Fractions, Decimals and Percentages

Transcription

1 G Teher Student Book SERIES Frtions, Deimls nd Perentges Nme

2 Contents Series G Frtions, Deimls nd Perentges Topi Setion Frtions Answers (pp. (pp. ) ) equivlent frtions frtions _ mixed deiml numerls frtions nd improper frtions _ simplifying frtions of frtions n mount / / / / / / ompring lulting nd ordering frtions _ / renming nd ordering frtions / / / spend nd sve solve Setion Assessment with nswers (pp. 0) trik or tret! pply frtions Dte ompleted / / / / deiml frtions Topi Deiml frtions (pp. 0) frtions of n mount tenths, lulting hundredths nd thousndths reding nd writing deimls ompring nd ordering deimls Setion Outomes (pp. ) renming deimls rounding perentges sk round pply perentge prolems solve / / / / / / / / / / / / / / / / Series Authors: Rhel Flenley Niol Herringer Copyright

3 Frtions equivlent frtions Equivlent frtions hve the sme vlue ut they hve different 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 = Frtions, Deimls nd Perentges Copyright P Lerning G SERIES TOPIC

4 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. 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. = Use the lues to help you mke the equivlent frtions: d = = = = 0 e = f = We n lso redue the numer of prts in whole. We divide to do this: g = 0 h = Whtever we do to the top, we do to the ottom. Whtever we do to the ottom, we do to the top. = = 0 = d = e = f 0 = Answer the following: Cssie s tle of kids won pizz for hving the most tle points t the end of term. There re kids t the tle. Wht frtion of the pizz will they eh reeive? The pizz hs een ut into piees. How mny slies does eh kid 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. No. It s the sme. = G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

5 Frtions mixed numerls nd improper frtions Mixed numerls re mde up of whole numers nd frtions. is mixed numer. Mixed numers n lso e expressed s improper frtions. n lso e written s. Complete the numer lines y filling in the oxes: 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 numerl is the sme s 0. A Q This improper frtion is equivlent to. A Q This mixed numerl omes diretly fter. A Q This improper frtion is equivlent to. A Q This improper frtion is equivlent to. A Q This improper frtion is equivlent to. A Q0 This mixed numerl is one third less thn. A0 Frtions, Deimls nd Perentges Copyright P Lerning G SERIES TOPIC

6 Frtions simplifying frtions These frtions re ll equivlent to one hlf: Whih is the simplest? 0 0 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 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 0 = 0 HCF is 0 = 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 SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

7 Frtions simplifying frtions Write the following frtions in their simplest form: e = = f 0 = = Solve the following prolems. Write your nswers in the simplest form: Luke sored 0 on test. Wht frtion ws inorret? g = = d h = = 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 kids in Yer ride their ikes to shool. Wht frtion does this represent? d Out of the students 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: Frtions, Deimls nd Perentges Copyright P Lerning G SERIES TOPIC

8 Frtions ompring nd ordering frtions Compring nd ordering frtions with like denomintors is simple proess: When there re different denomintors we need to renme the frtions so they hve the sme denomintors. This lets us ompre pples with pples. Whih is lrger? or We know tht is equivlent to so is lrger thn 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: Answers will vry. Rememer with equivlent frtions, we think out wht we did = to get from one to the other: G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

9 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. Answers will vry. Alright, 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? Frtions, Deimls nd Perentges Copyright P Lerning G SERIES TOPIC

10 Frtions renming nd ordering frtions Sometimes we hve to order nd ompre frtions with unrelted denomintors suh s, nd. To do this, we hve to find one ommon denomintor we n onvert ll the frtions to. 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,,,,, 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 SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

11 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? d This time, renme the frtions nd irle the lrgest. Underline the smllest. d 0 For eh frtion write lrger frtion elow. The new frtion must hve different denomintor. It n hve different numertor. If you n do this, you re whiz! This is rel extension Mths. Answers will vry. Frtions, Deimls nd Perentges Copyright P Lerning G SERIES TOPIC

12 Spend nd sve solve Getting redy In this tivity you will solve money prolems. Working kwrds is useful mths 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? $0 $ $ $0 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 dgwood dog, some hips nd some firy floss. Tht left him with $ to spend on show gs. How muh money did he hve to egin with? $ $ $ $ $ 0 G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

13 Trik or tret! pply Getting redy Sm nd his mtes deide to go trik or treting one Hlloween. They then divvy up the loot. Wht to do Use the hrt on the right to work out the nswers to the prolems elow: 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 0 mini hoolte rs nd Chupp Chups. 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? go stoppers. He missed 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 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? Wizz Fizzes sukers items + 0 hoolte rs 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. + = = whole 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. = = Frtions, Deimls nd Perentges Copyright P Lerning G SERIES TOPIC

14 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 unit 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, hundredths, thousndths tenths, hundredths, thousndths 0 d e 0 tenths, hundredths, thousndths 0 0 f g thousndths h G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

15 Deiml frtions reding nd writing deimls When we write deimls we follow this ple order: Thousnds Hundreds Tens Units 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 Units Tenths Hundredths Thousndths..0. d.0 e f 0. g. Red eh numer nd write it s deiml: four units, one hundred nd twenty two thousndths. one hundred nd eleven, nd sixty five hundredths. Wth out for the omms! They indite the end of whole numers. 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. No it s not, it s written s. forty eight hundredths is written s thousndths is written s 0.00 d eleven nd hundredths is written s.0 e hundredths is 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 Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

16 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 students on the numer line. The first one hs een done for you. Distne. m. m. m. m.0 m. m. m.0 m.0 m. m F J H B C A D G E I Use the ove informtion to nswer the following questions: Who shot the furthest on the dy? Doule Or Nothing Dnielle Whose shot ws the shortest? Did You See Tht One Big-noter Whih students shots were hundredth of metre prt? Lone Shooter nd Doule Or Nothing Dnielle d Wht ws the differene etween the shots of Shoot Dog nd Spitter Mgee? 0. m 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. Answers will vry. G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

17 Deiml frtions renming deimls We n express the sme deiml frtion in different wys. This shows hundredths. We n lso express this s unit, tenths nd hundredths or tenths nd hundredths or unit nd hundredths. Renme these frtions: hundredths is lso tenths + hundredths hundredths is lso tenths + hundredths hundredths is lso tenths + hundredths d tenths nd hundredths is lso e tenths nd hundredths is lso hundredths hundredths f tenths, hundredths nd thousndths is lso thousndths g 0 tenths, hundredths nd thousndths is lso thousndths It my help to write these numers in their deiml forms. Now try these. Fill in the missing informtion: units = 0 tenths = 00 hundredths = 000 thousndths units = 0 tenths = 00 hundredths = 000 thousndths. units = tenths = 0 hundredths = 00 thousndths d units = 0 tenths = 00 hundredths = 000 thousndths Renme these numers s mny wys s you n. Use the revition: H for hundredths, T for tenths nd U for units:... U H U T H T H U H U T H T H U H U T H T H H H H Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

18 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. Round these numers to the nerest tenth: d If the rounding numer is to, it rounds down. If it is to, it rounds up. e.. f.0. Now round these numers to the nerest hundredth: d.. e.0.0 f.. Use lultor to perform the following opertions. Round the nswers to the nerest tenth:. =. =.. =. d =. e =. f. = 0. Look t the following mel options. Round eh prie to the nerest dollr nd totl the estimted ost of eh option elow: Choie Choie Choie Hmurger $. $ Noodles with prwns $. $ Sld roll $. $ Cn of drink $. $ Green te $0. $ Juie $. $ Lrge hips $. $ Cr kes $. $ Cookie $. $ Totl $ Totl $ Totl $ You hve $0. Cirle the hoies you n fford. G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

19 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 = 0.0 = 0% We ommonly use perentges in sles % off everything TODAY ONLY; on tests I got %; nd when we re gthering nd reporting on dt % of people surveyed love hoolte. Fill in the missing vlues: d % % 0. 0% 0. % e f g h % % 0. % 0. 0 % It is useful to know some ommon perentges suh s %, 0%, % or 00%. Shde the grids to show the following perentges: d 0. % 0. 0 % 0. %.0 00 % Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

20 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% % 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: % preferred their veggies oiled till they were ll soggy nd wtery. % preferred their veggies stir fried..% preferred their veggies rw. d 0.% did not re how they were prepred euse they weren t going to et them nywy. G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

21 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 kids 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. Answers will vry Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

22 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 onveniene stores in Smllville. 0% of these stok your fvourite Slurpee 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? people 0 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. 0 G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

23 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. W O R L D M A T H S D A Y 0 0 L = D = of of Y = O = of 00 of A = S = of 00 of 000 Put this dte in your diry! Tell your friends! H = of 00 T = of M = of 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 soer for hr min. How would you express tht s n improper frtion? g Find time spns tht represent of n hour. Answers will vry nd my inlude:.00 to.0.0 to.0.0 to.0 Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

24 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, we first find of = of = of is times this = of = Find the following frtionl mounts: d of = of 0 = of = of = e 0 of 0 = f of 0 = 0 The Wlsh kids 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 kids work out their dily llotion nd sve them from fte worse thn deth: How mny minutes does eh kid get eh dy? Dyln Nin Ntsh How mny minutes must Dyln spend on study? minutes How mny minutes will Nin spend on Mthletis? minutes d Express the time llotions s frtions of n hour: Dyln Nin 0 0 or 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 G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

25 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: $00 00 = $ Eh squre or perent represents $. How do we then find % of $00? $ = $. PVG- Phone $00 Use the 00 grid to lulte: % of $00 is $0 0% of $00 is $0 0% of $00 is $0 d % of $00 is $ e % of $00 is $0 f 0% of $00 is $00 g If the store dvertises sle of % off the ost of the phone, wht is the sving in dollrs? $0 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 0 d 0% of 00 people is 0 e % of 00 people is f 0% of 00 people is 0 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 0% of 0 is % of 0 is 0% of 0 is 0% of 00 is 0 % of 00 is 0% of 00 is 0 0% of 00 is 0 % of 00 is 0% of 00 is 00 0% of 000 is 00 % of 000 is 0 0% of 000 is 00 0% of 000 is 00 % of 000 is 0 0% of 000 is 00 Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

26 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 0% of 0 is 0% of 0 is of 0 = 0 of 0 = of 0 = 0 0 = 0% = % = % = 0% 0 = 0% = % 0 = 0 0 = 0 = 0 d % of is e % of is f % of 0 is 0 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 = 0 ml % of 0 ml = ml % of 00 kg = 0 kg d % of 0 km =. km e % of 0 ml =. ml f % of $00 = $ g % of 00 = 0 h % of 00 ml = ml i 0% of 000 = 00 The nswer is. Use lultor to work out the perentges nd tik ll the squres tht mth the nswer: Wht is % of 00? Wht is % of 0? Wht is % of 00? Wht is % of 00? Wht is 0% of 0? Wht is 0% of 0? Wht is % of? Wht is 0% of? G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

27 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: Plsm TV $000 DVD $ eh Tiket $0 eh Puppy $0 0% off % off 0% off $00 $.0 $ $ 0% off $0 $ $.0 $.0 % off $00 $ $ $ 0% off 0% off % off 0% off 0% off % off 0% off 0% off $00 0% off $.0 $0 $0 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: $ $00 $0 Sving $ Sving $. Sving $ New prie $0. New prie $ New prie $ $ Sving $ New prie $ $0 Sving $ New prie $ Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

28 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 mll with things you like, then nother group memer will deide wht kind of disounts you n hve on eh item. Then you ll eh re round your own mll lulting the new pries. opy 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 % $ G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

29 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 off 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? No. Online store $0 nd Shop $ The online store is the etter del. DILEMMA Would you rther eome 0% poorer nd then 0% riher or eome 0% riher nd then 0% poorer? They result in the sme nswer. DILEMMA The new gme you wnt osts $ 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? Seond store $ Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

30 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 hours nd on Sundy we wthed for hours. How mny hours did we spend wthing movies in totl? + = First we dd the whole numers: + =. 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 = Express these s frtion sentenes. Solve them: Srh nd Rhel go to trsh nd tresure sle. Srh uys oxes of trsh nd Rhel uys oxes of tresure. How muh do they uy in totl? + = = oxes You hve oxes of hooltes nd you et oxes. How mny oxes do you hve left? = = oxes 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? + = hours 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? Answers will vry. + = = G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

31 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 numerls. You n use the models to help you with the renming: + = whih is equivlent to + = whih is equivlent to + = whih is equivlent to d + = whih is equivlent to 0 Sometimes we lso ome ross more omplited sutrtion prolems. Look t. We n t tke wy from so we will need to renme. is the sme s. = Use renming to solve these prolems. Convert your nswers to mixed numers. You n drw models if tht helps: = = = = 0 = = = = Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

32 Clulting dding nd sutrting ommon frtions Sometimes we need to dd nd sutrt frtions tht hve different ut relted 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: = 0 + = = 0 0 d + e f + + = = + = g Brd te of pket of hips. Jen te of pket of hips. How muh did they et ltogether? + = + = = pket h Write prolem for prtner to solve: Answers will vry. 0 G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

33 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: d = + + = + + = = + + = = = = Try these. Convert your nswers to whole numers: d = = 0 = = = = = = Sm thinks tht is the sme s. Is he right? Show how you know: = = = = = 0 = Yes, they re the sme. 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. He must not dd denomintors. + + = = = = Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

34 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 = 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 0 = 0 = Our nswers re ll improper frtions. How do we onvert these to mixed numerls? Look t. This is nine qurters. To hnge this to mixed numerl we divide the numertor y the denomintor: = with qurter left over. is the sme s. Wrm up with these prolems. There will e no reminders. = = = = d e f = = = 0 = g h 0 Now tke your nswers from Question nd write them here. Divide the numertors y the denomintors to find their mixed numerl equivlents: = = 0 = d = e = 0 f = G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

35 Clulting dding deiml frtions How do we dd deiml frtions using written strtegy? We rrnge the numers so the ple vlues line up nd then we strt with the smllest vlue. We first dd the tenths. tenths nd tenths is tenths. We renme this s unit nd tenths. We write the in the tenths olumn nd move the unit to the units olumn. Then we dd the units. + + = Don t forget the deiml point in your nswer!. +.. Add these deiml numers. The first one hs een done for you d. 0 e. f g. h. i We use the sme proess when dding more thn two numers. Add these ills: ol... $.0 lime milkshke... $. dim sims... $.0 r kes... $.0 Totl $. hild s entry tiket... $.0 disposle mer... $. fridge mgnets... $. t-shirt medium... $. Totl $. Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

36 Clulting dding deiml frtions Use mentl or written strtegy of your hoie to solve these prolems: Add.0 nd. Add. nd... We n lso use our mentl ddition strtegies when dding deiml frtions. Bo deided it ws time to drop some weight efore the ig gme. He lost. kg in the first week nd. kg in the nd week. How muh weight did he lose ltogether? d Kte spent $. t one shop, $. t the seond, nd $. t the third. How muh did she spend ltogether?. kg $. Use mentl or written strtegy of your hoie to omplete these mgi numer squres. Rememer in mgi numer squres, eh row, olumn nd digonl dds to give the mgi numer. Your knowledge of inverse opertions will ome in hndy. The mgi numer is. The mgi numer is.0 The mgi numer is Use this spe for ny working out: G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

37 Clulting sutrting deiml frtions How do we sutrt deiml frtions using written strtegy? We rrnge the numers so the ple vlues line up nd then we strt with the smllest vlue. We first sutrt the tenths. We hve tenths, n we sutrt tenths? No, so we renme unit s 0 tenths. Now we hve tenths. tenths sutrt tenths is tenths. We hve units, n we tkewy units? Yes, the nswer is.... Solve these prolems: d. 0 e. f g. h. i Sometimes we hve to work with numers tht hve different mount of digits suh s.. When this hppens, we renme. tenths eomes 0 hundredths:.0. Renme these prolems nd solve: Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

38 Clulting sutrting deiml frtions Use mentl or written strtegy of your hoie to solve these prolems:..0.. We n lso use our mentl strtegies when sutrting deiml frtions... Donny spent $.0 on new memory rd for his phone. The next dy it ppered on speil for $.. If he hd wited nother dy, how muh would he hve sved? d Ntsh uys Complete Girl t $. n issue. Her sister Nin uys Dolly t $.0 n issue. How muh more does Nin spend? $. $0. Find the nswers to these prolems nd solve the riddle: Why did the mn freeze his money? H E W A N T E D C O L D H A R D C A S H A. +. T. +. W. +. E. +. S. +. C. +. O. +. N. +. L. +. D. +. H. +. R. +. G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

39 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:. 0 =.. 00 = = 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 units Wht ple vlues re in your nswers? Multiply y 0: these units:,,... We get 0, 0, 0 (tens) these tenths: 0., 0. nd 0... We get,, (units) these hundredths: 0.0, 0.0 nd We get 0., 0., 0. (tenths) d these units nd tenths:.,. nd... We get,, (tens nd units) e these tenths nd hundredths: 0., 0., 0. nd 0... We get.,.,.,. (units nd tenths) Multiply these deimls y 0, 00 nd 000. Estimte first Estimte, then lulte the nswers: 0 0. = = = d = e = 0 f = g =. h 0 0. =. i = Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

40 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: 0 =. 00 = = 0.0 Divide these numers y 0, 00 nd 000. Estimte first Estimte, then lulte the nswers: 0 =. 000 = = 0. d.0 0 =.0 e. 000 = 0. f.0 00 = 0.0 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: Answers will vry. G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

41 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 unit nd tenths. We write the in the tenths olumn nd move the unit to the units olumn. is. We lso dd the.. =. We hek the nswer ginst our estimte. Do they fit?.. Multiply these deiml frtions: d. e. f.... Now try these: d. 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 $.. He hs sved $. Does he hve enough money? Yes Lis uys.. mgzines. Eh mgzine osts $.. How muh $. does she spend on $. mgzines in totl?. $. Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC 0

42 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.. =.. =.0. =. d. =.. is tenths. is tenths. is tenths. is tenths 0. =.. =.0. =.. =. Try these. These numers hve hundredths so we will renme the deiml frtions s hundredths. The first one hs een done for you.. =.. =.. =. d. =.. is hths. is hths. is hths. is hths 0. =.. =.. =.. =. Solve these prolems: Dnielle nd her twin rothers re eh. m tll. Wht is their omined height?. m 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 erel is on speil for $. per ox. You wit until your mum is in wekened stte nd then msterfully onvine her tht uying oxes is gret ide. How muh will this ost? $. 0 G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

43 Clulting multiplying deiml frtions 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? $.00 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? $.00 M $.0 L $.0 Drink S $.0 M $.00 L $.0 Choolte r $. Cho top $. Wter $. Chips/Crisps $. You nd your other friend wnt ho top nd lrge drink eh. Wht will tht ost? $.0 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? $.0 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. Answers will vry. Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

44 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 units nd rry it over to the units olumn. units divided y is with units 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.. 0 f 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 $0.0 Pd Thi... $.0 king prwns with veg... $.0 eef nd rooli... $.0 lrge rie... $.0 ols... $.0 Totl $.0 $.0 $.0 G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

45 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 rememer. And your teher wnts to see wht you hve een doing during the lesson or you n kiss reess goodye. Sve your reess nd work out wht the division prolem ws. You n try this with or without lultor.?? =. =. Frtions, Deimls nd Perentges G Copyright P Lerning SERIES TOPIC

46 Wht numer m I? solve Getting redy See if you n guess the seret numers elow. You n use lultor nd o-opt 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.. 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.. 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? Answers will vry. G SERIES TOPIC Frtions, Deimls nd Perentges Copyright P Lerning

47 Frtions Nme Divide nd shde the ojets to show the following equivlent frtions: = = = 0 Show the following equivlent frtions: = = = d = In eh group, irle the equivlent frtions: Find the highest ommon ftor (HCF) for eh pir: 0 d 0 Find the HCF then simplify these frtions to their lowest terms: = HCF 0 00 = HCF 00 = HCF d = HCF e 00 = HCF f 0 = HCF Mke pth ross the pge y olouring ny frtions tht re equivlent to 0 : START FINISH Series G Topi Assessment Copyright P Lerning Pty Ltd

48 Frtions Nme Look refully t the numer line nd fill in the missing informtion: Write the mthing improper frtion or mixed numerl for: = = = d = Order these frtions from smllest to lrgest. You my need to renme: Working spe 0 0 Write frtion tht is lrger thn the following. It must hve different denomintor. It n hve different numertor: d Skills Not yet Kind of Got it Reognises, represents nd retes equivlent frtions Finds HCF for relted numers Simplifies frtions to lowest ommon form Mthes improper frtions to mixed numerls Converts etween improper frtions nd mixed numerls Compres nd orders frtions with like denomintors Compres nd orders frtions with relted denomintors Series G Topi Assessment Copyright P Lerning Pty Ltd

49 Frtions Nme Divide nd shde the ojets to show the following equivlent frtions: = = = 0 Show the following equivlent frtions: = = = d = 0 In eh group, irle the equivlent frtions: Find the highest ommon ftor (HCF) for eh pir: 0 d 0 Find the HCF then simplify these frtions to their lowest terms: = HCF 0 00 = HCF = HCF d = HCF e 00 = HCF f 0 = HCF 0 Mke pth ross the pge y olouring ny frtions tht re equivlent to 0 : START FINISH Series G Topi Assessment Copyright P Lerning Pty Ltd

50 Frtions Nme Look refully t the numer line nd fill in the missing informtion: 0 Write the mthing improper frtion or mixed numerl for: = = = d = Order these frtions from smllest to lrgest. You my need to renme: Working spe Write frtion tht is lrger thn the following. It must hve different denomintor. It n hve different numertor: Answers will vry. d Skills Not yet Kind of Got it Reognises, represents nd retes equivlent frtions Finds HCF for relted numers Simplifies frtions to lowest ommon form Mthes improper frtions to mixed numerls Converts etween improper frtions nd mixed numerls Compres nd orders frtions with like denomintors Compres nd orders frtions with relted denomintors Series G Topi Assessment Copyright P Lerning Pty Ltd

51 Deiml frtions Nme Fill in the missing informtion: d Look t this numer line. Write wht the numers to h represent:.0 f.0.0 h d.0 e g Express these s deiml frtions: tenths, hundredths, thousndths 000 units, hundredths, thousndths d units, tenths, thousndths In eh exmple find the vlue of the digit in old. Write unit, tenth, hundredth or thousndth:..0. d.00 Cirle the lrger numer: Look t the deiml numer elow. Write deiml numer tht is smller thn it to the left. Write deiml numer tht is greter thn it to the right:. Series G Topi Assessment Copyright P Lerning Pty Ltd

52 Deiml frtions Nme Fill in the missing informtion: hundredths is lso tenths + hundredths hundredths is lso tenths + hundredths 0 tenths nd hundredths is lso d tenth nd hundredths is lso hundredths hundredths e tenths hundredths nd thousndths is lso thousndths f thousndths is lso tenths + hundredths + thousndths g thousndths is lso tenths + hundredths + thousndths Round these numers to the nerest tenth:..0. d 0. Round these numers to the nerest hundredth: d. 0 Shde the following frtions nd fill in the missing informtion: d 0. % 0. % 0. % 0 0. % Skills Not yet Kind of Got it Mthes ommon frtions to deiml frtions Ples deimls (units, tenths nd hundredths) on numer line Identifies ple vlue of numerls to deiml ples Compres nd orders deimls to deiml ples Renmes deimls Rounds to the nerest tenth/hundredth Reognises ommon perentges nd reltes to frtions 0 Series G Topi Assessment Copyright P Lerning Pty Ltd

53 Deiml frtions Nme Fill in the missing informtion: d (0) (0) Look t this numer line. Write wht the numers to h represent:.0.0 d f h.0.0 e g.0.0 Express these s deiml frtions: tenths, hundredths, thousndths 000 units, hundredths, thousndths d units, tenths, thousndths In eh exmple find the vlue of the digit in old. Write unit, tenth, hundredth or thousndth:. tenth. thousndth.0 hundredth d.00 hundredth Cirle the lrger numer: Look t the deiml numer elow. Write deiml numer tht is smller thn it to the left. Write deiml numer tht is greter thn it to the right: Answers will vry.. Series G Topi Assessment Copyright P Lerning Pty Ltd

54 Deiml frtions Nme Fill in the missing informtion: hundredths is lso tenths + hundredths hundredths is lso tenths + hundredths 0 tenths nd hundredths is lso d tenth nd hundredths is lso hundredths hundredths e tenths hundredths nd thousndths is lso thousndths f thousndths is lso tenths + hundredths + thousndths g thousndths is lso 0 tenths + hundredths + thousndths Round these numers to the nerest tenth: d Round these numers to the nerest hundredth: d.. 0 Shde the following frtions nd fill in the missing informtion: d 0. % 0. % 0. 0% % Skills Not yet Kind of Got it Mthes ommon frtions to deiml frtions Ples deimls (units, tenths nd hundredths) on numer line Identifies ple vlue of numerls to deiml ples Compres nd orders deimls to deiml ples Renmes deimls Rounds to the nerest tenth/hundredth Reognises ommon perentges nd reltes to frtions Series G Topi Assessment Copyright P Lerning Pty Ltd

55 Frtions of n mount Nme Wht is: of of 00 of 0 d of e of 00 f of Wht is: of of 0 of d 0 of 00 e 0 of 0 f of Wht is: % of 00 % of 00 % of 0 d % of 00 e % of 00 f % of 0 The following items re on speil. Clulte the svings nd the new prie: $0 % off Sving New prie $0 0% off Sving New prie $0 0% off $0 0 off Sving New prie Sving New prie Skills Not yet Kind of Got it Finds unit frtions of mounts when nswer is whole numer Finds frtions of mounts when nswer is whole numer Finds perentges of mounts using ptterns Clultes disounts Series G Topi Assessment Copyright P Lerning Pty Ltd

56 Frtions of n mount Nme Wht is: of of 00 0 of 0 0 d of e of 00 0 f of Wht is: of 0 of 0 of d 0 of 00 0 e 0 of 0 f of Wht is: % of 00 % of 00 0 % of 0.0 d % of 00 e % of 00 0 f % of 0 0 The following items re on speil. Clulte the svings nd the new prie: $0 % off Sving $ New prie $ $0 0% off Sving $ New prie $ $0 0% off $0 0 off Sving $ New prie $ Sving $ New prie $ Skills Not yet Kind of Got it Finds unit frtions of mounts when nswer is whole numer Finds frtions of mounts when nswer is whole numer Finds perentges of mounts using ptterns Clultes disounts Series G Topi Assessment Copyright P Lerning Pty Ltd

57 Clulting Nme Solve these ddition nd sutrtion prolems: + = + = = d = Solve these prolems. Show your working out: Lis hs of pket of hoolte. Brt lso hs of pket. How muh hoolte do they hve in totl? Nih hs pkets of ookies nd gives to her friend. How mny is she left with? + = d Ahmed spends of n hour on Live Mthletis on Mondy. On Tuesdy, he spends n hour. Write the mount of time he hs spent s frtion: Wht is this in minutes? Use repeted ddition to multiply these frtions. Express your nswer s n improper frtion nd s mixed numerl if neessry: = + + = = + = = = + + = = d = = = Multiply these frtions. Express the nswers s improper frtions: d = = = = Series G Topi Assessment Copyright P Lerning Pty Ltd

58 Clulting Nme Add these deimls: d. 0 e. f Sutrt these deimls: d. e. f Solve these multiplition prolems:... Solve these division prolems. Express ny reminders s deimls:.. Series G Topi Assessment Copyright P Lerning Pty Ltd

59 Clulting Nme Solve these prolems. Choose whih opertion you will use nd show your working out: Jok uys oxes of golf lls. Eh ox osts him $.. How muh does he spend in totl? Lizzie, Dniel nd Ky re ll. m tll. Wht is their omined height? You order hmurger osting $., drink osting $. nd fries osting $.. Wht is the totl ost of your order? d You nd friends go out for pizz. The ill omes to $.0. Wht is your shre if you split the ill evenly? 0 Multiply these numers y 0, 00 or 000: Divide these numers y 0, 00 or 000: Skills Not yet Kind of Got it Adds deimls numers with sme or different numer of deiml ples Sutrts deimls numers with sme or different numer of deiml ples Multiplies deimls y single whole numers Divides deimls y single whole numers Multiplies deimls y 0, 00, 000 Divides deimls y 0, 00, 000 Series G Topi Assessment Copyright P Lerning Pty Ltd