From. to 0.. From. to 60.. (d) From h to h.. Decrease 6 by 0%. Decrease 0 by %. Increase 0 kg by 0%. (d) Increase.6 m by 0%.. A bookshop sells its books at 0% less than the marked price. If a book is marked at, at what price will the shop sell it? 0. A long distance call costs If a.% service charge is added to it, what will be the total cost of this long distance call?

10 MEP Practice Book SA. Between and 0, the enrolment of a school fell from 00 to 00. What is the percentage decrease in the enrolment of the school from to 0? Give your answer correct to the nearest %.. Calculate the percentage increase in each of the following cases: A bus fare of 0p is now 0p. A train fare of 0p is now 60p.. The breakdown for different races for the population of Singapore in and is given in the table below. For each race, calculate the percentage increase from to, giving your answers correct to decimal place. Race Population () Population () Chinese Malay Indian (d) Others In 0, a charity sold million lottery tickets at p each. 0% of the money obtained was kept by the charity. Calculate the amount of money kept by the charity. In, the price of a lottery ticket fell by 0%. Sales of lottery tickets increased by 0%. 0% of the money obtained was kept by the charity. Calculate the percentage change in the amount of money kept by the charity. (LON). Janet invests 0 in a building society for one year. The interest rate is 6% per year. How much interest, in pounds, does Janet get? Nisha invests 60 in a different building society. She gets interest after one year. Work out the percentage interest rate that Nisha gets. (LON) 6. If the price of a watch is increased by % from p, give the new price in terms of p.

11 MEP Practice Book SA.6 Addition and Subtraction of Fractions. Evaluate the following, expressing your answers in the simplest form. + + (d) + (e) + (f) 6 6 (g) 0 (h) 6 + (i). Evaluate the following: (d) (e) 0 6 (f) (g) + 6 (h) Arrange the following in ascending order: 0, 0, 0,,, 6, (d),, (e), 6, 6. Jane used of a piece of ribbon and her sister used of it. What fraction of the ribbon was used?. Joe painted of a fence and Bill painted of it. What fraction of the fence did the boys paint? 6. Mr Smith had m of wire. He cut off a piece of wire m long. How many metres of wire did he have left?. Mrs Bell made 0 cookies. Her son ate of them. How many cookies did he eat?. Harban was given allowance each week. He spent did he save? How much did he save in pounds. of it. What fraction. Sue bought a record with of her allowance. She spent another to see a movie. What part of her allowance did she spend? 6

12 MEP Practice Book SA 0. At a sale, some shirts are sold at their original price. If the original price of these shirts is 0, what is the sale price?. I have one whole candy bar. I give of it to my brother and of it to my friend. What fraction of the candy bar do I have left?. Khalid spent of his money on a pen, of it on books and 6 of it on a magazine. What fraction of the money is left?. Mrs Holland spends of her money in the market and of the remainder in a shop. What fraction of her money is left?. Joan earns 00 a month. She spends of her salary every month. She gives her parents of the remainder and saves the rest. How much money does she save every month?. A group of students went to a fast food restaurant. of them bought a beef burger and The rest of them just bought drinks. of them bought a chicken burger. What fraction of the group bought food? of those who bought a beef burger also bought chips. What fraction of the whole group bought beef burger and chips? Give your answer as a fraction in its simplest form. (OCR) 6. On Monday Joe drinks pints of milk. On Tuesday he drinks pints of milk. Work out the total amount of milk that Joe drinks on Monday and Tuesday.. Work out the value of +.

13 MEP Practice Book SA. Multiplication and Division of Fractions. Evaluate the following: (d) (e) (f) (g) 0 (h) (i) 0 (j) (k). Evaluate the following: 0 (l) (d) (e) (f) (g) (h) (i) 0. Simplify the following: 6 6 (d) (e) 0 (f). Evaluate each of the following: (d) 6 (e) (g) (h). Evaluate the following: 6 (f) (d) 6 6 (e) (f) 6 (g) (h)

14 MEP Practice Book SA 6. You have to walk halfway? km to school. How far have you walked when you are. A recipe for 6 buns requires kg of sugar. How much sugar is needed for bun?. Work out the value of + Give your answer as a fraction in its simplest form. Work out the value of Give your answer as a fraction in its simplest form. (Edexcel). Compound Interest and Depreciation. Matthew invests 0 in a bank account which earns interest at a rate of % per annum. Find the value of the investment after: year, years, 0 years.. Using the compound interest formula, calculate the value of the following accounts: 00 invested for years at % interest per annum, 000 invested for years at % per annum, 000 invested for 0 years at % per annum.. A new network of computers costs a firm 000. The value of this computer network depreciates at a rate of 0% per annum. What is the value of the network after: years, years?. Louise has 0 to invest, and wants to invest this money for as long as it takes to reach a value of 00. If the account pays % interest per annum, how long will it take for Louise to reach her target?. Fare prices on a newly privatised railway are only allowed to rise in line with inflation. Assuming constant inflation at a % rate per annum, how much will a 0 fare cost after: year, years, years, (d) 0 years? 6. A car costs 000 when new. It depreciates 0% in the first year, and at a 0% constant rate for each subsequent year. What is its value after: year years years?

15 . MEP Practice Book SA. Jim borrows 000 to furnish a new flat. He has to pay interest at the rate of % per annum on this amount. Find the amount of interest to be paid at the end of the first year. If he pays 00 back at the end of each year, how much will he still owe at the end of the fourth year?. Annie invests 000 for years in a savings account that pays % compound interest per year. How much will she have in the account at the end of years?. Mrs Blake put 000 in a building society account that offered 6% interest per year. Interest was added to the account at the end of each year. How much did she have in her account years later, after the final interest had been added? An annual rate of interest between % and % would be required for a sum of money to double in ten years. Use a trial and improvement method to find this rate of interest. Give your answer as a percentage to decimal place. Show your calculations. (OCR). Reverse Percentage Problems. A stereo system is sold for and an % profit is made. Find the original cost of the stereo.. A dealer sells a television set to a man and makes a % profit. The man sells it to another man for at a loss of 0%. Find the original price of the television set.. At what price must an article costing 0 be sold in order to make a profit of 6 %?. A cash discount of % is allowed on an item which costs. How much money is saved if a customer decides to pay in cash? How much more can he save if the discount is %?. A dealer gains % by selling a washing machine for 0. Find the cost price of the washing machine. What percentage profit would he get if he were to sell it for 00? 6. A second-hand car dealer bought a second-hand car and spent 60 on repairs. He sold the car for 60, gaining 0% on the purchase price. For how much did he purchase it?. A dress marked '0% off usual price' sells for 0. What is the usual price?. A man bought a flat for and a second-hand car for 00. He sold the flat at a gain of % and the car at a loss of %. Find the total amount gained or lost from the two transactions. 0

16 MEP Practice Book SA. By selling a particular set of books for 0, a bookseller suffers a loss of %. Find the cost price of the books. What is the percentage gain or loss if the books are sold for 0? 0. Many articles are subject to VAT at %. Normally the quoted price of such articles includes VAT, but businesses can often obtain refunds on any VAT paid. It is therefore important to be able to determine the amount of VAT paid, given the quoted price of the article. The quoted price of an article is.. How much VAT is included in the quoted price? An approximate method of finding the amount of VAT is to divide the quoted price by the number 6.. This gives an answer that is not always accurate to the nearest penny. Find a more accurate number to use in place of 6., correct to significant figures. If VAT rises to %, determine, to significant figures, the number by which the quoted price should be divided to find the amount of VAT paid.. A television has a sale price of 0. This is a saving of % on the original price. What was the original price?. SALE Exercise Bike % off Now.0 How much was the exercise bike before the reduction?