Equivalent fractions have the same value but they have different denominators. This means they have been divided into a different number of parts.

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1 Frtions equivlent frtions Equivlent frtions hve the sme vlue ut they hve ifferent enomintors. This mens they hve een ivie into ifferent numer of prts. Use the wll to fin the equivlent frtions: Wht frtions n you fin tht re equivlent to? Wht frtions n you fin tht re equivlent to? How mny eighths re equivlent to? How mny qurters re equivlent to? e Divie the ottom row into twelfths. Fin some equivlent frtions for. Divie n she the shpes to show the following equivlent frtions. The first one hs een one for you. e Frtions, Deimls n Perentges Copyright P Lerning G

2 Frtions equivlent frtions To fin equivlent frtions without rwing igrms we use the numertors n enomintors to guie 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 oule the numer of prts (the enomintor) n y oing this you hve oule the numer of prts (the numertor). This metho n e use to fin ll equivlent frtions. Use the lues to help you mke the equivlent frtions: 0 e f g h We n lso reue the numer of prts in whole. We ivie to o this: Whtever we o to the top, we o to the ottom. Whtever we o to the ottom, we o to the top. 0 e f 0 Answer the following: Cssie s tle of kis won pizz for hving the most tle points t the en of term. There re kis t the tle. Wht frtion of the pizz will they eh reeive? The pizz hs een ut into piees. How mny slies oes eh ki get? Wht is this s frtion? Stvros rekons tht euse they got slies they got more thn they woul hve if the pizz h een ut into piees. Is he right? Explin your nswer with wors or igrms. G Frtions, Deimls n Perentges Copyright P Lerning

3 Frtions mixe numerls n improper frtions Mixe numerls re me up of whole numers n frtions. is mixe numer. Mixe numers n lso e expresse s improper frtions. n lso e written s. Complete the numer lines y filling in the oxes: 0 Use the numer lines ove to help you fin 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 one for you. My sore Q This improper frtion is equivlent to. A or Q This improper frtion omes iretly efore. A Q This improper frtion is one thir greter thn. A Q This mixe numerl is the sme s 0. A Q This mixe numerl omes iretly fter. A Q7 This improper frtion is equivlent to. A7 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 mixe numerl is one thir less thn. A0 Frtions, Deimls n Perentges Copyright P Lerning G

4 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 ivie y. We simplify frtions to mke reing n working with frtions esier. Cirle the simplest frtion in eh group: To fin the simplest frtion, we ivie oth the numertor n the enomintor y the sme numer. It mkes sense for this to e the iggest numer we n fin so we on t hve to keep iviing. This numer is lle the Highest Common Ftor (HCF). Look t:?? Wht is the iggest numer tht goes into oth n? is the iggest numer tht goes into n. Fin the highest ommon ftor n then simplify: 0 HCF is 0 0 HCF is 0 HCF is HCF is Wlly sys he hs simplifie these frtions s fr s he n. Is he right? If not, fin the simplest frtion: G Frtions, Deimls n Perentges Copyright P Lerning

5 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 sore 0 on test. Wht frtion ws inorret? g h If you re not sure wht the HCF is, guess, hek n improve is useful strtegy. Try your hoie out n then look t your new frtion. Coul it e ny simpler? Is the ONLY numer tht oul go into oth the numertor n the enomintor? Mrik sore 0 on the sme test. Wht frtion i she get right? out of the 7 kis in Yer rie their ikes to shool. Wht frtion oes this represent? Out of the stuents in F, rte Mths s their fvourite sujet. Wht frtion is this? e Wht frtion i not hoose Mths s their fvourite sujet? Colour n mth the frtions on the ottom row with their simplest form: Frtions, Deimls n Perentges Copyright P Lerning G

6 Frtions ompring n orering frtions Compring n orering frtions with like enomintors is simple proess: When there re ifferent enomintors we nee to renme the frtions so they hve the sme enomintors. This lets us ompre pples with pples. Whih is lrger? or We know tht is equivlent to so is lrger thn Orer these frtions: Hmm I h etter mke the mixe 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: 0 Write or rw frtion on the left tht woul result in the sle looking like this: Rememer with equivlent frtions, we think out wht we i to get from one to the other: G Frtions, Deimls n Perentges Copyright P Lerning

7 Frtions ompring n orering frtions Fin prtner to ply this gme with: Nme frtion etween 0 n n ple it on the numer line. Your prtner then hs to nme n ple frtion tht fits etween tht frtion n. Then you hve to fin one tht fits etween their frtion n n 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 o the tol you so ne. Alright, she put I m going to put euse I know tht is more thn 0 0 These frtions re ll out of orer. Cut them out n put them in orer 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 rs if this will help. Shre your thinking with prtner. Hve they orere them the sme wy? Frtions, Deimls n Perentges Copyright P Lerning G 7

8 Frtions renming n orering frtions Sometimes we hve to orer n ompre frtions with unrelte enomintors suh s, n. To o this, we hve to fin one ommon enomintor we n onvert ll the frtions to. You hve kes for lss prty. One hs een ut into hlves n one into thirs. 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 h one of these new slies, wht frtion of the ke woul you reeive? Tht is n exmple of how we renme frtions. We fin wy to re-ivie the wholes so tht they hve the sme numer of prts. To o this effiiently we fin the smllest shre multiple. This is then lle 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 fining the shre LCD n then onverting the frtions. Use the multiplition tle on the right to help you fin the LCD: G Frtions, Deimls n Perentges Copyright P Lerning

9 Frtions renming n orering frtions Look t eh group of frtions. Preit whih you think is the lrgest n irle your preition. Now, renme the frtions in the work spe elow so tht eh frtion in the group hs the sme enomintor. Use ifferent olour to irle the lrgest frtion. Are there ny surprises? This time, renme the frtions n irle the lrgest. Unerline the smllest. 7 For eh frtion write lrger frtion elow. The new frtion must hve ifferent enomintor. It n hve ifferent numertor. If you n o this, you re whiz! This is rel extension Mths. Frtions, Deimls n Perentges Copyright P Lerning G

10 Spen n sve solve Getting rey In this tivity you will solve money prolems. Working kwrs is useful mths working strtegy to use here. Wht to o Use the frtion pies to help you solve the following prolems: Srh s grn gve her some money for her irthy. Srh sve of the money n spent of the money on ook. Tht left her with $ in her purse. How muh money i her Grn give her? Mrth opene her piggy nk n eie to spen it this wy: on mgzines; on snks; on nekle. The nekle ost $. How muh money i she hve in her piggy nk? Ali went to the show. He spent of his money on ries n of wht ws left on gwoo og, some hips n some firy floss. Tht left him with $ to spen on show gs. How muh money i he hve to egin with? 0 G Frtions, Deimls n Perentges Copyright P Lerning

11 Trik or tret! pply Getting rey Sm n his mtes eie to go trik or treting one Hlloween. They then ivvy up the loot. Wht to o 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 y sukers Ester eggs turnip In the opening roun, Sm gets of the mini hoolte rs n Chupp Chups. How mny of eh oes he get? of the George wnte ll the go stoppers. In tense negotition with Sm, he mnge to sore of them. How mny i he get? How mny i he miss out on? To get his shre of the gostoppers, Sm hs to tre off he reeive in Question. How mny oes he lose? of the Chupp Chups Mr gets ll the Wizz Fizzes, the ll y sukers, n the remining of the hoolte rs. In totl, how mny items oes she get? e Here is frtion sentene tht shows how the go stoppers were shre: + or whole. Write the frtion sentene tht shows how the hoolte rs were shre. f Mr eies 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 n Perentges Copyright P Lerning G

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