Fractions, Decimals and Percentages

Transcription

1 Student Frtions, Deimls nd Perentges My nme Series G

2 Copyright 009 P Lerning. All rights reserved. First edition printed 009 in Austrli. A tlogue reord for this ook is ville from P Lerning Ltd. ISBN Ownership of ontent The mterils in this resoure, inluding without limittion ll informtion, text, grphis, dvertisements, nmes, logos nd trde mrks (Content) re proteted y opyright, trde mrk nd other intelletul property lws unless expressly indited otherwise. You must not modify, opy, reprodue, repulish or distriute this Content in ny wy exept s expressly provided for in these Generl Conditions or with our express prior written onsent. Copyright Copyright in this resoure is owned or liensed y us. Other thn for the purposes of, nd sujet to the onditions presried under, the Copyright At 9 (Cth) nd similr legisltion whih pplies in your lotion, nd exept s expressly uthorised y these Generl Conditions, you my not in ny form or y ny mens: dpt, reprodue, store, distriute, print, disply, perform, pulish or rete derivtive works from ny prt of this resoure; or ommerilise ny informtion, produts or servies otined from ny prt of this resoure. Where opyright legisltion in lotion inludes remunerted sheme to permit edutionl institutions to opy or print ny prt of the resoure, we will lim for remunertion under tht sheme where worksheets re printed or photoopied y tehers for use y students, nd where tehers diret students to print or photoopy worksheets for use y students t shool. A worksheet is pge of lerning, designed for student to write on using n ink pen or penil. This my led to n inrese in the fees for edutionl institutions to prtiipte in the relevnt sheme. Pulished P Lerning Ltd For more opies of this ook, ontt us t: Designed P Lerning Ltd Although every preution hs een tken in the preprtion of this ook, the pulisher nd uthors ssume no responsiility for errors or omissions. Neither is ny liility ssumed for dmges resulting from the use of this informtion ontined herein.

3 Series G Frtions, Deimls nd Perentges Contents Topi Frtions (pp. ) equivlent frtions mixed numers nd improper frtions simplifying frtions Dte ompleted ompring nd ordering frtions / renming nd ordering frtions / / / spend nd sve solve trik or tret! pply / / / / Topi Deiml frtions (pp. 9) tenths, hundredths nd thousndths reding nd writing deimls ompring nd ordering deimls renming deimls rounding perentges sk round pply perentge prolems solve Topi Frtions of n mount (pp. 0 ) finding frtions perentge finding disounts shopping spree pply disount dilemms solve

4 Series G Frtions, Deimls nd Perentges Contents Topi Clulting (pp. 9 ) dding nd sutrting ommon frtions multiplying frtions y whole numers dding deiml frtions sutrting deiml frtions multiplying deimls y 0, 00 nd,000 dividing deimls y 0, 00 nd,000 multiplying deiml frtions dividing deiml frtions wht numer m I? solve Dte ompleted Series Authors: Rhel Flenley Niol Herringer Copyright

5 Frtions equivlent frtions Equivlent frtions hve the sme vlue ut they hve different numertors nd denomintors. This mens they hve een divided into different numer of prts. Use the wll to find the equivlent frtions: Wht frtions n you find tht re equivlent to? Wht frtions n you find tht re equivlent to? How mny eighths re equivlent to? d How mny qurters re equivlent to? e Divide the ottom row into twelfths. Find some equivlent frtions for. Divide nd shde the shpes to show the following equivlent frtions. The first one hs een done for you. d e Copyright P Lerning G

6 Frtions equivlent frtions To find equivlent frtions without drwing digrms we use the numertors nd denomintors to guide us. Imgine your shre of ke is hlf. It is too ig to pik up so you ut your hlf into hlves. You now hve qurters of the ke. So you n see tht qurters re equivlent to hlf. You hve douled the numer of prts (the denomintor) nd y doing this you hve douled the numer of prts (the numertor). This method n e used to find ll equivlent frtions. Whtever you do to the numertor, you do the sme to the denomintor, nd vie vers. Use the lues to help you mke the equivlent frtions: d 9 0 e 9 f g h We n lso redue the numer of prts in whole. We divide to do this: 9 0 Whtever we do to the top, we do to the ottom. Whtever we do to the ottom, we do to the top. d e f 0 Answer the following: Cssie s tle won pizz for hving the most tle points t the end of term. There re pupils t the tle. Wht frtion of the pizz will they eh reeive? The pizz hs een ut into piees. How mny slies does eh pupil get? Wht is this s frtion? Stvros rekons tht euse they got slies they got more thn they would hve if the pizz hd een ut into piees. Is he right? Explin your nswer with words or digrms. G Copyright P Lerning

7 Frtions mixed numers nd improper frtions Mixed numers re mde up of whole numers nd frtions. Mixed numers n lso e expressed s improper frtions. Improper frtions re frtions where the numertor is igger thn the denomintor. n lso e written s. is mixed numer. Complete the numer lines y filling in the oxes: 0 Use the numer lines ove to help you find the mystery frtions. Sore points for orret nswer. Lose points for wrong nswer. For some questions, more thn nswer is orret. The first one hs een done for you. My sore Q This improper frtion is equivlent to. A or Q This improper frtion omes diretly efore. A Q This improper frtion is one third greter thn. A Q This mixed numer is the sme s 0. A Q This mixed numer omes diretly fter 9. A Q7 This improper frtion is equivlent to. A7 Q This improper frtion is equivlent to. A Q9 This improper frtion is equivlent to. A9 Q This improper frtion is equivlent to. A Q0 This mixed numer is one third less thn. A0 Copyright P Lerning G

8 Frtions simplifying frtions These frtions re ll equivlent to one hlf: Whih is the simplest? A frtion is in its simplest form when is the only numer tht oth numers n e divided y. We simplify frtions to mke reding nd working with frtions esier. Cirle the simplest frtion in eh group: d 9 To find the simplest frtion, we divide oth the numertor nd the denomintor y the sme numer. It mkes sense for this to e the iggest numer we n find so we don t hve to keep dividing. This numer is lled the Highest Common Ftor (HCF). Look t:?? Wht is the iggest numer tht goes into oth nd? is the iggest numer tht goes into nd. Find the highest ommon ftor nd then simplify: 0 HCF is HCF is 9 0 HCF is d HCF is Wlly sys he hs simplified these frtions s fr s he n. Is he right? If not, find the simplest frtion: d 0 G Copyright P Lerning

9 Frtions simplifying frtions Write the following frtions in their simplest form: e 9 f 0 9 Solve the following prolems. Write your nswers in the simplest form: Luke sored 0 on test. Wht frtion ws inorret? g d h 9 If you re not sure wht the HCF is, guess, hek nd improve is useful strtegy. Try your hoie out nd then look t your new frtion. Could it e ny simpler? Is the ONLY numer tht ould go into oth the numertor nd the denomintor? Mrik sored 0 on the sme test. Wht frtion did she get right? out of the 7 pupils in Yer ride their ikes to shool. Wht frtion does this represent? d Out of the pupils in F, rte Mths s their fvourite sujet. Wht frtion is this? e Wht frtion did not hoose Mths s their fvourite sujet? Colour nd mth the frtions on the ottom row with their simplest form: Copyright P Lerning G

10 Frtions ompring nd ordering frtions Compring nd ordering frtions with like numertors nd denomintors is simple proess: When the denomintors re different, we need to hnge the frtions so they hve the sme denomintor. This lets us ompre like with like. Whih is lrger? or To onvert qurters to eighths we doule the denomintor nd numertor, so eomes. is lrger thn, so is lrger then. Order these frtions: Hmm I hd etter mke the mixed numers into improper frtions s well. Tht will mke them esier to ompre. Renme frtion in eh group so tht you n ompre them more esily. Cirle the lrger frtion: d 0 Write or drw frtion on the left tht would result in the sle looking like this: Rememer with equivlent frtions, we think out wht we did to get from one to the other: G Copyright P Lerning

11 Frtions ompring nd ordering frtions Find prtner to ply this gme with: Nme frtion etween 0 nd nd ple it on the numer line. Your prtner then hs to nme nd ple frtion tht fits etween tht frtion nd. Then you hve to find one tht fits etween their frtion nd nd so on. The gme ontinues until one plyer nnot think of frtion, or n t fit one in. You n hllenge frtion plement. If you re right, your prtner hs to remove their frtion. If you re wrong, they get to do the told you so dne. All right, she put. I m going to put euse I know tht is more thn. 0 0 These frtions re ll out of order. Cut them out nd put them in order from smllest to lrgest. Ple ny equivlent frtions on top of eh other. There is spe for you to renme the frtions on eh of the rds if this will help. Shre your thinking with prtner. Hve they ordered them the sme wy? Copyright P Lerning G 7

12 Frtions renming nd ordering frtions Sometimes we hve to order nd ompre frtions with different numertors nd denomintors suh s, nd. To do this, we hve to find one ommon denomintor for ll the frtions. You hve kes for lss prty. One hs een ut into hlves nd one into thirds. The prolem is tht you wnt eh slie to e fir frtion of the kes. Continue utting the kes so tht eh ke hs the sme numer of fir slies: If you hd one of these new slies, wht frtion of the ke would you reeive? Tht is n exmple of how we renme frtions. We find wy to re-divide the wholes so tht they hve the sme numer of prts. To do this effiiently we find the smllest shred multiple. This is then lled the Lowest Common Denomintor (LCD): The multiples of re,,,, The multiples of re,, 9,,, is the LCD so we onvert oth frtions to sixths: Renme these frtions y first finding the shred LCD nd then onverting the frtions. Use the multiplition tle on the right to help you find the LCD: G Copyright P Lerning

13 Frtions renming nd ordering frtions Look t eh group of frtions. Predit whih you think is the lrgest nd irle your predition. Now, renme the frtions in the work spe elow so tht eh frtion in the group hs the sme denomintor. Use different olour to irle the lrgest frtion. Are there ny surprises? 9 d This time, renme the frtions nd irle the lrgest. Underline the smllest. 7 d For eh frtion write lrger frtion elow. The new frtion must hve different denomintor. It n hve different numertor. 9 If you n do this, you re whiz! This is rel extension Mths. Copyright P Lerning G 9

14 Spend nd sve solve Getting redy In this tivity you will solve money prolems. Working kwrds is useful working strtegy to use here. Wht to do Use the frtion pies to help you solve the following prolems: Srh s grn gve her some money for her irthdy. Srh sved of the money nd spent of the money on ook. Tht left her with in her purse. How muh money did her Grn give her? Mrth opened her piggy nk nd deided to spend it this wy: on mgzines; on snks; on nekle. The nekle ost. How muh money did she hve in her piggy nk? Ali went to the show. He spent of his money on rides nd of wht ws left on hot dog, some hips nd some ndy floss. Tht left him with to spend on show gs. How muh money did he hve to egin with? 0 G Copyright P Lerning

15 Trik or tret! pply Getting redy Wht to do Sm nd his mtes deide to go trik or treting one Hlloween. They then divvy up the loot. Use the hrt on the right to work out the nswers to the prolems elow: Totl 0 mini hoolte rs go stoppers Chupp Chups Wizz Fizzes ll dy sukers Ester eggs turnip In the opening round, Sm gets of the mini hoolte rs nd Chupp Chups. How mny of eh does he get? of the George wnted ll the go stoppers. In tense negotition with Sm, he mnged to sore of them. How mny did he get? How mny did he miss out on? To get his shre of the gostoppers, Sm hs to trde off he reeived in Question. How mny does he lose? of the Chupp Chups d Mr gets ll the Wizz Fizzes, the ll dy sukers, nd the remining of the hoolte rs. In totl, how mny items does she get? e Here is frtion sentene tht shows how the go stoppers were shred: + or whole. Write the frtion sentene tht shows how the hoolte rs were shred. f Mr deides to give of her Wizz Fizzes to George. Write the frtion sentene to show how mny she hs left. Now, write the sentene using whole numers. Copyright P Lerning G

16 Deiml frtions tenths, hundredths nd thousndths Common frtions nd deiml frtions re relted s they oth show prts of whole. In ommon frtions, we divide whole into prts suh s hlves or sixths. In deiml frtions, the whole is prtitioned using the se 0 system into tenths, then hundredths, then thousndths nd so on. We use deiml point fter the ones numer to indite the end of whole numers:. If the numer hs no whole numers, we use zero to mke sure we don t miss the deiml point: 0. Divide these wholes into tenths nd shde the speified mounts. Write eh s deiml frtion: Now divide these wholes into hundredths nd shde the speified mounts. Write eh s deiml frtion: Express these s deiml frtions: tenths, 7 hundredths, thousndths 0 tenths, 9 hundredths, thousndths 0 d e 0 tenths, hundredths, 9 thousndths 0 f g thousndths 0 h,000 9,000 7,000,000, G Copyright P Lerning

17 Deiml frtions reding nd writing deimls When we write deimls we follow this ple order: Thousnds Hundreds Tens Ones Tenths Hundredths Thousndths Numers efore the deiml point re whole numers. Numers fter the deiml point re prts of whole numer. The further the digit is to the left in the numer, the greter its vlue. The further it is to the right, the smller its vlue. Wht is the vlue of the digit in old? Tik the orret olumn: Thousnds Hundreds Tens Ones Tenths Hundredths Thousndths d 9.0 e f 0. g.9 Red eh numer nd write it s deiml: four ones, one hundred nd twenty two thousndths Wth out for the omms! They indite the end of whole numers. one hundred nd eleven, nd sixty five hundredths three hundred, nd forty two thousndths d four thousnd, nd twelve hundredths e twelve, nd thousndths f two hundred nd thirteen, nd forty-three hundredths These nswers re ll lose ut inorret. Write the orret nswers: twenty seven tenths is written s 0.7 forty eight hundredths is written s thousndths is written s d eleven nd hundredths is written s.0 e 7 hundredths is written s.7 No it s not, it s written s No it s not, it s written s No it s not, it s written s No it s not, it s written s No it s not, it s written s Copyright P Lerning G

18 Deiml frtions ompring nd ordering deimls We need to refully onsider the ple vlue of digits when ordering nd ompring deimls. Nme A Spitter Mgee B Did You See Tht One Big-noter C Seret-ingredient Spitski D Ded-eye Jones E The Long Distne Shooter F Slly Strw G Tehnique Tezz A hs very ool teher who deides to hrness, not n, the lss urrent osession with pe shooting. After week of intense trining, shootoff ours. The results for the top ten shooters re tled on the right. H I J Lone Shooter Doule Or Nothing Dnielle Shoot Dog Ple the pupils on the numer line. The first one hs een done for you. Distne. m. m. m. m.0 m. m.9 m.0 m.0 m.9 m A Use the ove informtion to nswer the following questions: Who shot the furthest on the dy? Whose shot ws the shortest? Whih pupils shots were hundredth of metre prt? d Wht ws the differene etween the shots of Shoot Dog nd Spitter Mgee? e Do you think you ould et this? Something to try t home perhps? Even A s teher eventully hd enough of the pe shooting. G Copyright P Lerning

19 Deiml frtions rounding We often round deimls to prtiulr ple vlue. We do this to mke the numers esier to work with. Look t.. We n round this to the nerest whole numer, tenth or hundredth. Let s round it to the nerest tenth. To do this, we look t the numer in the hundredths ple. This is, whih is loser to 0 thn, so we round the tenth up. The rounded numer is now.7 Round these numers to the nerest tenth: d 90. If the rounding numer is to, it rounds down. If it is to 9, it rounds up. e. f 7.0 Now round these numers to the nerest hundredth: d 7. e 9.0 f. Round the nswers to the nerest tenth: 0. (nerest 00th).99 (nerest 00th) 7 (nerest whole numer) d,09.07 (nerest 00th) Look t the following mel options. Round eh prie to the nerest pound nd totl the estimted ost of eh option elow: Choie Choie Choie Hmurger.9 Jket potto with heese 7.9 Sld roll. Cn of drink. Hot hoolte 0.9 Juie. Lrge hips. Sld.9 Bisuit.9 Totl Totl Totl You hve 0. Cirle the hoies you n fford. Copyright P Lerning G

20 Deiml frtions perentges Perent omes from the Ltin per entum nd mens prts per hundred. It is expressed using the symol %. Here, 0% hs een shded. This is the sme s 0 hundredths % We ommonly use perentges in sles % off everything TODAY ONLY; on tests I got %; nd when we re gthering nd reporting on dt 7% of people surveyed love hoolte. Fill in the missing vlues: d % % 0. 90% 0. % e f g h % 0.7 % 0. % 0. % It is useful to know some ommon perentges suh s %, 0%, 7% or 00%. Shde the grids to show the following perentges: d 0. % 0. % 0. % % G Copyright P Lerning

21 Deiml frtions perentges Not ll perentge vlues re whole numers etween nd 00. We n hve suh things s 00% growth or perentges tht ontin deimls suh s.%. Shde the grids to show the following perentges: 0% 0% 7% How would you show hlf perent? Cirle the option you think is orret. Disuss your hoie with prtner. Do they gree? Option A Option B 00 people were surveyed. They were sked to nominte their preferred wy of eting vegetles. Shde the grids to show the survey results: 7% preferred their veggies oiled till they were ll soggy nd wtery. % preferred their veggies stir fried. 9.% preferred their veggies rw. d 0.% did not re how they were prepred euse they weren t going to et them nywy. Copyright P Lerning G 7

22 Ask round pply Getting redy In this tivity you re going to design survey nd then sk 00 people your questions. You will then find wy to ommunite your results. Work in smll group. Wht to do As group, think out wht informtion you re going to gther. Some things to onsider might e: l Wht kind of nswers re you fter? l Will you provide options? How mny? Wht if someone gives n nswer you hven t inluded in your list? Wht if you get 00 different nswers? l Who is your trget udiene nd when will you sk them? If you re surveying pupils out their fvourite ie rem flvours, sking t lunh times would e good time. If you wnt dult responses, when is the est time to e le to tlk to 00 dults? l How will you reord the nswers? Pln your survey nd run it y your teher. If it ll looks good, ondut it. Wht to do next Use pie grph to represent your informtion. You my use this model elow or rete your own using spredsheet progrm. G Copyright P Lerning

23 Perentge prolems solve Getting redy We hve een using 00 grids to represent perentge, with eh squre representing %. Wht to do These grids re set up little differently. Work with prtner to figure out wht eh squre represents nd then nswer the questions. Prolem These squres hve vlue of. Wht is the vlue of squre? Wht is the vlue of the entire grid? If 0% of the grid is shded, wht vlue is shded? Prolem There re 0 orner shops in Smllville. 0% of these stok your fvourite Slush Puppy flvour. Use the grid to represent this informtion. How mny stores sell your fvourite flvour? 00 people Prolem If this grid represents 00 people, wht does eh squre represent? How mny people re represented y ten squres? 0 of the 00 people like wthing sports. Represent this on the grid in red. d people prefer plying sport to wthing it. Represent this in green. Copyright P Lerning G 9

24 Frtions of n mount finding frtions Wht proess do we use to find frtions of mounts? When we find of 0, we re shring 0 into groups. We use division to find frtions. Wrm up with this puzzle. Use division to find the nswer to eh lue. The solved puzzle will tell you the nme of very importnt dy of the yer L D 7 of of Y O of 00 of A of 9 S 00 of,000 Put this dte in your diry! Tell your friends! H of 00 T of M of 9 W of R of 00 We use frtions of time regulrly in our lives. Use the lok to work out: Wht frtion of n hour is minutes? Wht frtion of n hour is 0 minutes? Wht frtion of n hour is minutes? d Wht frtion of n hour is 0 minutes? e If Lus prtises guitr from :0 to : eh dy, wht frtion of n hour does this represent? f Ptrik prtises footll for hr min. How would you express tht s n improper frtion? g Find time spns tht represent of n hour. to to to 0 G Copyright P Lerning

25 Frtions of n mount finding frtions One we know how to find one prt of group, we n use this to find other frtionl mounts: To find of 9, we first find of 9 9 of 9 of 9 is times this of 9 Find the following frtionl mounts: d of of 0 of 9 e 9 0 of 0 f of of 0 The Wlsh hildren fight like ts nd dogs over omputer time nd their dd hs hd enough. He hs drwn up shedule nd sys tht if they don t stik to it, he will hide the keyord till Christms nd ut off the internet. Help the hildren work out their dily llotion nd sve them from fte worse thn deth: How mny minutes does eh hild get eh dy? Dyln Nin Ntsh How mny minutes must Dyln spend studying? How mny minutes will Nin spend on Mthletis? d Express the time llotions s frtions of n hour: Dyln Nin Dyln gets twie s muh time s Nin s he hs more homework. of his time is to e spent on study, the other hlf is free time. Ntsh gets of n hour more thn Nin ut 0 minutes less thn Dyln. She must spend of her time prtising her Frenh. Nin gets of n hour eh dy. of this is to e spent on Mthletis, the rest is free time. This one is puzzle. Red ll the lues refully one of them is your strting point. One you hve solved tht ll importnt first lue, the rest will follow. Ntsh Copyright P Lerning G

26 Frtions of n mount perentge We often hve to find perentges in rel life suh s 0% off tody only! 0% of 00 is 00 0 or 0. A 00 item would e redued y 0. Tht s esy if everything osts 00 ut how do we find perentges of numers other thn 00? There re numer of wys to do this here re some of them. Look t this 00 grid. It represents the totl ost of this phone whih is 00. Eh of the 00 squres represents % of this. To find the vlue of single squre we divide: Eh squre or perent represents. How do we then find 7% of 00? 7. PVG- Phone 00 Use the 00 grid to lulte: % of 00 is 0% of 00 is 0% of 00 is d % of 00 is e % of 00 is f 0% of 00 is g If the store dvertises sle of % off the ost of the phone, wht is the sving in pounds? Use the 00 grid to lulte the following. squre represents people: 00 people % of 00 people is % of 00 people is 0% of 00 people is d 0% of 00 people is e % of 00 people is f 0% of 00 people is g If % of the 00 people surveyed liked hoolte, how mny people liked hoolte? Ptterns n lso help us understnd perentges. Use ptterns to lulte. The first row hs een done for you. 0% of 0 is % of 0 is 0% of 0 is 0% of 0 is % of 0 is 0% of 0 is 0% of 0 is % of 0 is 0% of 0 is 0% of 00 is % of 00 is 0% of 00 is 0% of 00 is % of 00 is 0% of 00 is 0% of,000 is % of,000 is 0% of,000 is 0% of,000 is % of,000 is 0% of,000 is G Copyright P Lerning

27 Frtions of n mount perentge We n use frtions to help us lulte perentges. How n we lulte % of 0? We know tht % is the sme s. To find of 0 we divide y. 0 0 % of 0 is 0. Use your knowledge of frtions to lulte the perentges: % of 0 is 0% of 0 is 0% of 0 is 0% % % 0% 0 0% 7% of 0 of 0 of d % of is e % of is f 7% of 0 is Clultors re lso hndy for working out perentges. This is how we lulte 0% of 0: We enter 0 0 % Our nswer ppers 0 Use lultor to find these perentges: 0% of 00 ml % of 0 ml % of 00 kg d % of 70 km e % of 0 ml f 9% of 700 g % of 00 h % of 00 ml i 90% of,000 The nswer is 7. Use lultor to work out the perentges nd tik ll the squres tht mth the nswer: Wht is % of 00? Wht is 7% of 00? Wht is 0% of 70? Wht is % of? Wht is % of 0? Wht is % of 00? Wht is 0% of 0? Wht is 0% of 7? Copyright P Lerning G

28 Frtions of n mount rtio nd proportion A rtio is omprison etween two different things. red red red lue There re three red squres nd one lue squre, so we n sy tht the rtio of red squres to lue is to. This n e written s :. The order of the numers follows the order of the words. The rtio of lue to red squres is to or :. You n lso express rtios in reltion to totl s frtion. There re totl of four squres. Therefore, the rtio of red squres to the totl is. The rtio of lue squres to the totl is. We n sometimes simplify rtios. Two of the squres re green nd four re white, so the rtio of green to white is :. Both sides of this rtio n e divided y so it n e simplified to :. For every one green squre there re two white squres. green white white green white white If two rtios re the sme, we sy they re in proportion. : nd : re in proportion. The rtio of green loks to the totl numer of loks s frtion is. This n e simplified to, so nd re in proportion. Complete the following word prolems: There re 7 oys nd girls in lss. Express the rtio of oys to girls in the form :, nd the rtio of girls to the totl numer of hildren in the lss s frtion: There re sweets in g. re red nd the rest re green. Express the rtio of green to red sweets in the form :, nd the rtio of green to the totl numer of sweets s frtion: In litter of kittens qurter re ty nd the rest re lk nd white. Write the rtio of ty to lk nd white ts in the form :, nd rtio of ties to the totl s frtion: Cirle the pirs of rtios tht re in proportion: : nd :0 : nd : 7 nd nd nd 0 : nd : : nd :0 G Copyright P Lerning

29 Frtions of n mount rtio nd proportion I hve reipe for mking 0 up kes, ut I wnt to mke 0 kes. How muh of eh ingredient will I need? For 0 up kes For 0 up kes ups flour ups flour tespoon slt tespoons slt tespoons king powder tespoons king powder up utter ups utter up sugr ups sugr eggs eggs up milk ups milk These two Indin flgs re in proportion. (They re not drwn to sle.) The length of the smller one is 0 m. The rtio of the smller to the lrger is :. How long is the lrger one? The lrger flg is 0 m high. How high is the smller flg? These drwings re in proportion (ut not to sle). Wht is the rtio of the smller to lrger r in form :? The rtio of the smller to the lrger mn is :. How tll is the lrger mn? 7. m. m. m 7. m Copyright P Lerning G

30 Frtions of n mount finding disounts We hve to lulte disounts quite often in rel life. Stores hve mny speil offers nd nny onsumers n quikly lulte the svings to help them mke deisions out their purhses. How muh would you sve if the following disounts were offered? Choose method to lulte: DVD h e TV Plsm 00,0 t Tike h 0 e 0% off 0% off 0% off 0% off % off % off % off % off 0% off 0% off 0% off 0% off 0% off 0% off 0% off 0% off You re helping your grndp with his holidy shopping t Svers. Everything in the store mrked is % off, everything mrked is % off nd everything mrked is 0% off. Help your grndp lulte oth the svings nd the new osts: 0 Sving Sving New prie New prie Sving New prie 0 G 00 Sving New prie y Pupp 0 Sving New prie Copyright P Lerning

31 Shopping spree pply Getting redy Get redy to shop! Work in smll group for this tivity. You ll ll need opy of this pge. Clultors my not e used. You re eh going to fill your own shopping mll with things you like, then nother group memer will deide wht kind of disounts you n hve on eh item. opy Then you ll eh re round your own shopping mll lulting the new pries. You my keep ny items you lulte orret pries for. You hve to put k ny mistkes! Wht to do In eh shop is prie tg. Next to eh tg, drw something you think you d like tht would proly ost round this mount. Now swith your pper with someone else in the group. Choose disount of %, 0%, 0%, % or 0% to put next to the prie. You must pply eh disount t lest one. When everyone in your group is done, swith your pges k. On go, strt lulting. Who finishes first? The gme ontinues until everyone finishes their lultions. Use lultor to hek everyone s mths. Who kept ll their purhses? Exellent shopping. 0 % 00 % 0 % 0 % 0 % 0 % 0 % 0 % Copyright P Lerning G 7

32 Disount dilemms solve Getting redy Solve these shopping dilemms. You n work with prtner or y yourself. Show your mthemtil resoning for eh prolem. Wht to do DILEMMA You hve een eyeing up new pir of jens ville t your lol jens shop nd lso online. They re 00 t oth suppliers. In the sles, your jens shop offers disount of 0%, followed y further redution of 0% on the mrked sle prie. The online supplier offers stright 0% disount. Are these disounts the sme? If not, whih is the etter del? DILEMMA Would you rther eome 0% poorer nd then 0% riher or eome 0% riher nd then 0% poorer? DILEMMA The new gme you wnt osts 7 t one store nd 0 t nother. The first store then offers disount of % while the seond offers disount of 0%. Whih del gives you the hepest prie? G Copyright P Lerning

33 Clulting dding nd sutrting ommon frtions How do we dd or sutrt frtions? Look t this exmple: We hd movie mrthon on the weekend. On Sturdy, we wthed movies for 7 hours nd on Sundy we wthed for hours. How mny hours did we spend wthing movies in totl? 7 + First we dd the whole numers: 7 +. Then we dd the frtions: + Then we dd the two nswers together: + We use the sme proess to sutrt frtions. Solve these prolems: + + d + e f 7 Express these s frtion sentenes. Solve them: Srh nd Rhel go to jumle sle. Srh uys oxes of jumle nd Rhel uys oxes of jumle. How muh do they uy in totl You hve oxes of hooltes nd you et oxes. How mny oxes do you hve left? Before World Mths Dy, Akhil prties Live Mthletis for hours on Mondy nd hours on Tuesdy. How mny hours of prtie hs he put in ltogether? d Amn relly gets into sport for while then drops it nd moves on to his ltest rze. As onsequene, he hs five nd hlf upords of old sports equipment. His mother mkes him tke some of it to the lol hrity shop. This leves him with full upords. How muh hs he tken to the shop? Wht numers ould go in the oxes? + Copyright P Lerning G 9

34 Clulting dding nd sutrting ommon frtions Look t this prolem: Our nswer is 0 whih is little onfusing. is the sme s. So let s dd the to our nswer of 0. Our nswer is now. Solve these prolems, onverting ny improper frtions in your nswer to mixed numers. You n use the models to help you with the renming: + whih is equivlent to + whih is equivlent to 7 + whih is equivlent to d + whih is equivlent to Sometimes we lso ome ross more omplited sutrtion prolems. Look t. We n t tke wy from is the sme s. so we will need to renme. Use renming to solve these prolems. Convert your nswers to mixed numers. You n drw models if tht helps: 0 G Copyright P Lerning

35 Clulting dding nd sutrting ommon frtions Sometimes we need to dd nd sutrt frtions tht hve different ut relted numertors nd denomintors. Look t + How do we do this? One wy is to use frtion strips to find equivlent frtions. We n see tht is the sme s Use the frtion strips ove to help you dd or sutrt the like frtions. Renme the frtions in old: d + e f g Brd te of pket of risps. Jen te of pket of risps. How muh did they et ltogether? h Write prolem for prtner to solve: Copyright P Lerning G

36 Clulting multiplying frtions y whole numers We n use repeted ddition to multiply frtions y whole numers. lots of two eighths is + + Use repeted ddition to multiply these frtions. Show eh of the steps: 7 d Try these. Convert your nswers to whole numers: d Sm thinks tht is the sme s. Is he right? Show how you know: Sm s dd helped him with his homework. And we ll know how tht works out Here is wht his dd did. Is he right? If not, explin to him where he went wrong G Copyright P Lerning

37 Clulting multiplying frtions y whole numers There is nother wy to multiply frtions y whole numers. Look t. We hve lots of three fifths. We n express this s 9 We don t multiply the fifths euse these don t hnge we still hve fifths. Multiply these frtions y whole numers. Express the nswers s improper frtions: d e f Our nswers re ll improper frtions. How do we onvert these to mixed numers? Look t 9. This is nine qurters. To hnge this to mixed numer we divide the numertor y the denomintor: 9 9 with qurter left over. is the sme s. Wrm up with these prolems. There will e no reminders. 9 d e f 7 g h 0 7 Now tke your nswers from Question nd write them here. Divide the numertors y the denomintors to find their mixed numer equivlents: d e f Copyright P Lerning G

38 Clulting dividing frtions y whole numers To divide frtion y whole numer, you multiply the denomintor (the ottom prt) y the whole numer. So, A hlf divided in two is qurter: Sometimes you might need to simplify the nswer. For exmple, Solve these prolems: d e f Fill in the missing numers: d e 0 f G Copyright P Lerning

39 Clulting multiplying pirs of frtions To multiply two frtions you multiply the numertors of oth, then multiply the denomintors. The lultion elow is sking, Wht is hlf of third? Sometimes you will need to simplify the nswer. 0 0 Solve these multiplition prolems: d 7 Solve these multiplition prolems nd simplify the nswers: d 7 Find the missing numers in these multiplition prolems: d e 0 Copyright P Lerning G

40 Clulting multiplying deimls y 0, 00 nd,000 When we multiply y 0 the numer eomes lrger y ple vlue. When we multiply y 00 the numer eomes lrger y ple vlues. When we multiply y,000 the numer eomes lrger y ple vlues. Look wht hppens to. when we pply these rules: ,..,000, Wrm up with these. Work with prtner nd lultor. Predit your nswers to the following then try out the prolems. Your nswers will e one or more of the following. The first one hs een done for you. tens tenths hundredths ones Wht ple vlues re in your nswers? Multiply y 0: these ones:,,... We get 0, 0, 0 (tens) these tenths: 0., 0. nd 0... We get these hundredths: 0.0, 0.0 nd We get d these ones nd tenths:.,. nd... We get e these tenths nd hundredths: 0., 0., 0. nd We get Multiply these deimls y 0, 00 nd,000. Estimte first. 0 00, Estimte, then lulte the nswers: d e, f g h 0 0. i, G Copyright P Lerning

41 Clulting dividing deimls y 0, 00 nd,000 When we divide y 0 the numer eomes smller y ple vlue. When we divide y 00 the numer eomes smller y ple vlues. When we divide y,000 the numer eomes smller y ple vlues. Look wht hppens to when we pply these rules: , Divide these numers y 0, 00 nd,000. Estimte first. 0 00, Estimte, then lulte the nswers: 7 0, d e.7,000 f You ll work with prtner for this tivity. You ll lso need lultor. Tke turns giving eh other deiml numer to trnsform. Give them the strting numer nd the numer you wnt it to eome. Your prtner then hs to do so in one move on the lultor, dividing y either 0, 00 or,000. OK, strt with. Turn it into. in move. If they n do so, they sore 0 points. If they get it wrong, you sore 0 points. If you give them prolem tht n t e solved y dividing y 0, 00 or,000, they sore the 0 points. d Swp roles. First person to 0 points wins. Reord the numers elow: Copyright P Lerning G 7

42 Clulting multiplying deiml frtions How do we multiply deiml frtions using written strtegy? First we estimte:. Our nswer will e round. tenths is tenths. We renme this s one nd tenths. We write the in the tenths olumn nd move the one to the ones olumn. is. We lso dd the... We hek the nswer ginst our estimte. Do they fit?.. Multiply these deiml frtions:.. 7. d. e. f. 7 Now try these:... d 7. e. f... Use the templtes to set up nd solve these money prolems: Ysmin uys rtons of ho milk. Eh rton osts.. How muh money does she spend? Omr wnts to uy gmes for his omputer. Eh gme is.9. He hs sved. Does he hve enough money?.... Lis uys mgzines. Eh mgzine osts.9. How muh does she spend on mgzines in totl?.. G Copyright P Lerning

43 Clulting multiplying deiml frtions We n lso use renming to multiply deiml frtions. Look t.: tenths. n lso e expressed s tenths. Then we onvert k to deimls: tenths is. Renme these deiml frtions then multiply. The first one hs een strted for you d is 7 tenths 7.7 Try these. These numers hve hundredths so we will renme the deiml frtions s hundredths. The first one hs een done for you d 7.9. is hths.. Solve these prolems: Dnielle nd her twin rothers re eh.7 m tll. Wht is their omined height? Unless there s zero t the end, if I multiply tenths, I will lwys hve tenths in my nswer. If I multiply y hundredths, I ll lwys hve hundredths in my nswer. It s good wy to hek tht my nswers re right. Your fvourite hooltes re on speil for. per ox. You wit until your mum is in wekened stte nd then msterfully onvine her tht uying 7 oxes is gret ide. How muh will this ost? Copyright P Lerning G 9

44 Clulting multiplying deiml frtions 7 You nd your friends re going to the movies nd it s your shout. Look t the prie list elow nd use multiplition strtegy of your hoie to nswer the following questions. Show your thinking: How muh will it ost you for Under tikets? Tiket Pries Under 0.0 Adult.0 Refreshments Poporn S.0 Two of your friends eh wnt lrge drink nd medium poporn. Wht will tht ost you? M.0 L.0 Drink S.0 M.00 L.0 Choolte r.9 Cho topped ie rem. Wter.9 Crisps.9 You nd your other friend wnt ho topped ie rem nd lrge drink eh. Wht will tht ost? d Hlfwy through the movie, you re ll dying of thirst nd you go out nd uy ottles of wter. You py for them with 0 note. How muh hnge do you reeive? Whih opertions do I need to use here? Is it only multiplition? e Use the refreshment prie list to design nd lulte the ost of snk tht would help get you through this Mths lesson. 0 G Copyright P Lerning

45 Clulting dividing deiml frtions Look t. divided y. We strt with the lrgest ple vlue. tens divided y is ten with reminder of ten. We renme this s 0 ones nd rry it over to the ones olumn. ones divided y is with ones left over. We renme this s 0 tenths nd rry it. We now hve tenths. tenths divided y is with remnder of. We renme this s 0 hundredths. 0 hundredths divided y is.. divided y is... 0 Divide these: d. e f 7. 0 Shring money is time when we divide deiml frtions. Add the ills then divide them evenly mong people. Don t listen to the guy who sid he only te the rie he s hepskte. hot hooltes....0 milkshkes....0 muffins....0 lrge owl hips....0 Totl sweet & sour hiken king prwns with veg eef nd rooli....0 lrge rie....0 ols....0 Totl Copyright P Lerning G

46 Clulting dividing deiml frtions Solve these deiml word prolems using mentl or written strtegy of your hoie: You nd friends win jkpot totlling.. If you shre the prize eqully, how muh will eh of you reeive? Two of these friends deide tht money is the root of ll evil nd forgo their shre. How muh do you eh reeive now? To elerte you go out nd uy ie rems, osting totl of.. Wht ws the ost of n individul ie rem? You rememer the nswer is.. But you hve lost the question! You know it ws division prolem nd tht you divided whole numers to get to the nswer. Both the numers were smller thn 0. But tht s ll you n rememer. And your teher wnts to see wht you hve een doing during the lesson or you n kiss plytime goodye. Sve your plytime nd work out wht the division prolem ws. You n try this with or without lultor.??. G Copyright P Lerning

47 Wht numer m I? solve Getting redy See if you n guess the seret numers elow. You n use lultor nd sk prtner if you like. Wht to do I strt with the numer. I hlve it, dd. to tht nswer, divide this new numer y nd then I dd 0.. My nswer is.. Wht numer did I strt with? I strt with new seret numer. I dd. to this, divide the new numer y, hlve the quotient nd then hlve it gin. My nswer is.. Wht numer did I strt with? I strt with numer, then hlve it. I sutrt.0 from the nswer nd then multiply this numer y. I dd to the totl nd my nswer is 9.. Wht numer did I strt with? I strt with numer nd divide it y. I multiply the nswer y. nd then sutrt. from this new nswer. I multiply this y nd end up with.9. Wht numer did I strt with? Work kwrds! You hve to do the opposite proess for eh step. Wht to do next Now you know how these work, n you write your own prolem for prtner to solve? Copyright P Lerning G