Fractions, Decimals and Percentages

Transcription

1 Series Stuent Frtions, Deimls n Perentges My nme F

2 Copyright 009 P Lerning. All rights reserve. First eition printe 009 in Austrli. A tlogue reor for this ook is ville from P Lerning Lt. ISBN Ownership of ontent The mterils in this resoure, inluing without limittion ll informtion, text, grphis, vertisements, nmes, logos n tre mrks (Content) re protete y opyright, tre mrk n other intelletul property lws unless expressly inite otherwise. You must not moify, opy, reproue, repulish or istriute this Content in ny wy exept s expressly provie for in these Generl Conitions or with our express prior written onsent. Copyright Copyright in this resoure is owne or liense y us. Other thn for the purposes of, n sujet to the onitions presrie uner, the Copyright At 9 (Cth) n similr legisltion whih pplies in your lotion, n exept s expressly uthorise y these Generl Conitions, you my not in ny form or y ny mens: pt, reproue, store, istriute, print, isply, perform, pulish or rete erivtive works from ny prt of this resoure; or ommerilise ny informtion, prouts or servies otine from ny prt of this resoure. Where opyright legisltion in lotion inlues remunerte sheme to permit eutionl institutions to opy or print ny prt of the resoure, we will lim for remunertion uner tht sheme where worksheets re printe or photoopie y tehers for use y stuents, n where tehers iret stuents to print or photoopy worksheets for use y stuents t shool. A worksheet is pge of lerning, esigne for stuent to write on using n ink pen or penil. This my le to n inrese in the fees for eutionl institutions to prtiipte in the relevnt sheme. Pulishe P Lerning Lt For more opies of this ook, ontt us t: Designe P Lerning Lt Although every preution hs een tken in the preprtion of this ook, the pulisher n uthors ssume no responsiility for errors or omissions. Neither is ny liility ssume for mges resulting from the use of this informtion ontine herein.

3 Series F Frtions, Deimls n Perentges Contents Topi Fr ons (pp. ) fr ons of shpes fr ons of olle on ompring n orering fr ons fin the fr on solve oin olle on pply Dte omplete Topi Types of fr ons (pp. 9 ) equivlent fr ons mixe numerls n improper fr ons equivlent fr on snp pply feeing me pply Topi Fr ons, eimls n perentges (pp. 7 ) tenths tenths n hunreths eiml ple vlue perentges mth n snp pply Topi Clul ng (pp. ) Series Authors: Rhel Flenley Niol Herringer ing n sutr ng fr ons with like enomintors ing n sutr ng fr ons to n from whole ing n sutr ng fr ons ing eiml fr ons sutr ng eiml fr ons you ut, I hoose solve Copyright

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5 Frtions frtions of shpes A fr on is prt of whole. This shpe hs equl prts. of these hve een she. she prts prts ltogether The top numer is the numertor, the o om numer is the enomintor. Wht fr on of eh shpe hs een she? 9 e f g h Answer the following ques ons out the shpes ove: Wht prt of is unshe? Wht fr on of e is unshe? In f, is more of the shpe she or unshe? Wht fr on of is unshe? e Look t shpe h. Wht n you sy out the mount of she n unshe prts? She the given fr on for eh shpe: Frtions, Deimls n Perentges Copyright P Lerning F

6 Frtions frtions of shpes Are these sttements true or flse? 9 is she is she is she 7 is she Colour the shpes to show: one thir one qurter two thirs Now fin nother wy to olour the shpes to show the sme fr on: one thir one qurter two thirs 7 Wht fr on of eh hunre squre is she? e F Frtions, Deimls n Perentges Copyright P Lerning

7 Frtions frtions of olletion We n lso hve fr ons of groups. This is group of ots. out of the ots re irle. We express this s Wht fr on of eh group hs een irle? e f Look t the metre ruler n work out how mny en metres re represente y the fr on: m m m m m m Some mes we re ske to fin the fr on of n mount suh s: Fin one qurter of this rry. There re ots in the rry. First we ivie the rry into equl prts. There re ots in eh prt or qurter so one qurter of is. Use the rrys to help fin the given fr ons of the groups: of this rry is ots of this sme rry is ots of this rry is ots of this sme rry is ots Frtions, Deimls n Perentges Copyright P Lerning F

8 Frtions frtions of olletion There is nother wy to fin fr ons of mounts: Wht is of 0? 0 ivie into groups is in eh group 0 Fin the fr onl mounts. You n use loks or ounters to help or solve the prolems in your he using ivision: of 0 of of of 0 e of f 9 of 7 g of h 7 of One we know how to fin one prt of group, we n use this to fin other mounts: To fin of 9, we first fin of 9 9 of 9 of 9 is mes this of 9 Fin the fr onl mounts. Use the spe elow to work out the ifferent steps: Wht is of 0? Wht is of? Wht is of? 0 0 Wht is of? e Wht is of? f Wht is 7 of? 7 7 F Frtions, Deimls n Perentges Copyright P Lerning

9 Frtions ompring n orering frtions We n use numer lines or fr on strips to help us ompre n orer fr ons Use the strips ove to help you nswer the following ques ons. Cirle the orret nswers: Whih is igger? or Whih is smller? 0 or Whih is smller? or Use the fr on strips to: Fin fr ons tht re the sme s Fin fr ons tht re the sme s Fin the fr on tht is greter thn ut less thn Write similr prolems for frien to solve: Frtions, Deimls n Perentges Copyright P Lerning F

10 Frtions ompring n orering frtions Lel the missing fr ons on the numer line: Are these sttements true or flse? Use the numer lines ove to help you with your eision. Rememer the lrge en < ets the lrge numer. < > > < e > 7 f > g 7 > h > Use the numer lines ove to help you put these fr ons in orer from smllest to lrgest: F Frtions, Deimls n Perentges Copyright P Lerning

11 Fin the frtion solve Wht to o Your jo is to work out wht fr on of eh shpe is she. Some of them re simple to work out, others will tke li le more thinking. Hmm wht will help me work these out? I oul flip the she prts roun in my he or mye I oul ut the shpes out n re-orer them. Frtions, Deimls n Perentges Copyright P Lerning F 7

12 Coin olletion pply Ge ng rey In this vity you will use your knowlege of fr ons to shre ol oins mong fmily. Wht to o Mum gve you n your (imginry) rothers n sisters ox of ol oins to shre (lso imginry, unfortuntely). She hs eie to shre them out se on how well you ll lene your rooms. There re 7 oins in the ox. Follow the ire ons to fin how mny you eh reeive: Your sister Srh n hve of the oins. How mny oins is this? Your sister Clire wishe she h known this oni on when she lene up her room. She n only hve of the oins. How mny is this? Your rother Angus i stellr jo on his room n is en tle to How mny is this? of the oins. You get the rest! How mny o you get? e Wht is your shre expresse s fr on? Wht to o next Write n i on sentene to show how the oins were shre. Now write fr on i on sentene to show how they were shre F Frtions, Deimls n Perentges Copyright P Lerning

13 Types of frtions equivlent frtions Different fr ons n hve the sme mount. They re equivlent. This helthy vegetle pizz hs een ut into prts. hs een eten. This helthy vegetle pizz hs een ut into prts. hs een eten. Do this foling pper vity to help you unerstn how equivlent fr ons work: You'll nee seprte retngulr piee of pper similr to the one elow. Fol it into equl prts n then unfol it. Lel eh se on with its fr on here: Rememer the o om numer tells us how mny prts there re in the whole. Refol your pper into thirs n fol the thirs into hlves. Unfol the pper. Wht fr on oes eh of the new se ons represent? Lel them here: Fol the pper k gin n fol it in hlf one more. Unfol it n lel the fr ons here: Use the igrms in Ques on to help you nswer the following ques ons: Wht fr ons n you fin tht re equivlent to? Wht fr ons n you fin tht re equivlent to? Wht other fr ons n you think of tht might e equivlent to? F Copyright P Lerning Frtions, Deimls n Perentges 9

14 Types of frtions equivlent frtions Write the equivlent fr on for eh of these: e f 0 Fin n equivlent fr on for eh of these. Divie the igrms to rete ifferent numer of equl prts. The first one hs een one for you. e f Is equivlent to? Use igrms to help explin your resoning: Is equivlent to? Use igrms to help explin your resoning: 0 F Frtions, Deimls n Perentges Copyright P Lerning

15 Types of frtions equivlent frtions 7 This se on hs een omplete y our work experiene oy. How i he go? Give him some feek: Your feek: Complete the numer lines. The first hs een one for you: Use the numer lines to nswer the following: How mny equivlent fr ons n you fin for? Di you fin p ern? Cn you on nue it? F Copyright P Lerning Frtions, Deimls n Perentges

16 Types of frtions mixe numerls n improper frtions Mixe numerls onsist of oth whole numer n fr on. Ky hs full pkets of penils n one hlf pket of penils. This is shown s Write mixe numerl for eh of the she sets of shpes: e f Drw some igrms or pitures tht woul represent: n n n n Wht might the missing numers e? > < The li le pointy prt of the sign > points to the smller numer! < > e > F Frtions, Deimls n Perentges Copyright P Lerning

17 Types of frtions mixe numerls n improper frtions Mixe numerls n lso e wri en s improper fr ons. Look gin t Ky s full pkets n one hlf pket of penils. This is five hlves. Wri en s n improper fr on, this is. Express these s fr ons. Cirle ny improper fr ons: An improper fr on is ny fr on where the prts up to more thn. Colour the shpes to rete the following improper fr ons. Rememer eh shpe is one whole. 7 7 e f 0 Whih is igger? Cirle the lrger fr on: or or 9 or F Copyright P Lerning Frtions, Deimls n Perentges

18 Types of frtions mixe numerls n improper frtions 7 Complete the numer lines y filling in the oxes: 0 Use your omplete numer lines to help you nswer these ques ons: Wht is expresse s n improper fr on? Write s mixe numer. Fin n improper fr on tht is greter thn ut less thn 0. Your teher offers you the hoie etween 0 or hours of ruish uty. Whih shoul you hoose? 9 Show the improper fr ons. The numer line t the top of the pge will help: 7 e f g h i F Frtions, Deimls n Perentges Copyright P Lerning

19 Equivlent frtion snp pply Ge ng rey Ply this gme with frien. You ll nee two sets of these rs. Mke opies of this pge, ut out the rs n omine the two sets into one pile. opy Wht to o Plyer els the rs fe own etween the two plyers. Plyer strts the gme y pling r in the entre. Plyers tke turns in turning over the top r on their pile n pling it in the entre pile. Cll, Snp! n tke the entre pile if the r is ien l to or n equivlent fr on to the r lrey fe up. The four wil rs n e use to mke Snp! When plying wil r, you must nme orret equivlent fr on. The person with ll the rs t the en is the winner.?? 9?? F Copyright P Lerning Frtions, Deimls n Perentges

20 Feeing time pply Ge ng rey Emm is onfuse. She unerstns mixe numerls ut not improper fr ons. Her hs ske her to help out t their willife zoo ut he hs use improper fr ons in his ire ons. Wht to o She the orret mounts on the ontiners, then onvert the improper fr ons to mixe numerls for Emm so the nimls n e fe orretly. Der Em, Off to see mn out n igun. Be love n fee the nimls for me, will you? Bk for the fternoon fee. At m, fee the lms ups of pellets. ups At 9 m, give Culi the ro her ukets of stek. (Rememer Culi onsiers your hn to e one of her fvourite foo groups). ukets At m, fee the snkes their 7 Snkes eserve to e fe too. oxes of rts. Stop griming. oxes At miy, fee the womts their ukets of mushrooms n grss. They won't e out for it till the evening ut they wnt it now. Who woul hve thought womts woul e so preious? Go figure ukets D xxx F Frtions, Deimls n Perentges Copyright P Lerning

21 Frtions, eimls n perentges tenths Deiml fr ons lso express prts of whole. This strip hs een ivie into 0 equl prts. Three out of ten or 0 is she We n lso express this s 0.. There re no wholes n tenths. Write the she ommon fr on n its equivlent eiml fr on: She the fr on strips to mth the ommon fr on or eiml fr on: Use ruler n penil to ivie the wholes into tenths. She the given mounts n express s eimls: F Copyright P Lerning Frtions, Deimls n Perentges 7

22 Frtions, eimls n perentges tenths n hunreths A hunreth is tenth of tenth. Here, hunreths hve een she. We write this s 0. There re no ones, tenths n hunreths. Use ruler n penil to ivie these into hunreths n then she the speifie mounts: Six tenths re she here. Sixty hunreths re she here. Wht o you no e? Sixty hunreths n six tenths hve the sme vlue Chek tht the ove sttement is true y shing the mounts. Are they the sme? tenths tenths tenths tenths 0 hunreths 0 hunreths 0 hunreths 0 hunreths F Frtions, Deimls n Perentges Copyright P Lerning

23 Frtions, eimls n perentges tenths n hunreths Complete these sttements. The first one hs een one for you. This is 00 It n e renme s: 0 n 00 This is 7 00 It n e renme s: This is 00 It n e renme s: e This is 7 00 It n e renme s: This represents wholes n 7 00 It n e renme s: Complete the missing inform on: F Copyright P Lerning Frtions, Deimls n Perentges 9

24 Frtions, eimls n perentges eiml ple vlue A hunreth is tenth of tenth. Ones Tenths Hunreths This numer hs ones, tenths n hunreths. Write these numers in the ple vlue hrt: Thousns Hunres Tens Ones Tenths Hunreths tens, ones n tenths 7 hunres, tens, ones, tenths n hunreths 9 tens n tenths hunres, tenths n hunreths 0 0 e ones, 9 tenths n hunreths f ones, tenths n hunreths g tens, ones n hunreths 0 Answer true or flse to the following ques ons. Sore 0. points for eh orret nswer. T or F Sore The vlue of in. is hunreths. The vlue of in. is tens. The vlue of 7 in 0.7 is 7 hunreths. Thoms thought of eiml numer etween. n.9. The numer oul hve een.. e 97. is 9 tens, 7 ones n hunreths. Totl 0 F Frtions, Deimls n Perentges Copyright P Lerning

25 Frtions, eimls n perentges eiml ple vlue When ompring n orering eimls, the ple vlue of igit is ruil. The further the igit is to the le, the greter its vlue. Even though one hunreth souns ig, it is tully very smll. Rememer, one hunreth is just single piee of whole ivie into hunre prts. One tenth is tully ten mes igger thn one hunreth. Whih is igger? Cirle the orret nswer: 0.7 or or tenths 7. or 7 0 or 0. e or 0. f or. Use < or > or to show the rel onship etween the two numers: This hrt shows the vitl st s s of some Roosters Footll Clu plyers. Nme Height Weight Lnky.0 m 79.0 kg Crusher.9 m 0. kg Crumer.7 m 79.9 kg Czly. m.9 kg Stomper. m 99. kg Whle.0 m. kg Twinkle Toes.7 kg Who is tllest? Who is shortest? Put these plyers in orer of lightest to heviest: Crumer, Stomper, Czly: Who re the two tllest plyers? Who woul you lest like to hve tkle you? Why? e Twinkle Toes le the lu efore his height ws mesure. We know he is tller thn Crumer n shorter thn Czly. Wht oul his height e? A it to the tle. F Copyright P Lerning Frtions, Deimls n Perentges

26 Frtions, eimls n perentges perentges Perent mens prt per hunre n is expresse using the symol %. Here, 0% hs een she grey. It is the sme s 0 hunreths % Think of t lest five mes you see the % sign or use perentges: Fill in the missing vlues n she the gris: % % 0. 90% 0. % e f g h % 0.7 % 0. 9% 0. % Are these sttements orret? 7% is greter thn 0. One qurter is the sme s 0% % is greter thn is equivlent to e You sore 00% on test. Your frien sores 0/0. You oth reeive the sme sore. F Frtions, Deimls n Perentges Copyright P Lerning

27 Frtions, eimls n perentges perentges It is useful to know some ommon perentges suh s %, 0% or 7%. She the gris n show the following fr ons y omple ng the missing inform on: 0. % 0. % 0. %. % She these shpes to show the following perentges: 0% % 7% e f 00% 0% % Jmes goes on holiy. He hs $00 spening money n spens it s outline elow. Show this on the pie grph n lel eh se on of the pie with the orret perentge: $ on ries $ on snks $ on new flip flops $ on souvenirs F Copyright P Lerning Frtions, Deimls n Perentges

28 Mth n snp pply Ge ng rey This is gme for or more plyers. You will re ginst eh other to ome up with equivlent fr ons, eimls or perentges to mth those on rs. You ll nee one opy of this pge n one opy of pge etween you. opy Wht to o Cut out the plying rs, mix them up n put them fe own in pile. Cut out the lnk rs on pge n ivie them etween the two of you. Mke sure you oth hve penil eh. Turn over the first plying r. Both plyers write n equivlent fr on, eiml or perentge to mth it on one of the lnk rs n over the plying r s quikly s possile. For exmple, the plying r my sy 0% you oul write or 0 or The first person to over the r with orret mth wins n tkes the pir. The plyer t the en of the gme with the most rs is the winner. Plying Crs 7 00 % % % 0.7 F Frtions, Deimls n Perentges Copyright P Lerning

29 Mth n snp pply Blnk Crs opy F Copyright P Lerning Frtions, Deimls n Perentges

30 Clulting ing n sutrting frtions with like enomintors I use of lof of re for rekfst. Then I use nother for lunh. How mny qurters i I use ltogether? + She the shpes to help you nswer the prolems: Try these. Drw some igrms if tht will help you Write i on fr on sentenes for the following prolems. Write your nswers: of the kis in Biley s lss plye sketll t reess. of the kis plye footll. of the kis st roun n h e. Wht fr on of the lss plye sport? + Josh spent of his poket money t the milk r n uying reits for his gme. Write fr on sentene to show the fr on he spent. + Look t the prolem +. Why oes the sty s why isn t it +? F Frtions, Deimls n Perentges Copyright P Lerning

31 Clulting ing n sutrting frtions with like enomintors I h of snwih in the frige. I te. I h le. Fin nswers to these sutr on prolems. The first one hs een one for you e f Use the igrms to help you solve these prolems: Mrit ut lof of re into equl slies n serve of them t rekfst. Wht fr on ws le? Sm plye soer gme. He plye golie for qurter of the gme n in k for the rest. Wht fr on of the gme i he spen in k? Jint spent of her poket money on lunh n Wht fr on i she hve le? of it on mgzine. 7 Use the numer lines to help you work out the nswers to these prolems: F Copyright P Lerning Frtions, Deimls n Perentges 7

32 Clulting ing n sutrting frtions to n from whole Aing fr ons to whole numers is simple proess. + + A these fr ons n whole numers: e + f g + h + i + How o we sutrt fr ons from whole? We renme the wholes to mke it simpler. Look t the prolem. How mny re in whole? There re Now the prolem is esier: in whole. Renme the wholes s fr ons n use the igrms to help you solve these prolems: e f F Frtions, Deimls n Perentges Copyright P Lerning

33 Clulting ing n sutrting frtions Wht oul the missing numers e? Crete two ifferent op ons for eh: Solve these prolems. Drw igrms if they help: You hve unles of penils. One frien tkes n nother tkes n nother tkes. Wht fr on o you hve le? Wht fr ons o you know tht hve ifferene of? Now I oul lso use equivlent fr ons or improper fr ons here F Copyright P Lerning Frtions, Deimls n Perentges 9

34 Clulting ing eiml frtions How o we eiml fr ons using wri en strtegy? We rrnge the numers so the ple vlues line up n then we strt with the smllest vlue. We first the tenths. tenths n 7 tenths is tenths. We renme this s whole n tenths. We write the in the tenths olumn n move the to the wholes olumn. Then we the ones Knowing how to renme is useful skill when ing eiml fr ons. Pr se your renming skills here y olour oing the mthing oxes: tenths 0 tenths hunreths tenths hunreths 7 ones n tenths ones n tenths hunreths 7 tenths tenth n hunreths one one n tenths ones, tenth n hunreths tenths n hunreths A these eiml fr ons: e. f Now try these. Strt with the hunreths n rememer to renme if neessry: F Frtions, Deimls n Perentges Copyright P Lerning

35 Clulting ing eiml frtions Use mentl or wri en strtegy of your hoie to solve these prolems: A.0 n. A. n 7. We n lso use our mentl i on strtegies when ing eiml fr ons. Jk sore 7. for his first ive n. for his seon. Wht ws his totl sore? Kte ought n ult movie ket os ng $9.0 n hil s ket os ng $.9. How muh i she spen in totl? This is smple of the menu t Lur s Lunhes. Br orers souvlki, soup n n ornge juie. How muh will this ost him? Angelin orers sushi roll, o le of wter n piee of fruit. Wht will this ost her? Choose your own lunh. Itemise your list n lulte the totl vlue of your orer. Sl snwih. Sushi rolls.0 Soup.9 Souvlki 7. Fruit.0 S rfry nooles.9 Sl. Ornge juie.9 Bo le of wter. Fruit sl. F Copyright P Lerning Frtions, Deimls n Perentges

36 Clulting sutrting eiml frtions How o we sutrt eiml fr ons using wri en strtegy? We rrnge the numers so the ple vlues line up n then we strt with the smllest vlue. We first sutrt the tenths. We hve tenths, n we sutrt tenths from this? No, so we renme one s 0 tenths. Now we hve tenths. tenths sutrt tenths is 7 tenths. We hve ones, n we sutrt ones? Yes, the nswer is whole Solve these sutr on prolems: e. f Now try these. Strt with the hunreths n rememer to renme if neessry: Some mes we hve to work with numers tht hve ifferent mount of igits suh s.. When this hppens, we renme. tenths eomes 0 hunreths:.0. Renme these prolems n solve: F Frtions, Deimls n Perentges Copyright P Lerning

37 Clulting sutrting eiml frtions Use mentl or wri en strtegy of your hoie to solve these prolems: We n lso use our mentl strtegies when sutr ng eiml fr ons. In 9 Jesse Owens roke the long jump reor with lep of.0 m. His reor stoo for yers un l fellow Amerin, Rlph Boston lept. m. Wht i he et Jesse s reor y? The 00 m sprint reor ws roken in 009 with me of 9.9 se. Another thlete nere tht reor month lter, with me of 9.7 se. Wht is the ifferene etween their mes? Belle s sketll tem mesure their heights n entere them on the hrt. Wht is the ifferene in heights etween: Suzy n Luy? Belle s Tem Suzy. m Ti.7 m Gre.7 m Ti n Ntsh? Mrie. m Mison. m Luy. m Belle. m Nin n Belle? Ntsh. m Donn. m Nin. m The tllest n shortest girl? F Copyright P Lerning Frtions, Deimls n Perentges

38 You ut, I hoose solve Ge ng rey You n your frien hve een ske to en te prty. Your host, Mr H er, hs me sugr free hoolte lok ke for the fes vi es, ut lerly he got li le mixe up with his numers. It must hve een ll those pre-prty nerves. Wht to o Anywy, he hs ske you to ut the ke into piees so tht eh of you gets piee with the numers ing to the sme totl. How o you o it? Show your uts on the lok ke elow. Eh piee totls Work out wht fr on of the ke eh of you reeive. I shoul wrn you, Mr H er wnts the iggest piee. I reeive my frien reeives n Mr H er reeives F Frtions, Deimls n Perentges Copyright P Lerning