EDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 2. Chapter 2. Working with fractions, decimals and percentages

Transcription

1 EEXEL FUNTIONL SKILLS PILOT Maths Level 2 hapter 2 Working with fractions, decimals and percentages SETION Types of fraction 2 Using a calculator for fractions 7 Fractions of quantities 8 4 One number as a fraction of another 20 dding and subtracting fractions 22 6 what you have learned 24 SETION ecimal numbers 26 2 alculating with money 28 what you have learned 0 SETION Percentages 2 2 Using percentages 4 Percentage change 6 4 onverting between forms 8 Using fractions, decimals and percentages in practical problemss 40 6 what you have learned 4 Pearson E ducation 2008 Functional Maths Level 2 hapter 2 raft for Pilot

2 Working with shape and space EEXEL FUNTIONL SKILLS: INTERIM SUPPORT MTERIL Maths Level 2 Su Nicholson hapter 2: Working with fractions, decimals and percentages Use these free pilot resources to help build your learners skill base We are delighted to continue to make available our free pilot learner resources and teacher notes, to help teach the skills learners need to pass Edexcel FS Mathematics, Level 2. ut use the accredited exam material and other resources to prepare them for the real assessment We developed these materials for the pilot assessment and standards and have now matched them to the final specification in the table below. They ll be a useful interim measure to get you started but the assessment guidance should no longer be used and you should make sure you use the accredited assessments to prepare your learners for the actual assessment. New resources available for further support We re also making available new learner and teacher resources that are completely matched to the final specification and assessment and also providing access to banks of the actual live papers as these become available. We recommend that you switch to using these as they become available. overage of accredited specification and standards The table below shows the match of the accredited specification to the unit of pilot resources. This table supersedes the pilot table within the teacher notes. overage and Range Exemplification Learner Unit Understand and use equivalences between common fractions, decimals and percentages Simplifying fractions Finding fractions of a quantity Improper and mixed numbers Percentages of a quantity onvert between fractions, decimals and percentages Order fractions, decimals and percentages Writing one number as a fraction of another Types of fraction 2 Using a calculator for fractions Fractions of quantities 4 One number as a fraction of another dding and subtracting fractions Order fractions, decimals and percentages is covered in our new publishing (see below) 6 what you have learned Percentages 2 Using percentages Percentage change 4 onverting between forms Using fractions, decimals and percentages in practical problems 6 what you have learned Where to find the final specification, assessment and resource material Visit our website then: for the specification and assessments: under Subjects, click on Mathematics (Levels 2) for information about resources: under Support, click on Published resources. Published by Pearson Education, Edinburgh Gate, Harlow M20 2JE. First published Pearson Education Typeset by Oxford esigners and Illustrators, Oxford This material was developed for use with Edexcel pilot and development centres and is available for continued use with development centres. To become a development centre you need to offer Edexcel Functional Skills. The material may be used only within the Edexcel development centre that has retrieved it. It may be desk printed and/or photocopied for use by learners within that institution. ll rights are otherwise reserved and no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanic, photocopying, recording or otherwise without either the prior written permission of the Publishers or a licence permitting restricted copying in the United Kingdom issued by the opyright Licensing gency Ltd, Saffron House, 6 0 Kirby Street, London EN 8TS.

3 Working with fra c tions, d e cimals and p erc e nt a g e s 2 Working with fractions You should already know how to: read, write, order and compare common fractions and mixed numbers find parts of quantities or measurements. y the end of this section you will know how to: find fractions of quantities express one number as a fraction of another use fractions to add and subtract amounts use fractions to solve practical problems use a calculator to calculate with fractions. Types of fraction Learn the skill fraction is a way of expressing a part of a whole. The fraction 4 means parts out of 4. The number on the top,, is called the numerator, the number on the bottom, 4, is called the denominator. In 4 2 You write a fraction in its lowest terms by dividing the numerator and denominator by any common factor. the numerator and denominator have a common factor of 7. You can divide top and bottom by 7: and are equivalent fractions. You can fi nd equivalent fractions by multiplying: 4 is equivalent to is bigger than bigger than 4. which is Pearson Education 2008 Functional Maths Level 2 hapter 2 page raft for Pilot

4 In an improper fraction the numerator is bigger than the denominator. You can write an improper fraction as a mixed number: 8 + mixed number has a whole number part and a fraction part. You can change mixed numbers to improper fractions. Example: hange to an improper fraction. ecause the denominator of the fraction is 8 you need to change the mixed number to eighths. One whole is 8 8, so two wholes is This means that quick way of working this out is nswer: 2 8 Try the skill. Write these as fractions in their lowest terms. 2 a 6 b 20 c 22 2 d Write these improper fractions as mixed numbers. a 6 6 b 7 c 2 8 d 6 9. Write these mixed numbers as improper fractions. a 6 b 2 c 7 d 4 0 Pearson Education 2008 Functional Maths Level 2 hapter 2 page 6 raft for Pilot

5 Working with fra c tions, d e cimals and p erc e nt a g e s 2 2 Using a calculator for fractions Learn the skill You can use a calculator to write fractions in their lowest terms by making use of the ab/c key. Try keying in: 4 ab/c 2 You should see 2 on the screen, which means 2. Use the ab/c key on your calculator to check your answers to question on the previous page. You can also use the ab/c key for improper fractions. Try keying in: 8 ab/c You should see on the screen, which means. Use the ab/c key on your calculator to check your answers to question 2 on the previous page. You can use a calculator to convert mixed numbers to improper fractions. Try keying in: 2 ab/c 7 ab/c 8 Some calculators have a to input fractions. Some calculators will show 2 to represent 2. key You should see on the screen which means Now press 2 nd F ab/c You should see 2 8 on your screen which means 2 8. Try the skill Use the ab/c key on your calculator to check your answers to question on the previous page. Pearson Education 2008 Functional Maths Level 2 hapter 2 page 7 raft for Pilot

6 Fractions of quantities Learn the skill To fi nd of a quantity, divide by. To fi nd 2 of a quantity, divide by, then multiply by 2. Out of 92 students own a mobile phone. How many of 4 the students own a mobile phone? To fi nd divide by To fi nd multiply this answer by nswer: 44 students To divide by 4, divide by 2 then divide by 2 again. Example 2: 2 of the money spent on the National Lottery is paid to the Treasury in duty. In a year when billion is recorded in sales, how much money will be paid to the Treasury? The easiest way to work out this question is to write 2 equivalent fraction with a numerator of To fi nd 00 To fi nd 2 00 as an 2 00 divide by million multiply this answer by 2 0 million million nswer: 600 million Example : man earns 420 a week. He spends of this on rent and of what is left on food. How much does he spend on food? You have to tackle this question in two stages. To fi nd out how much he spends on rent, fi nd spent on rent. He has left. To fi nd out how much he spends on food, fi nd of 420. of 6. nswer: 2 raft for Pilot Functional Maths Level 2 hapter 2 page 8 Pearson Education 2008

7 Working with fra c tions, d e cimals and p erc e nt a g e s 2 Try the skill people attended a football match. 8 of those who attended were children. How many children attended the football match? 2. In a business employing 080 people, 2 of the employees are under 2. How many of the employees are under 2?. 20 people went to the local cinema on a Saturday night. Of these people, 2 paid the student rate of 7.0 and the remainder paid the full adult rate of 0. What was the total amount of money paid to the cinema that night? 4. When 72 students sat the driving test theory exam, 6 of them passed. Of these, 4 went on to pass the driving test practical. How many of these students passed both the theory and the practical driving test exams? First fi nd the number of students who passed the exam.. man earns 200 a month. He spends 4 of his earnings on food and accommodation and saves of the rest. How much money does he save each month? 6. In a street with 420 houses, 6 of the houses are owned by the occupiers, and 0 of the rest are rented. How many houses in the street are rented? Pearson Education 2008 Functional Maths Level 2 hapter 2 page 9 raft for Pilot

8 4 One number as a fraction of another Learn the skill One number as a fraction of another number is: fi rst number second number Example : Express 8 as a fraction of 2. You should always write the fraction in its lowest terms. 8 as a fraction of 2 is nswer: 2 To express one quantity as a fraction of another, the quantities must be in the same units. Example 2: Express 60 g as a fraction of kg. Write the quantities in the same units. kg 000 g nswer: 0 heck answers on your calculator using the ab/c key. You can work out a fraction increase or decrease. Find the actual increase or decrease fi rst. Example : On Monday 200 students used the college canteen. On Tuesday, 0 students used the canteen. y what fraction did the number of students using the canteen increase? The actual increase in the number of students using the canteen on Tuesday is You express this as a fraction of the number of students using the canteen on Monday You always compare with the original value unless you are expressly told otherwise. This will be the denominator. nswer: 4 raft for Pilot Functional Maths Level 2 hapter 2 page 20 Pearson Education 2008

9 Working with fra c tions, d e cimals and p erc e nt a g e s 2 You can round numbers to fi nd an approximate fraction. Example 4: college has a total of 060 students. 220 of them are studying mathematics. pproximately what fraction of the college students are studying mathematics? The exact fraction is Writing both top and bottom correct to signifi cant fi gure gives: nswer: Try the skill. In a class of 0 students, 2 are girls. What fraction of the class are girls? 2. In a car park of 20 cars, 4 are made in Europe and the rest are made in Japan. What fraction of the cars are made in Japan?. Express 4 mm as a fraction of 20 cm in its simplest form. 4. Sales at a clothes shop in January totalled 220. In February the sales totalled 70. y what fraction did the sales decrease in February?. In a survey, 20 students were asked how long they spent using a computer in one week. The results are shown below. cm 0 mm The denominator of the fraction will be the original sales amount. Number of hours Number of students What fraction of the students spent 0 or fewer hours using a computer in one week? Pearson Education 2008 Functional Maths Level 2 hapter 2 page 2 raft for Pilot

10 dding and subtracting fractions Learn the skill You use fractions when working with time. You can only add or subtract fractions with the same denominator. If the denominators are different, you need to express them as equivalent fractions with the same denominator. Example : Work out +. Here the denominators are different, so you need to decide on a common denominator to use, then write them both as equivalent fractions with the same denominator. This denominator should be the smallest number that and will divide into, the LM. The LM of and is. hange and to equivalent fractions with a denominator of. and nswer: 4 Example 2: Evaluate First add the whole numbers: + 2 Now add the fractions: The LM of 4 and is and nswer: 4 20 The LM (lowest common multiple) is the smallest number that two numbers will both divide into. If the denominators do not have a common factor, you can fi nd their LM by multiplying the denominators together. The most common fractions used in practical questions involving addition and subtraction of fractions are halves, thirds, quarters, fi fths, eighths and tenths. Example : Work out The method is similar to addition. The LM of 8 and is and nswer: 40 raft for Pilot Functional Maths Level 2 hapter 2 page 22 Pearson Education 2008

11 Working with fra c tions, d e cimals and p erc e nt a g e s 2 Example 4: Evaluate 0 4. First subtract the whole numbers: 2 Then work out 0 4. The LM of 0 and is becomes in its lowest terms. Questions involving fractions may ask you to work out, calculate or evaluate. These all mean the same thing. The answer is: nswer: 2 Try the skill. Three TV programmes last for 2 hours, 4 hour and hours. If you watch them all, how long would this take? 4 heck answers on your calculator using the ab/c key. 2. girl walks to the shops. It takes her 2 hour to get there, she shops for 4 hours and it takes her 4 hour to get back. How long did the shopping trip take?. boy cycles to his friend s house. It takes him 4 hours to get there and 2 4 hours to cycle back. How much longer did it take him to cycle back from his friend s house? 4. fi lm lasts for 4 hours. n edited version of the fi lm lasts for 2 2 hours. How much shorter is the edited fi lm than the original version? Read the question carefully. To fi nd out how much longer, or shorter, you count on or subtract. It can help to sketch a number line: Pearson Education 2008 Functional Maths Level 2 hapter 2 page 2 raft for Pilot

12 6 what you have learned First complete this You write a fraction in its lowest terms by any common factors. In an fraction the numerator is bigger than the denominator. To fi nd To fi nd 2 of a quantity, by. of a quantity, by 2. by, then One number as a fraction of another number is: number number You can only add or subtract fractions with the same. When dividing by a fraction, multiply top and bottom to make the denominator a. To multiply by a mixed number, partition it into a whole number and a. efore you can express one quantity as a fraction of another, you must write them in the same units. Try the skill. The total receipts for a football club match in one particular week were The club spends 8 of its income on salaries. How much of the week s receipts was spent on salaries? boy gets 0 a week in pocket money. He also receives 8 a week for delivering newspapers. What fraction of his total income is the money he receives for delivering newspapers? It takes a girl 4 hours to travel to the Trafford centre in Manchester. She spends 2 2 hours shopping and it takes her 4 hours to get home. How long does she take in total? 4 2 hours 4 4 hours 4 hours 2 hours raft for Pilot Functional Maths Level 2 hapter 2 page 24 Pearson Education 2008

13 Working with fra c tions, d e cimals and p erc e nt a g e s 2 4 Out of a group of students, 2 travel to college by bus, travel by train and the rest walk to college. 4 What fraction of the students walk to college? In an audience of people watching a fi lm, are under 6 0 years old, are between 6 and 40 years old and the rest are over 40 years old. What fraction are over 40 years old? The price of a dress is reduced from to 2 in a sale. What calculation would you do to fi nd the decrease in price as a fraction of the original price? There are 90 cars in a car park. 2 of these cars are red. of the red cars have three doors. How many cars in the car park are red with three doors? 6 cars 0 cars 2 cars cars 8. In a survey of 22 students, 47 of them had their own ipod. pproximately what fraction of the students had their own ipod? There were 26 people in a village. t an election 9 voted onservative. pproximately what fraction of the people in the village voted onservative? 2 2 Pearson Education 2008 Functional Maths Level 2 hapter 2 page 2 raft for Pilot

14 Working with decimals You should already know how to: read, write, order and compare decimals add, subtract, multiply and divide decimals with up to 2 decimal places multiply and divide decimals by 0 and 00. y the end of this section you will know how to: order, approximate and compare decimals calculate with decimals with up to decimal places calculate and estimate amounts of money and convert between currencies. ecimal numbers Learn the skill In a decimal number, the decimal point separates the whole number from the part that is less than. In the number 0.7: Tens Units Tenths Hundredths Thousandths 0 7 The stands for 0, three tenths alculations involving decimals follow the rules for whole numbers and fractions. To round a number: The stands for 00, fi ve hundredths 7 The 7 stands for 000, seven thousandths Identify the last digit that is needed in rounded form. Look at the next digit to the right. If the next digit is, 6, 7, 8 or 9, round the last digit up. If the next digit is 0,, 2, or 4, leave the last digit. nswers to money calculations in pounds should be written correct to the nearest penny (two decimal places). The number 2.09 is: 2.0 to three decimal places 2. to two decimal places 2. to one decimal place. Example Next digit Round.76 to three decimal places Last digit needed Last digit that is needed is, next digit is 6 so round the last digit up. nswer.74 raft for Pilot Functional Maths Level 2 hapter 2 page 26 Pearson Education 2008

15 Working with fra c tions, d e cimals and p erc e nt a g e s 2 Example 2: plumber cuts three lengths of pipe measuring.02 m,.204 m and m. What is the total length of pipe he uses? Line up the numbers using the decimal points nswer: 2.72 m Example : One yard is equal to feet. One foot is equal to 2 inches. inch is approximately equal to 2.4 cm. What is one yard, in centimetres? The calculation is: (0 + 6) ( ) nswer: 9.44 cm Multiplying by 0.4 is the same as multiplying by 4 and dividing by 0. Multiplying by 0.04 is the same as multiplying by 4 and dividing by 00, and so on. eg: Try the skill. inch 2.4 centimetres. pproximately how long is 8 inches in centimetres? 2. One petrol station sells petrol for.069 per litre, another sells petrol for per litre. a What is the difference in the price per litre? b How much could a driver save by buying 20 litres at the lower price?. boy weighs 7 stones 2 pounds. 4 pounds stone and kg 2.2 pounds. How much does the boy weigh, in kilograms? 4. car s petrol tank holds 2 gallons of petrol when full. gallon is approximately 4. litres. What is 2 gallons, in litres? Pearson Education 2008 Functional Maths Level 2 hapter 2 page 27 raft for Pilot

16 2 alculating with money Learn the skill Money problems often involve decimal calculations. Example : company charges a fi xed cost of 7 for specially designed cards, plus a printing charge of p for each card. a How much will they charge for an order of 20 cards? b How many cards would you get for 20? The fi nal price is in pounds, so change the pence to pounds. p 0.0 a The cost for the cards i s So the total cost is nswer: Test tip If the fi nal answer is in pounds, change any pence to pounds b To fi nd the printing charge, subtract the fi xed cost of 7. The printing charge is 20 7 Each card costs p to print, so work out how many ps there are in : nswer: 260 cards Example 2: $.8 a Use the above exchange rate to change 20 to dollars. b What calculation would you do to check your answer? a Every is worth $.8. There will be more dollars than pounds, so multiply: 20.8 (20 ) + (20 0.8) + (20 0.0) nswer: $462.0 To change from pounds to dollars, multiply by.8. b The calculation is: 20!.8! $462.0 To check the calculation, start from $462.0 and work backwards, doing the inverse operation. 20 ".8 " $462.0 nswer: $ is the inverse of is the inverse of raft for Pilot Functional Maths Level 2 hapter 2 page 28 Pearson Education 2008

17 Working with fra c tions, d e cimals and p erc e nt a g e s 2 Try the skill. The cost of hiring a carpet cleaner is basic charge plus 2.0 per day. What is the cost of hiring a carpet cleaner for four days? 2. man earns a basic rate of 2.20 per hour for a -hour week. For each hour worked over hours he earns.2 times the basic rate. How much does the man earn in a week when he works 40 hours? You need to be able to work out the answers to these questions without a calculator, but remember to use your calculator as a check for your calculations.. T-shirt company sells personalised T-shirts with names printed on them. The company charges 0.99 for each T-shirt plus 8p for each letter printed on it. How much will it cost to buy a T-shirt with the name lexander printed on it? 4. children s entertainer charges a fi xed fee of 60 plus 8.0 per hour to attend a party. How much does she charge to attend a party for. hours?. woman is buying an outfi t for a wedding. She spends 2.99 on a dress, 6 on shoes and 70.0 on a hat. Round the prices to the nearest pound to estimate the total cost of her outfi t. 6. girl receives 464 euros in exchange for 20. The exchange rate is.4 euros. What calculation would you do to check this is correct? 7. car is priced at euros. Use the approximate conversion to approximate the price of the car, in pounds. heck your answer is sensible. euros, so you need fewer pounds than euros. 8. $.8. Use this rate to change 280 to dollars. Pearson Education 2008 Functional Maths Level 2 hapter 2 page 29 raft for Pilot

18 what you have learned First complete this In a decimal number, the separates the whole number from the part that is less than. To round a number: ount along to the last digit that is needed. If the next digit is, 6, 7, 8 or 9, the last digit up. If the next digit is 0,, 2, or 4, the last digit. nswers to money calculations in pounds should be written correct to the nearest penny ( decimal places). Try the skill. car travels at 60 mph. mile is roughly.6 km. What is the speed in km per hour? 7 km per hour 8 km per hour 90 km per hour 96 km per hour 2. garage records the carbon monoxide emissions of two cars. One emits 0.4 g/km and the other emits.4 g/km. What is the difference in the emissions, to the nearest tenth of a g/km? 0.7 g/km 0.8 g/km 0.9 g/km.0 g/km. The exchange rate on a particular day is euro 69.2 pence. How would you calculate the value of 0 in euros? raft for Pilot Functional Maths Level 2 hapter 2 page 0 Pearson Education 2008

19 Working with fra c tions, d e cimals and p erc e nt a g e s 2 4. dog weighs 26 pounds. kg is approximately 2.2 pounds. How much does the dog weigh, in kilograms, to the nearest kilogram? 2 kg kg 8 kg 7 kg. garage charges 2.0 per hour for labour plus the cost of parts. The repairs to a woman s car take.2 hours and the parts cost.70. Which of these calculations works out the total bill?.70 + (2.0.2) ( ).2 (.70.2) ( ) boy is buying hristmas presents. He buys a for 9.0, a pair of gloves for 2.99, a book for.7 and a game for Round the prices to the nearest pound to estimate the total On a particular day the exchange rate between pounds and dollars is $.8 dollars. How much is 400 worth, in dollars? $26 $48.0 $720 $ The diagram shows the work surface in a hotel kitchen. The surface is to be covered with stainless steel. What is the area of the work surface? 9. n offi ce manager is buying IT equipment. She buys three desktop P base units at each, two small monitors at each and one large monitor at She rounds the prices to the nearest pound to estimate the total. What is the total?.6 m m m m Pearson Education 2008 Functional Maths Level 2 hapter 2 page raft for Pilot

20 Working with percentages, fractions and decimals You should already know how to: read, write, order and compare simple percentages understand simple percentage increase and decrease find simple percentage parts of quantities and measurements. y the end of this section you will know how to: calculate percentage increase and decrease calculate using percentages in everyday contexts evaluate one number as an (approximate) percentage of another calculate percentage change use a calculator to work out percentage calculations identify equivalence between fractions decimals and percentages use fractions, decimals and percentages in practical problems. Percentages Learn the skill percentage is a way of expressing a number as a proportion of 00. For example, 0% Example : Find 0% of 60. 0% of 60 is 6, so 0% of 60 is 6 8 nswer: 8 0% To fi nd 0%, divide by 0. % 0% 2 20% 0% 2 You can increase a quantity by a percentage. The original quantity is 00%. The increased quantity will be more than 00%. Example 2: Increase 40 by 2%. First fi nd 2% of This is the amount it is increased by nswer: 0 heck your answer is more than the original amount. raft for Pilot Functional Maths Level 2 hapter 2 page 2 Pearson Education 2008

21 Working with fra c tions, d e cimals and p erc e nt a g e s 2 You can work out a percentage increase in a single calculation: 00% + 2% 2% 2% You can decrease a quantity by a percentage. The original quantity is 00%. The decreased quantity will be less than 00%. Example : ecrease 80 by 7%. First fi nd 7% of This is the amount it is decreased by nswer: 20 You can also fi nd 2% mentally: 2% 4 4 of 40 0 so 2% of In a single calculation: 00% 7% 2% 2% of Try the skill Try out each of the above methods in these questions and decide which you like best.. ecrease 7 by 4%. 2. Increase 80 by %.. Increase 4 by 40%. 4. ecrease 400 by %. Using the % key on a calculator: Example Find 2% of 240 Solution of means input % gives the answer 28.8 Note: do not press Use the % key on your calculator to check your answers.. Increase 20 by 20%. 6. ecrease 620 by %. 7. ecrease 80 by 2%. 8. Increase by 0%. Pearson Education 2008 Functional Maths Level 2 hapter 2 page raft for Pilot

22 2 Using percentages Learn the skill Prices can be increased by a percentage, for example when VT is added, or they can be decreased, for example in a sale. Example : clothes shop reduces its prices by 0% in a sale. What is the sale price of a dress that cost 0 before the sale? Original price is 00%. Sale price is 00% 0% 70%. 00% 0 0% 70% 7 nswer: Example 2: television costs 00 plus VT at 7 2 %. What is the total price of the television, including VT? 00% 00 0% 0 % 2 2 % 7.0 so 7 2 % Total cost of television nswer: 2.0 When working with questions involving money, give your answers to two decimal places. For example, an answer of. means.0. VT is Value dded Tax. One number as a percentage of another is: fi rst number second number 00 Example : Express p as a percentage of. 00p nswer: % To express one quantity as a percentage of another, you must write them in the same units. Sometimes test questions ask for the approximate percentage. Example 4: company has 794 employees. In a survey, 7 said they travelled to work by motorbike. pproximately what percentage of the employees travel to work by motorbike? pproximate 794 to 800 and 7 to 60 (8 is a factor of 6). Now work out the fraction as a percentage. nswer: 20% raft for Pilot Functional Maths Level 2 hapter 2 page 4 Pearson Education 2008

23 Working with fra c tions, d e cimals and p erc e nt a g e s 2 Try the skill. Mconut s reduce the price of their food by 20% in a sales promotion. double burger usually costs.0. How much will it cost in the sales promotion? 2. girl puts 200 into a savings account that has an interest rate of 4.% ER. She leaves the money in the account. How much will she have in the account at the end of the year? The ER is the nnual Equivalent Rate, used to help compare rates for savings.. The VT on gas and electricity bills is %. How much VT will be added to a monthly gas bill of? 4. V player costs 20 before VT of 7 2 % is added. What is the cost of the V player, including VT?. Write 2 as a percentage of Express 4 mm as a percentage of 20 cm. 0 mm cm 7. The price of a sandwich in a canteen goes up from.24 to.. Express the increase in price as an approximate percentage of the original price. 8. In a car park of 200 cars, 42 were made in Europe and the rest were made in Japan. pproximately what percentage of the cars were made in Japan? Pearson Education 2008 Functional Maths Level 2 hapter 2 page raft for Pilot

24 Percentage change Learn the skill You fi nd a percentage change using this formula: percentage change actual change original value 00 Example : In 2004, 640 million mobile phones were sold. In 200, 720 million mobile phones were sold. What is the percentage increase in the number of mobile phones sold from 2004 to 200? For percentage increase the formula is: percentage increase actual increase original value ctual increase million Percentage increase % nswer: 2.% The word change may be replaced by increase, decrease, profi t or loss. Example 2: shopkeeper buys 0 kg of bananas for 0 and sells them for 90 pence per kilogram. What is his percentage profi t? Give your answer to one decimal place. For percentage profi t the formula is: percentage profi t ost price 0 actual profi t original value 00 Selling price (90 0) pence (90 00) + (90 0) pence ctual profi t 0 2 Percentage profi t ) % nswer: 22.7% Make sure the quantities are in the same units. lways check your answers are sensible. y estimation: % approximately. raft for Pilot Functional Maths Level 2 hapter 2 page 6 Pearson Education 2008

25 Working with fra c tions, d e cimals and p erc e nt a g e s 2 Try the skill. In pril, 20 people visited an art exhibition. In May, 67 people visited the art exhibition. What was the percentage increase in the number of visitors to the art exhibition between pril and May? 2. hockey club bought 0 sweatshirts for 00. The same club sold the sweatshirts for 2.0 each. What was the percentage profi t? In percentage change questions, fi rst write down the original amount, which is the amount before the increase or decrease. The denominator is the original value.. man bought a car for 00. He later sold it for 200. What was his percentage loss? 4. factory employed 60 workers. The number of workers decreased to 42. What was the percentage decrease in the number of workers?. In 2004, a large company makes a profi t of In 200 the company makes a profi t of m. What is the percentage increase in the profi t? 6. clothes shop reduces the price of T-shirts from 2.0 to 2. What is the percentage discount? 7. shopkeeper buys 00 umbrellas for 00. He sells the fi rst 7 for 6 each and the rest for 4 each. What is his percentage profi t? Pearson Education 2008 Functional Maths Level 2 hapter 2 page 7 raft for Pilot

26 4 onverting between forms Learn the skill To convert a fraction to a decimal, divide the numerator by the denominator. Example : onvert to a decimal. which gives 0. nswer: 0. You use place value to convert a decimal to a fraction. Example 2: onvert 0.2 to a fraction is an example of a recurring decimal. It can be written as 0.. To write fractions in their lowest terms, cancel any common factors. 0.2 has three places of decimals which means you use thousandths. nswer: 8 s a percentage is a proportion of 00: To convert a percentage to a fraction or decimal, divide by 00. Example : onvert 6% to a fraction. 6% nswer: 20 ividing by 00 moves all the digits two places to the right Example 4: onvert 2.% to a decimal. 2.% nswer: 0.02 To convert a fraction or a decimal to a percentage you do the opposite operation. To convert a fraction or decimal to a percentage, multiply by 00. Example : onvert to a percentage % nswer: 62.% Example 6: onvert to a percentage. You need to work out nswer: 46.2% to simplify the multiplication by cancelling. Multiplying by 00 moves all the digits two places to the left raft for Pilot Functional Maths Level 2 hapter 2 page 8 Pearson Education 2008

27 Working with fra c tions, d e cimals and p erc e nt a g e s 2 Try the skill. hange each of these fractions to a decimal and a percentage. a c 4 b d hange each of these decimals to a percentage and a fraction. a 0.6 b 0.2 c 0.08 d 0.6. hange each of these percentages to a decimal and a fraction. a 64% b 24% c 4% d 8.% Pearson Education 2008 Functional Maths Level 2 hapter 2 page 9 raft for Pilot

28 Using fractions, decimals and percentages in practical problems Learn the skill You can decide which of fraction, decimal or percentage form to use in practical problems. Example : In a sale, a dress shop reduces its prices by 2%. What is the sale price of a dress which cost 60 before the sale? The original price is 00%, so the sale price is 00% 2% 7% 7% Using percentages: 60 7 % nswer: 4 Using decimals: nswer: 4 Using fractions: 60 4 nswer: 4 Example 2: MP player costs 220 before VT of 7 2 % is added. What is the cost of the MP player, including VT? The original price is 00%, so the cost including VT is 7 2 %. 7 % is the same as 7.% 2 7.% 7..7 as a decimal 00 Using percentages: % nswer: 28.0 Using decimals: nswer: 28.0 Using fractions: nswer: 28.0 Try the skill Try out each of the above methods in these questions, both with and without a calculator and decide which you like best.. Find the price of a sofa costing 0 after a discount of 40%. 2. company employs 480 people. Find the total number employed by the company after an increase of % in the number of people employed. ecide which of these methods you would fi nd easiest without using a calculator. n answer of 28. should be written as 28.0 in pounds and pence.. Emma s salary is a year. What is her new salary after an increase of 4%? 4. The value of a car depreciates by % in the fi rst year. car costs 000 when new. What is its value after one year? To depreciate means to go down in value.. Rebecca invests 000 in a savings account with an interest rate of 6.2% per annum. How much will be in her account at the end of the fi rst year? raft for Pilot Functional Maths Level 2 hapter 2 page 40 Pearson Education 2008

29 Working with fra c tions, d e cimals and p erc e nt a g e s 2 6 what you have learned Learn the skill percentage is a way of expressing a number as a proportion of. To fi nd 0%, divide by. % 0% 2 20% 0% 2 The original quantity is. The increased quantity will be than 00%. The decreased quantity will be than 00%. Read VT questions carefully do you want the VT, or the price including VT? The quantities must be in the same units. One number as a percentage of another is: number number 00 percentage change actual change 00 The word change may be replaced by increase, decrease, profi t or loss. To convert a fraction to a decimal, divide the by the. To convert a fraction or decimal to a percentage, by 00. To convert a percentage to a fraction or decimal, by 00. these equivalences: Fraction ecimal Percentage 0. 0% 4 2%.. % or % % or 66 2 % 0.7 7% Pearson Education 2008 Functional Maths Level 2 hapter 2 page 4 raft for Pilot

30 Use the skill. 28% of the money spent on the National Lottery goes to good causes. How much money went to good causes in a year when was spent on the National Lottery?.68 million 6.8 million 68 million 680 million 2. shopkeeper changes his opening hours. He used to open from 9.00am to.00pm, but he now opens from 8.00am to 6.00pm. What is the percentage increase in the number of hours the shop is open? 20% 2% 7% 80%. cleaner s basic rate of 8.60 per hour is increased by %. Which calculation gives the new basic rate per hour? ( ) shopkeeper bought a television for 00 and sold it for. Which calculation gives the percentage profi t? In a survey, 2 students were asked how much time they had spent on revision and homework in one week. The results are shown in the table below. Number of hours Number of students 0 to less than 2 to less than to less than 2 to less than or more What percentage of the students spent between 0 and hours on their homework? 2% 48% 2% % raft for Pilot Functional Maths Level 2 hapter 2 page 42 Pearson Education 2008

31 Working with fra c tions, d e cimals and p erc e nt a g e s 2 6. In a sale, a carpet store reduces the price of its carpets by 40%. efore the sale, one particular carpet cost 20.0 per square metre. What is the sale price of this carpet per square metre? In a survey of 00 shoppers in Oxford High Street, 7 of them had used the park-and-ride scheme to get to the city centre. pproximately what percentage is this? 0% 29% 28% 27% 8. health-and-fi tness club offers membership for 2 per month for 2 months, or 27 for the whole year. Which calculation gives the percentage saved by paying 27 for the year? shopkeeper keeps a record of the different types of Vs she sells. bout of the Vs are children s Vs. 8 What percentage is closest to 8? 6% 8% 6% 8% 0. On average, only 8% of people who attend a local cinema buy membership. Which fraction is closest to 8%? Pearson Education 2008 Functional Maths Level 2 hapter 2 page 4 raft for Pilot

32 . In a survey of 6- to 8-year-olds at FE colleges: 2 were studying economics 2 in every 00 were studying physics 22% were studying law 2 in every ten were studying psychology ccording to the survey, what was the most common subject studied? economics physics law psychology 2. survey of a sample of library users showed that 8 were children. What is this fraction as a decimal? Four friends estimate the amount of fat in their Indian takeaway as, 22%, 0.26 and 4. Which is the highest estimate? 22% Estimates for the number of vegetarians in a company are 8, 0%, 0.08 and 7. Which is the smallest estimate? 8 0% of the people questioned in a survey said they did not vote in the last election. What percentage is closest to 6? 6% 4% 7% 20% raft for Pilot Functional Maths Level 2 hapter 2 page 44 Pearson Education 2008