Number: Fractions and percentages

Transcription

1 Numer: Frctions nd percentges. One quntity s frction of nother HOMEWORK A FM FM AU PS 7 Write the first quntity s frction of the second. p, 0p kg, kg c hours, hours d dys, 0 dys e dys, weeks f 0 minutes, hours vid scored gols out of his tem s seson totl of gols. Wht frction of ll the gols did vid score? Jmes works for weeks yer. Wht frction of the yer does he work for? Mrk erns 0 nd sves 0 of it. Bev erns 0 nd sves 0 of it. Who is sving the greter proportion of their ernings? In test, Kevin scores 7 out of 0 nd Slly scores out of 0. Which is the etter mrk? Explin your nswer. In dncing group, there re 0 dncers, of whom re women. Hlf of the men re single. Wht frction of the dncers re single men? Give your nswer in its simplest form. A us driver sys tht t lest two out of every three pssengers on her us hve trvel pss. A different driver sys it is less thn three out of four. If oth sttements re true nd the us is crrying 0 pssengers, how mny hve trvel pss? Write down ll possile nswers.. Adding nd sutrcting frctions HOMEWORK B Evlute the following. + + c + 0 d + e + f + g + h + Evlute the following. + + c + d + Evlute the following. 7 c d Evlute the following. + + c + d + 0 FM Functionl Mths AU (AO) Assessing Understnding PS (AO) Prolem Solving

2 HAPTER : Numer: Frctions nd percentges AU 7 PS 9 PS FM 0 At footll clu, hlf of the plyers re English, qurter re Scottish nd one-sixth re Itlin. The rest re Irish. Wht frction of plyers t the clu re Irish? One of the following is the numer of plyers t the clu: 0 How mny plyers re t the clu? On firm s coch trip, hlf the people were employees nd two-fifths were prtners of the employees. The rest were children. Wht frction of the people were children? Five-eighths of crowd of 000 people were mle. How mny femles were in the crowd? Wht is four-fifths of dded to five-sixths of? Here re four frctions. Which three of them dd up to? Pipes re mde in m nd m lengths. Show how it is possile to mke pipe exctly m long using the lest numer of m nd m pipes. Assume tht you cnnot cut pipes to size.. Multiplying frctions HOMEWORK AU PS AU 7 Evlute the following, leving your nswer in its simplest form. c d e f g h i j Kris wlked three-qurters of the wy long rterknowle Rod which is km long. How fr did Kris wlk? Jen te one-fifth of cke, Les te hlf of wht ws left. Nick te the rest. Wht frction of the cke did Nick et? A formul for working out the distnce trvelled is: istnce trvelled = Speed Time tken A snil is moving t one-tenth of metre per minute. It trvels for hlf minute. How fr hs it trvelled? George is given 0. Ech week he spends hlf of the mount left. Wht frction of the 0 will he hve left fter weeks? You re given tht litre = 00 cl. A ottle holds. litres. Tupc drinks hlf of the contents. Belind drinks cl of the contents. Wht frction of the contents re left? Evlute the following, leving your nswer s mixed numer where possile. c d 0 e f g h

3 HAPTER : Numer: Frctions nd percentges PS AU 9 Which is the smller, of or of? I estimte tht I need 0 litres of lemonde for prty. I uy ottles, ech contining litres. Hve I ought enough lemonde for the prty? PS 0 AU FM Pizzs re often cut into equl pieces. If pizz is cut into six equl pieces how much more pizz is in ech piece? Give your nswer s frction of the whole pizz. A compny employs 00 people. The mnger sys tht exctly two-thirds of the employees re women nd three-qurters of the employees re full-time. One of the sttements is true nd one is not ccurte. Explin which sttement is which. A fish frmer is trying to work out how mny fish re in pond. He cptures 00 fish, mrks them nd puts them ck in the pond. Lter he cptures 00 fish nd finds tht re mrked. Approximtely how mny fish re in the pond?. ividing y frction HOMEWORK FM AU Evlute the following, leving your nswer s mixed numer where possile. c d 7 9 e f g h i j 7 k l A pet shop hs kg of hmster food. Tom, who owns the shop, wnts to pck this into gs, ech contining three-qurters of kilogrm. How mny gs cn he mke in this wy? Bo is putting fence down the side of his grden, it is to e 0 m long. The fence comes in sections; ech one is m long. How mny sections will Bo need to put the fence ll the wy down the one side of his grden? PS An Africn ullfrog cn jump distnce of m in one hop. How mny hops would it tke n Africn ullfrog to hop distnce of 00 m? AU FM PS 7 Three-fifths of ll -yer-olds in school visit the dentist ech yer. One-third of those who do not visit the dentist hve prolem with their teeth. Wht frction of the -yer-olds do not visit the dentist nd hve prolem with their teeth? How mny hlf-litre tins of pint cn e poured into. litre pint try without spilling? I work hours in dy. Short tsks lst hour. Long tsks lst hour. I hve to complete t lest three long tsks. How mny short tsks cn I lso do in one working dy?

4 HAPTER : Numer: Frctions nd percentges Evlute the following, leving your nswer s mixed numer wherever possile. c d e f. Incresing nd decresing quntities y percentge HOMEWORK E B 9 0 PS FM 7 Increse ech of the following y the given mount. 0 y % kg y % c y % Increse ech of the following y the given mount. 0 g y 0% m y % c y 0% Keith, who ws on slry of 00, ws given py rise of %. Wht ws his new slry? In 99 the popultion of ripfield ws 00. By 00 tht hd incresed y %. Wht ws the popultion of ripfield in 00? In 99 the numer of ikes on the rods of oncster ws out 0. Since then it hs incresed y %. Approximtely how mny ikes re on the rods of oncster now? A dining tle costs 00 efore the VAT is dded. If the rte of VAT goes up from % to 0%, how much will the cost of the dining tle increse? A resturnt mel is dvertised t 0 ( service chrge will e dded to ll ills). Romno s Bistro Prwn ocktil.0 hicken Risotto.0 Se Bss.0 Fries.0 Tirmisu.0 hoc fudge cke.0 offee.00 Service chrge.00 Totl.00 PS The ill for two people is shown. Show tht the service chrge is %. A shopkeeper decides to increse prices y % or, whichever is greter. Wht is the price rnge of the items tht will rise y? HOMEWORK F ecrese ech of the following y the given percentge. (Use ny method you like.) 0 y 0% 0 y 0% c 90 kg y 0% d 00 m y % e 0 y % f 0 cm y % g 00 g y % h y % i kg y 7% j y 7% 7

5 HAPTER : Numer: Frctions nd percentges FM FM Mrs enghli uys new cr from grge for 00. The grge owner tells her tht the vlue of the cr will lose % fter one yer. Wht will e the vlue of the cr fter one yer? The popultion of villge in 00 ws 00. In 00 the popultion hd decresed y %. Wht ws the popultion of the villge in 00? A Trvel Agent is offering % discount on holidys. How much will the dvertised holidy now cost? NEW YORK FOR A WEEK 0 FM FM 7 AU PS PS 9 New Yer s Sle: All prices reduced y 0% Mtt ws given 0 t hristms. n he fford to uy shirt tht normlly costs 0, suit tht normlly costs 0 nd pir of shoes tht normlly cost? On the first dy of new term, school expects to hve n ttendnce rte of 99%. If the school popultion is 700 pupils, how mny pupils will the school expect to e sent on the first dy of the new term? By putting cvity wll insultion into your home, you could use 0% less fuel. A fmily using n verge of 0 units of electricity yer put cvity wll insultion into their home. How much electricity would they expect to use now? A shop increses ll its prices y 0%. One month lter it dvertises 0% off ll mrked prices. Are the goods cheper, the sme or more expensive thn efore the price increse? Show how you work out your nswer. Prove tht 0% increse followed y 0% decrese is equivlent to % increse overll.. Expressing one quntity s percentge of nother HOMEWORK G PS Express ech of the following s percentge. Give your nswers to one deciml plce where necessry. of 0 0 kg of 0 kg c m of 0 m d of 0 e 00 g of 00 g f cm of 0 cm g of h minutes of hour i 7 of 0 j dys of weeks Wht percentge of these shpes is shded?

6 HAPTER : Numer: Frctions nd percentges AU PS 7 PS FM 9 0 In clss of 0 pupils, re girls. Wht percentge of the clss re girls? Wht percentge of the clss re oys? The re of frm is 0 hectres. The frmer uses 0 hectres for psture. Wht percentge of the frm lnd is used for psture? Give your nswer to one deciml plce. Find the percentge profit on the following items. Give your nswers to one deciml plce. Item Retil price (selling price) Wholesle price (price the shop pid) Micro hi-fi system 0 0 rdio cssette 90 0 Miniisc plyer.99 0 ordless hedphones 9.99 Pul nd Vl tke the sme tests. Both tests re worth the sme numer of mrks. Here re their results. Test A Test B Pul 0 0 Vl 9 Whose result hs the greter percentge increse from test A to test B? Show your working. A smll trin is crrying pssengers. At sttion, more pssengers get on so tht ll sets re filled nd no one is stnding. At the next sttion, 70% of the pssengers leve the trin nd 0 new pssengers get on. There re now pssengers on the trin gin. How mny sets re on the trin? In secondry school, 0% of students hve younger rother or sister t primry school. 0% of students hve two younger rothers or sisters t primry school Altogether there re 700 rothers nd sisters t the primry school. How mny students re t the secondry school? Jmes cme home from school one dy with his end-of-yer test results. hnge ech of Jmes results to percentge. Mths out of 7 English out of 0 Science 7 out of 0 French 7 out of 0 uring the wet yer of 99, it rined in London on 0 dys of the yer. Wht percentge of the dys of the yer were wet? Give your nswer to two significnt figures..7 ompound interest nd repeted percentge chnge HOMEWORK H A smll plnt increses its height y 0% ech dy in the second week of its growth. At the end of the first week, the plnt ws cm high. Wht is its height fter further: dy dys c dys d week? 9

7 HAPTER : Numer: Frctions nd percentges FM PS The hedmster of new school offered his stff n nnul py increse of % for every yer they styed with the school. Mr Speed strted teching t the school on slry of 000. Wht slry will he e on fter yers if he stys t the school? Miss Tuck strted teching t the school on slry of 00. How mny yers will it e until she is erning slry of over 0 000? Billy put gift of 0 into specil svings ccount tht offered him % compound interest if he promised to keep the money in for t lest yers. How much ws in this ccount fter: yers yers c yers? The penguin popultion of smll islnd ws only 00 in 99, ut it stedily incresed y out % ech yer. lculte the popultion in: c 00 A sycmore tree is 0 cm tll; it grows t rte of % per yer. A conifer is 0 cm tll. It grows t rte of % per yer. How mny yers does it tke efore the conifer is tller thn the sycmore? B AU PS 7 The popultion of smll town is 000. The popultion is flling y 0% ech yer. The popultion of nery villge is 00. This popultion is rising y 0% ech yer. After how mny yers will the popultion of the town e less thn the popultion of the villge? Ech week, oy tkes out 0% of the mount in his nk ccount to spend. After how mny weeks will the mount in his nk ccount hve hlved from the originl mount?. Reverse percentge (working out the originl quntity) HOMEWORK I B A FM Find wht 00% represents when: 0% represents 0 g % represents m c % represents cm. Find wht 00% represents when: 0% represents kg 0% represents c % represents hours. VAT is government tx dded to goods nd services. With VAT t 7.%, wht is the pre-vat price of the following priced goods? Jumper.0 Socks. Trousers.0 Pul spends 9 ech week on s. This is 0% of her weekly income. How much is Pul s weekly income? Aln s weekly py is incresed y % to 7.0. Wht ws Aln s py efore the increse? Jon s slry is now 90. This is 0% more thn he erned two yers go. Lst yer his slry ws % more thn it ws two yers go. How much ws his slry lst yer? By wht percentge ws his slry incresed lst yer? 0

8 HAPTER : Numer: Frctions nd percentges PS AU 7 PS Twice s mny people visit shopping centre on Sturdys thn on Fridys. The numer visiting on oth dys increses y 0% in the week efore hristms. How mny more visit on this Sturdy thn on this Fridy? Give your nswer s percentge. A mn s svings decresed y 0% in one yer nd then incresed in the following yer y 0%. He now hs 7. How much did he hve two yers go? A Functionl Mths Activity Tsk omplete the tles. Vlue Added Tx You re shopkeeper nd need to use tle to work out the VAT you chrge on items for sle. VAT tle Rte % p 0p % 0 % 0 7.% 0 0% 000 Totl cost tle Rte % % 0 % 0 7.% 0 0% 000 Tsk All Prices Exclusive of VAT Here re some items from the shop priced excluding VAT. Use the tles to help you work out the price including VAT t 7.%.

9 HAPTER : Numer: Frctions nd percentges Functionl Mths Activity (continued) Tsk All Prices Inclusive of VAT Here re some items priced including VAT. Use the tles to help you work out the price excluding VAT t 7.%. Work out the VAT chrged.