Percentage Calculations

Transcription

1 Perentge Clultions Curriulum Rey

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3 This ooklet is ll out perentge lultions n where they re use in our ily lives. Wht o you lrey know out perentges? Fill in the piees with some fts you lrey hve. Piees of perentge fts Q Look t this nutritionl informtion for pket of foo. Nutritionl nformtion Serving size: g Avg Qty per Serve Avg Qty per 00g Energy 78 kj 0 kj Protein 0. g 8.0 g Ft, totl 0. g. g -sturte 0.0 g 0. g Crohyrte.8 g 7.0 g -sugrs. g.9 g Soium 8 mg 6 mg Vitmin C 7 mg 00 mg Vitmin A 9 U 890 U The stnr metho use y nutritionists to estimte our minimum ily grms of protein neee is to multiply the oy weight in kilogrms y 0.8. Clulte your minimum ily requirement of protein. How mny servings of this foo will 7 kg ult nee to et to get their minimum ily requirement of protein? Work through the ook for gret wy to o this Mthletis Pssport P Lerning SERES 0 TOPC

4 How oes it work? Frtions n perentges Perent (%) for every (per) 00 (ent) ` 0% mens 0 for every 00, whih s frtion 0 00 To hnge frtions to perentge, write s n equivlent frtion with enomintor of 00. Proper frtions (for mounts smller thn the whole n perentges 00%) # # Alwys write in simplest form nitil frtion Equivlent frtion (00 in enomintor) 00 % Another simple wy to hnge frtions to perentge is y multiplying the frtion y 00. ' ' Mixe numers n improper frtions (for mounts lrger thn the whole n perentges 00%) Mixe numer Convert these frtions n perentges using the metho given # # 0 0 nitil frtion Equivlent frtion 0 0% 00 mproper (00 in enomintor) frtions ' 0 ' 0 # 00 % % ` j # 00 % 0% ` j (i) 7% (Equivlent frtion metho) 7% 7 00 Perent signs mens 'over 00' Simplify frtion (ii) 8 00 (Equivlent frtion metho) ' 00 ' 00 Divie numertor n enomintor y Equivlent frtion with 00 s enomintor % (iii) 6 (Multiplition metho) 6 6 ` # 00 % j 0% Multiply frtion y 00 SERES 0 TOPC Mthletis Pssport P Lerning

5 How oes it work? Frtions n perentges FRACTONS % AND % PERCENTAGES % Write these frtions s perentge..../.../ 0... % 00 % 0 % 00 % Write these perentges s frtion. 7% 89% 7% 6% Write these perentges s frtion with 00 in the enomintor n then simplify. 0% % 80% Simplifie Simplifie Simplifie % e % f 96% Simplifie Simplifie Simplifie g % h 80% i 0% Simplifie improper Simplifie improper Simplifie improper Write these s equivlent frtions with enomintor of 00 n then s perentge. ' ' 8 ' ' 7 ' ' 00 % % % Mthletis Pssport P Lerning SERES 0 TOPC

6 How oes it work? Frtions n perentges Write these s equivlent frtions with enomintor of 00 n then s perentge. # 0 0 # # # 6 # 6 # 00 % % % 6 Write these s equivlent mixe numers with enomintor of 00 n then s perentge. 7 # # # 0 0 # # # % % % 7 Use the multiplition metho to write these frtions s perentges. % % 8 % % % % 0 0 e f 8 Chnge these to improper frtions n use the multiplition metho to hnge to perentge. % % 0 7 % 9 % SERES 0 TOPC Mthletis Pssport P Lerning

7 How oes it work? Frtions n perentges Sometimes the equivlent frtion with enomintor of 00 hs eiml numertor. ' ' 7 nitil frtion Equivlent frtion (00 in enomintor) # # So the equivlent perentges in ll forms (eiml, mixe numer n improper frtion) re: ` 7 00.% % 7 % Deiml Mixe numer mproper frtion 9 Write these s perentge in eiml n mixe numer form. % % % % Deiml Mixe numer Deiml Mixe numer 7 % % 00 6 % % 00 Deiml Mixe numer Deiml Mixe numer e 7 % % f % % Deiml Mixe numer Deiml Mixe numer 0 Write these s perentge in eiml n improper frtion form. % % % % 00 Deiml mproper frtion Deiml mproper frtion 9 % % % % 70 Deiml mproper frtion Deiml mproper frtion Mthletis Pssport P Lerning SERES 0 TOPC

8 How oes it work? Deimls n perentges Chnging etween eimls n perentges is ll out multiplying n iviing y 00. Move eiml point spes right 0.. #00 0. Deiml Perentge % ' Move eiml point spes left Let's look t two more exmples moving in opposite iretions. Write these s their equivlent perentge or eiml (i) % % ' 00 Divie y 00 to get equivlent eiml.0. Move eiml point spes left 00. Equivlent eiml (ii) ^0.7 # 00 h% Multiply y 00 to get equivlent perentge % 70% Move eiml point spes right Equivlent perentge (iii) ^00. # 00h% Multiply y 00 to get equivlent perentge %. % or % or % Move eiml point spes right Equivlent perentge in ll forms (iv) 0.% 0. % 0. ' 00 Divie y 00 to get equivlent eiml. 0. % 0. Move eiml point spes left Equivlent eiml 000 ` 00 j Equivlent mixe numer SERES 6 0 TOPC Mthletis Pssport P Lerning

9 How oes it work? Deimls n perentges Write these perentges s eiml. % 0% % 9% e %. f 0% g 0% h 0% Write these eimls s perentges. 0.0 % 0.6 %. %. % e 0. % f 0. % g 0.08 % h 0. % Write these eimls s eiml perentges n either mixe numer or improper frtions. 0.0 % 0.8 % 0.0 % 0.8 % Deiml Deiml Deiml Deiml % % % % mproper frtion Mixe numer mproper frtion Mixe numer Write these perentges s eimls, mixe numers n improper frtions. % 8% Deiml Mixe numer mproper frtion Deiml Mixe numer mproper frtion 00.% 0.% Deiml Mixe numer mproper frtion Deiml Mixe numer mproper frtion e 7.0% f.8% Deiml Mixe numer mproper frtion Deiml Mixe numer mproper frtion Mthletis Pssport P Lerning SERES 0 TOPC 7

10 How oes it work? Deimls n perentges Write eh of these perentges in ll their equivlent forms: %.% /.../0... DECMALSANDPERCENTAGES * * * 8 % % e.% f 7.% g 7.% h 7 % 6 i.7% j 00 8 % SERES 8 0 TOPC Mthletis Pssport P Lerning

11 How oes it work? Repeting eimls n perentges Repeting eimls re trete just like terminting eimls when hnging to perentges. Move eiml point spes right f # o f Deiml Perentge f % 66.6% o ' f Move eiml point spes left t is usully nier to write repeting eimls s mixe numer perentge where possile. ` 66. 6o % 66 6 % 66 % Alwys simplify 9 These tles show tht there re ptterns for writing simple repeting eimls s frtions: 0.o 0.o 0.o 0.o 0.o 0.6o 0.7o 7 0.8o 8 0.9o o 0.0o n so on... 0.o o + 8 n so on Here re some more exmples with slight ifferenes involving repeting eimls (i) (ii) Convert o to its equivlent perentge vlue o 0. 00f Rememer: Chnge so the repeting pttern strts from the eiml point. Convert % ^0. 00f # 00h% 0. f% 0. o % % 9 to its equivlent eiml n frtion vlues. % 6. o % 6 o ' f 006. o 0.06o Multiply the eiml y 00 Repeting eiml perentge Perentge form from the tle Divie y 00 Deiml point moves two spes to the left Equivlent repeting eiml Equivlent frtion Mthletis Pssport P Lerning SERES 0 TOPC 9

12 How oes it work? Repeting eimls n perentges 0.o 0.o 0.o 0.o 0.o 0.6o 0.7o 7 0.8o 8 0.9o o 0.0o n so on... 0.o o + 8 n so on Use the tles ove to help write these perentges s frtions. 0.% o % 0.% o % 0.07% o % 006. o % % Use the tles ove to help write these perentges s the sum of two frtions then simplify. 0. o % + % % 08. o % + % % 008. o + % % o % + % % Convert these mixe numer perentges into their equivlent eimls n frtions. % % 9 % % Deiml form Equivlent eiml Deiml form Equivlent eiml Frtion Frtion % % 9 9 % % Deiml form Equivlent eiml Deiml form Equivlent eiml Frtion Frtion SERES 0 0 TOPC Mthletis Pssport P Lerning

13 .RECURRNG DECMAL AND PERCENTAGES... How oes it work? Repeting eimls n perentges Join eh equivlent perentge, eiml n frtion with stright lines to rete symmetril tringle rt o 00. o 0 %.../.../ 0... % o o o % 0 % o o % 7 % o o 00 9 %. o % 90 % 00. o 0. 0 o 0 7 % Mthletis Pssport P Lerning SERES 0 TOPC

14 How oes it work? Repeting eimls n perentges Here re some exmples of the mny other repeting eimls long with their equivlent frtions oo f 0.0 o o 0.0 f 0.00 oo f 0. 6 o f oo f 0.0 o 0. 0f 8 Rememer: A ot is ple ove the first n lst igit of the repeting pttern. To hnge the frtion into the repeting eiml, just ivie the numertor (top) y the enomintor (ottom) on your lultor. Write these frtions s repeting eimls n then s equivlent perentges roune to.p. 8 ' 9 ' Repeting eiml Repeting eiml # % # % % % Equivlent perentge to.p. Equivlent perentge to.p. 6 Repeting eiml Repeting eiml e 8 Repeting eiml % Perentge to.p. % Perentge to.p. % Perentge to.p. f 9 Repeting eiml g 7 Repeting eiml h Repeting eiml % Perentge to.p. % Perentge to.p. % Perentge to.p. i Repeting eiml j 7 Repeting eiml k 6 Repeting eiml % Perentge to.p. % Perentge to.p. % Perentge to.p. SERES 0 TOPC Mthletis Pssport P Lerning

15 How oes it work? Complementry perentges Perent (%) for every 00 (per) (ent) 00% 00 for every 00 n other wors, 00% represents the whole mount. Complementry perentges split up the whole mount into two prts. So omplementry perentges to 00% For exmple, 0% of the people prtying elow hve ht. Wht perentge re not wering hts? People without prty hts All the people prtying - the people prtying with hts 00% - 0% 60% Perentge without prty hts n perentge with prty hts re omplementry perentges 60% + 0% 00% Complementry frtions n eimls to (whih is 00% in eiml/ frtion form). Fin the omplement for eh of these (i) 0.% 00% - 0.% 79.% ` The omplement of 0.% is 79.% Sutrt from 00% (ii) ` The omplement of is 7 7 Sutrt from frtion equivlent of 00%, (iii) 0. o ^ 0f. h Sutrt from eiml equivlent of 00%, ` The omplement of 0. o is 0.6 o Corresponing eiml ples to 9 Mthletis Pssport P Lerning SERES 0 TOPC

16 How oes it work? Complementry perentges Write the omplement of these perentges: 0% Complement % % Complement % PERCENTAGES % Complement % * COMPLEMENTARY.../.../ 0... * 7% Complement % e % Complement % f 99% Complement % Write the omplement of these eimls: 0. Complement 0.8 Complement 0.7 Complement 0.6 Complement e 0. Complement f 0.07 Complement g 0.6 o Complement h 0.8 o Complement i 0. o Complement Write the omplement of these frtions: Complement Complement Complement Complement e 7 0 Complement f Complement Write the omplement of these perentges: 6.% Complement % 0.% Complement %.7% Complement % 0.% Complement % e 7.% Complement % f 90.99% Complement % g % Complement % h 90 % 6 Complement % i % 0 Complement % SERES 0 TOPC Mthletis Pssport P Lerning

17 Where oes it work? Perentge of n mount # Using the equivlent frtion Clulte % of 60 'of' mens # or 0. # 60 Using the equivlent eiml These types of lultions let you to work out how muh of n ojet the perentge represents. For exmple, pint 6% of the shpe elow: This shpe is ivie into 0 equl tringles. ` The question is just sking you to lulte 6% of 0. ` 0.6 # 0 6% of this shpe ( tringles) hs een pinte. Here re some other perentge of n mount wor exmples (i) (ii) 0 people form n rrow, with the front person resse in re n the reminer in white. f 0% of the group resse like the person t the front, how mny will e resse in re? 0% of YY 00 YY 0 ` 6 people in the group will e resse in re. # Multiply y equivlent frtion (or eiml) Simplifie frtion Answer question with sttement f ske to she in 0.7 of the re shown, how mny hexgons will you nee to she? 0.7 7%, n 6 hexgons re use to mke the shpe. ` 0.7% of 6 hexgons 0.7 # 6 hexgons hexgons ` Shing 0.7 of the re mens hexgons must e she. Mthletis Pssport P Lerning SERES 0 TOPC

18 Where oes it work? Perentge of n mount Complete the steps for these perentge lultions: % of 0 # 8% of 7 7 6% of 60 # # 60.% of # 60 # Clulte these perentge mounts showing ll working. 0% of 6 60% of % of % of 0 e 67.% of 8 f % of These ones will result in nswers lrger thn the originl mount. g % of h 0% of 0 i 0% of j 7% of 79 SERES 6 0 TOPC Mthletis Pssport P Lerning

19 Where oes it work? Perentge of n mount Wht perentge of these shpes hs een she?.../.../ 0... % % % ** PERCENTAGE OF AN AMOUNT PERCENTAGE OF AN AMOUNT e % % % f Hint: the next three hve more thn one whole shpe in them (so 00%). g h % % % i She these shpes me using 0 ientil tringles to mth the given perentge vlues. 0% 0% % 7% e 0% f 6% She the perentge of these shpes tht mth the given eiml vlues o. 08 o 6 She the perentge of these shpes tht mth the given vlues. Some shpes will nee to e ivie up into smller prts to she orretly. 90% % % 9% Mthletis Pssport P Lerning SERES 0 TOPC 7

20 Where oes it work? Perentge of n mount 6 Show ll working for these questions n nswer with sttement: At inner funtion, 0% of the 9 iners hose the vegetrin min ourse ish. How mny iners hose the non-vegetrin min ourse option? During one 8-hour work y, Mith spent 0% of the time in meetings with his tem. How mny hours i he spen in meetings on tht y? Only.% of the 800 tikets on sle for onert were still ville one hour fter tikets went on sle. How mny tikets re there left fter hour? A kyker use the right-sie ple 0. of the time n the left sie ple 0.8 of the time while trvelling own river. How mny times i the right ple enter the wter if there were totl of 60 ple strokes me? 7 This one will ern you n wesome pssport stmp! Use working to show tht 0% of 7 the sme s 7% of 0. Briefly explin why this is true for ll perentge lultions..../.../ 0... WESOME AWESOME AAWESOME AWESOME SERES 8 0 TOPC Mthletis Pssport P Lerning

21 Where oes it work? Perentge of n mount Complementry perentges n e use to simplify perentge prolems: Fin the omplement for eh of these At ll entre, % of the 0 people working there re urrently not tking phone lls. How mny people re urrently tking phone lls? The perentge of people tking phone lls is the omplement of %. The omplement of % is 68%. ` 68% of the 0 people re tking lls. ` 0.68 # 0 ` people re urrently tking phone lls in the ll entre. 8 7% of 6GB (gigytes) musi evie is fille with tunes from the owner s musi olletion. How mny gigytes oes the owner hve left ville for more musi ownlos? 9 A shopping list ontine 96 ifferent items. f the shopper hs only.% of the liste items remining to ollet, how mny items from the shopping list re in the trolley? 0 A 900 piee jigsw puzzle hs 0. of the piees ple orretly into the puzzle. Use the omplementry eiml to lulte how mny piees re left to omplete the jigsw. (i) A snow-sle is 0. o of the wy own 0 metre hill. Clulte the omplementry eiml tht represents how fr the sle hs left to go. (ii) How fr oes the sle hve left to go to get to the ottom of the hill? Mthletis Pssport P Lerning SERES 0 TOPC 9

22 Where oes it work? Perentge of n mount When thuner storm psse over the town of Zppville, the golf-ourse reeive of the 78 lightning strikes use y the storm. (i) Clulte the omplementry perentge tht represents the numer of strikes tht i not our on the golf ourse. (ii) How mny lightning strikes were not on the golf ourse? A survey ws poste out to houses in suur to see wht servies resients woul like to hve improve for their lol ommunity. The post offie reeive k 8 % of the envelopes mile out with omplete surveys. How mny surveys were not returne? % of the ots printe on norml six-sie ie re lote in the entre of the sie. 7 How mny other non-entre ots re there on norml six-sie ie? The wter level in n 8 metre eep well is 079. o of the well s epth from the top. (i) How fr from the top of the well is the wter level, urte to eiml ple? (ii) The well is only ever less thn % full uring rought onitions. Determine if this wter level inites rought onitions or not. SERES 0 0 TOPC Mthletis Pssport P Lerning

23 Where oes it work? One mount s perentge of nother The results of ompring vlues suh s sores out of totl mount re often given s perentge. Sore of 7 out of 'out of' mens 'over' Frtion 7 either or Equivlent frtion 0.68 Equivlent eiml 68% Perentge 7 # 00 or 7 ' # 00 f using lultor, here re two wys to o it Here is where this type of perentge lultion n e pplie: 0 seons hve psse on stop-wth. f the person pushes stop fter further 6 seons, wht perentge of one minute (60 seons) hs psse? 0 seons + 6 seons 6 seons ` 6 60% 60 Let s look t few more exmples efore trying some for yourself. These exmples re more omplex n require the use of lultor (i) Wht perentge oes out of represent? (ii). out of. # 00% 0 % 8.8% or 8 % You n lso e ske to lulte the omplementry perentge. Points not sore Equivlent eiml Multiplie y 00 Deiml n mixe numer form Hugo sore. out of possile 0 points in reent ompetition. Wht perentge represents the numer of points he i not sore? ` 6. out of 0 6. # 00% 0 60 % 0. 6 o or % Multiplie y 00 Deiml n mixe numer form Mthletis Pssport P Lerning SERES 0 TOPC

24 Where oes it work? One mount s perentge of nother Clulte these perentge mounts: out of 0. out of **** ONE **** AMOUNT AS A PERCENTAGE OF ANOTHER.../.../ 0... Clulte these perentge mounts, leving your nswers s mixe numer perentges: 7 out of out of Clulte these perentge mounts, rouning your nswers to eiml ples: 0. out of 8.. o out of 0 Four ifferent. grm piees of le were stuie n foun to ontin.,.0, 8. n 6.8 grms of grphite. Clulte the perentge of grphite foun in eh le n then use the tle elow to etermine wht penil type eh le ws from. Penil Type Grphite Cly, Wx, et. 6H 0% 0%. grms of grphite Penil type H % 7% H % % H 8% %.0 grms of grphite Penil type H 6% 9% H 6% 7% HB 68% % 8. grms of grphite Penil type B 7% 7% B 7% % B 78% % 6.8 grms of grphite Penil type B 8% 9% 6B 8% 6% Eh stuent in lss of twenty five is ske to selet one of forty ifferent vegetles to write nutrition report out it. The sme vegetle nnot e pike twie. Wht perentge of vegetles o not get nutrition report written out them? SERES 0 TOPC Mthletis Pssport P Lerning

25 Where oes it work? One mount s perentge of nother 6 t s time for 8 irs to migrte. 68 of the irs strt their migrtion while the reminer of the irs wit until the first flok hs left. Wht perentge of irs leve s prt of the seon flok? Roun your nswer to the nerest whole perentge. 7 The surfe re of the Erth is roughly km (or squre miles). f km of the Erth s surfe is overe with slt wter oens, wht perentge of the Erth s surfe is overe in slt wter? Use the perentge lulte in prt to lulte the surfe re of the Erth overe in slt wter oens in squre miles (urte to the nerest whole squre mile). 8 A vieo goes virl n ttrts n verge of 980. hits every seon in the first five minutes. After one hour it hs h 00 hits. Wht perentge of the hits ourre in the first five minutes? Psst: minute 60 seons 9 f 70 gllons of rin wter hs een relese from wter tnk, wht perentge of wter remins if the gllon tnk ws full efore the wter ws relese? Roun nswer to.p. Mthletis Pssport P Lerning SERES 0 TOPC

26 Wht else n you o? Perentge hnge There re two types of perentge hnges: inreses n ereses. An inrese mens you finish with more thn wht you strte with. So we the perentge mount to the whole mount (00%) tht we h to egin with. f jvelin thrower ets their personl est istne y %, then the new personl est istne is: nitil personl est istne thrown 00% + % 0% of the previous personl est Perentge of extr istne NCREASE, MORE, GROW, LARGER, FURTHER, NFLATE, A erese mens you finish with less thn wht you strte with. So sutrt the perentge from the whole mount (00%) tht we h to egin with. f skter reues their personl est time roun trk y %, then the new personl est time is: 00% - % 89% of the previous personl est time LESS, REDUCE, SHRNK, SHORTEN, QUCKER, DECREASE, nitil personl est time roun trk Perentge of time reue y Perform these perentge hnge lultions (i) nrese 0 y %. (ii) Derese. y %. An inrese of % 00% + % % of originl mount `% of 0. # 0 A Derese of % 00% - % 7% of originl mount ` 7% of. 0.7 #..9 or 0 9 (iii) How mny hexgons must e fille to inrese the numer of she hexgons y %? ` just fousing on the nine she hexgons, not ll the hexgons. An inrese of % 00% + % % of originl mount ` % of 9 hexgons. o # 9 hexgons hexgons ` more hexgons must e she to inrese the numer of she hexgons y %. SERES 0 TOPC Mthletis Pssport P Lerning

27 Wht else n you o? Perentge hnge Complete these lultions to see the two ifferent wys you n lulte perentge hnges. nrese y 0% Derese 6 y 0% 0% inrese 00% 0% 0% erese 00% 0% % of initil mount % of initil mount ` nrese of 0% # ` Derese of 0% # 6 Deiml form Deiml form Other metho: Other metho: Fin 0% of n to Fin 0% of 6 n sutrt from 6 0% of # 0% of 6 # 6 Deiml form Deiml form ` nrese of 0% + ` Derese of 0% 6 - Clulte these perentge hnges: Derese 0 y 0%. nrese 76 y %. nrese 6. y %. Reue 8 y.%. e Mrk 8 lrger y %. f A further 9% to %. Derese 0 rs y 00%. Cn you erese physil quntity (suh s rs) y more thn 00%? Briefly explin your nswer. Mthletis Pssport P Lerning SERES 0 TOPC

28 PERCENTAGE CHANGE * PERCENTAGE CHANGE Wht else n you o? Perentge hnge.../.../0... nrese 70 y 00% Write own nother mthemtil lultion whih lso inreses numer y 00%. nrese 70 y 00%. Write own nother mthemtil lultion whih lso inreses numer y 00% e Write own generl rule you oul use to mke inresing numer y multiple of 00% quik n simple. nrese $0 y 0%. Reue the nswer to prt y 0%. Di you expet to get the sme mount of $0 for prt euse you were inresing n eresing y the sme perentge? Explin riefly why you think the nswer to prt oul not e $0. 6 Lengthen 80 m y 0%, then inrese this length y further %. s inresing numer y 0% n then inresing the nswer y % the sme s inresing the originl mount y %? Briefly explin why/why not. SERES 6 0 TOPC Mthletis Pssport P Lerning

29 Wht else n you o? Perentge hnge 7 nrese 60 y %, then erese the nswer y 0%. Reue 00 y %, then reue the result y 70.%. Derese $ y %, then inrese the result y 6%. Roun nswer to eiml ples. nflte $90 y %, then reue the result y %. Roun the finl nswer to eiml ples. 8 nrese the numer of tringles in this imge y %. Cross out enough nns elow so the totl numer of nns hs shrunk y 66 %. 60% of the squres elow were she in efore 7% of the she squres were lere gin. Clulte how mny squres woul now e she n she the igrm ppropritely. Mthletis Pssport P Lerning SERES 0 TOPC 7

30 Wht else n you o? Perentge hnge 9 All the ingreients elow re use to prepre prtiulr ish. The mss/quntity of eh ingreient require is shown next the nme of the ingreient. The vlues in squre rkets inite how mny people eh given mount is use for. A hef is mking the ish for people. Using perentge hnge lultions, mth eh ingreient to the orret perentge hnge n ingreient mount require for people y rwing stright line etween the ots. Write eh letter in the mthing numer squres elow to revel the ish this hef is mking. Psst: lulte the perentge hnge for the numer of serves n pply this to the ingreients ngreients Perentge hnge neee 0.7 re onions [serves ] 0. g mrinte fet [serves ] 7% erese viii 0 g Slt [serves 6] 7. tomtoes [serves 0] 0 ml vinegr mix [serves 8] 0 g olives [serves 7] 87. ml olive oil [serves 6] 0% less vi ix 7% more 00% inrese iii i 0% remove g 00 g S A 0 g A E E 8 0 SERES TOPC (ii) (iii) (iv) (v) (vi) Mthletis Pssport P Lerning (vii) G 9. g ml 80 g. R (viii) g 0 ml D (i) 70 ml 7. g 6 % erese 7 00% inrese 60 ml 6 ii 7 % inrese g hoppe re peppers [serves ] K 80 ml.o % erese iv 6 g of oregno [serves ] D % inrese vii of lenese uumer [serves ] 7 % erese L 60% reution v 66.6o % erese x Quntity neee for people (ix) (x)

31 Wht else n you o? Unitry metho Unitry metho for perentges is mthemtiin s wy of sying fin how muh % is first. One you know wht mount % represents, you n lulte ny other perentge mount. A 0 g slie of irthy ke is % of the whole ke. Wht is the mss of the irthy ke? % of the irthy ke 0 g ` % of the irthy ke 0 g ' g Divie y % mount y to get % ` 00% of the irthy ke g # g ` The mss of the irthy ke 00 g or. kg Multiply % mount y 00 to get 00% Answer with stement Here re some more exmples using unitry metho for ifferent irumstnes (i) After reent survey, 7 new splings of rre tree were isovere. f this is n inrese of % from previous survey, how mny splings of this rre tree were isovere uring the previous survey? % of the previous survey 7 splings ` % of the previous survey 7 splings ' 0. splings Divie y to get % 00% of the previous survey 0. splings # 00 ` 00% of the previous survey 0 splings ` The splings isovere in the previous survey 0 Multiply % mount y 00 Answer with sttement (ii) 66 % of n imge me entirely of equl-size hexgons is visile elow. How mny hexgons woul you see if 80% of this imge ws me visile? The numer of hexgons visile 0 ` 66 % of the full piture 0 hexgons ` % of the full piture 0 hexgons ' 66 % 0. hexgons ` 80% of the full piture 0. hexgons # 80 hexgons ` The numer of hexgons visile in 80% of the full imge Divie y 66 % to get % Multiply y 80 to get 80% Answer with sttement Mthletis Pssport P Lerning SERES 0 TOPC 9

32 Wht else n you o? Unitry metho Complete these lultions using the unitry metho to fin 00% of the given mount. % of the mount is 0. % of the mount is 8. % of the mount % of the mount ` % of the mount ' ` % of the mount ' ` 00% of the mount # ` 00% of the mount # Clulte the mount represente y 00% for eh of these vlues. Show ll your working. % of the mount is 0. % of the mount is 87...% of the mount is 8.. % of n mount is e 86% of the mount is f % of n mount is 76. o. UNTARY * * * METHOD * * *.../.../0... SERES 0 0 TOPC Mthletis Pssport P Lerning

33 Wht else n you o? Unitry metho Clulte the perentge mount for eh of these given quntities. Show ll your working. 6% of length is 90 units. How long is % of the sme length? % of n ingreient is 6 g. How muh is 0% of the sme ingreient? 0% of mss is kg. Wht is % of the sme mss? 90% of the initil moe popultion is 096. How mny moe re there in of 7 % the initil popultion? Use the unitry metho to solve these prolems: Conrete is me y mixing ement with sn n grvel. f sn mkes up % of the whole mixture, wht mss of onrete is proue if 6 kg g of sn ws use? n one prtiulr termite nest there re 87 worker termites. They ount for 87 % of the entire olony. How mny solier termites re there in the sme nest if they ount for.% of the olony? Two fifths of the 0 people t sport venue represent 60% of ll the registere fns of the Pesky Pi-rtes tem. How mny people re registere fns of the Pesky Pi-rtes? Mthletis Pssport P Lerning SERES 0 TOPC

34 Wht else n you o? Unitry metho Here re some more exmples using unitry metho for ifferent irumstnes. (i) (ii) Newperentge nitil perentge % of numer is 0. Wht is the numer (ie 00%)? 00 # 0 80 # nitil perentge mount % of numer is. Wht is 7% of the sme numer? The lultion of % still 7 hppens within this formul. # 6 Cn you see how? Use this rule to lulte these rouning your nswers to eiml ples. % of numer is 6. Wht is the numer? 0% of numer is 96. Wht is the mount? 7% of numer is. Wht is % of the sme numer? 8% of vlue is.8. Wht is 0% of the sme vlue? e 0% of frtion is 8. Wht is 0% of the sme frtion? f % of timefrme is 0 seons. How long is 0 % of the sme timefrme? 7 6 Only.% of these imges me entirely of equl-size ojets re visile. How mny ojets woul you see in eh imge if 70% of the imge ws me visile? SERES 0 TOPC Mthletis Pssport P Lerning

35 LOSS, LOSS,LOSS, LOSS, LOSS, LOSS, Wht else n you o? Profit n loss Profits n losses re usully money vlues relting to the sle or tre of items y retilers. Some importnt terms first: ost prie: The prie retilers py for the items they re going to sell. mrke prie: The prie retilers put on the items they re selling to ustomers sle prie: The prie retilers tully sell the items for. A profit is wht you gin from sle A loss is wht you lose from sle PROFT, PROFT, PROFT, PROFT, Sle prie Cost prie Sle prie - Cost prie Positive nswer Sle prie Cost prie Sle prie - Cost prie Negtive nswer Here is n exmple inluing some new terms importnt to these types of perentge lultions To mke profit, shops inrese the ost prie of items y perentge. This is lle mrkup. Mrke prie Cost prie + The mrkup (i) A retiler uys some sketlls for $ eh n eies to 7% mrk-up to sell them. $ inrese y 7% $ #.7 $8.0 ` Mrke prie of sketll in the shop is $8.0. Alwys nswer money questions urte to eiml ples. To mke n item sell quiker, they erese the ost prie y perentge. This is lle isount. Disount/On-Sle Prie Mrke prie - the isount (ii) The retiler then isounts the mrke prie of the sketlls y % to sell them fster. $8.0 erese y % $8.0 # 0.88 $.88 ` Disounte (or on sle ) prie of sketll in the shop is $.88 (iii) Clulte the profit or loss for the retiler if sketll ws sol t the isounte prie. Sle prie - Cost prie $.88 # $ $.88 Positive nswer, so the retiler me profit of $.88 Mthletis Pssport P Lerning SERES 0 TOPC

36 Wht else n you o? Profit n loss Clulte the profit or loss for eh of these ost n sle pries. Cost prie $ Sle prie $ Cost prie $.00 Sle prie $6.0 Cost prie $0. Sle prie $0.7 ` Profit Loss ` Profit Loss ` Profit Loss To lulte the profit or loss s perentge of the ost prie, we use this formul: Profit/loss s perentge of the ost prie (profit/loss ' ost prie) # 00% Complete these lultions whih follow this formul to fin the perentge profit/loss Cost prie $8.00 Sle prie $.0 Profit Loss Cost prie $.0 Sle prie $.6 Profit Loss ` ( ' ) # 00% ` ( ' ) # 00% % Profit of the ost prie Loss of the ost prie % Profit of the ost prie Loss of the ost prie To lulte the profit or loss s perentge of the sle prie, we use similr formul: Profit/loss s perentge of the sle prie (profit/loss ' sle prie) # 00% Complete these lultions whih follow this formul to fin the perentge profit/loss. Cost prie $.6 Sle prie $.60 Profit Loss Cost prie $9.66 Sle prie $. Profit Loss ` ( ' ) # 00% ` ( ' ) # 00%. % Profit of the sle prie Loss of the sle prie. % Profit of the sle prie Loss of the sle prie Clulte the perentge profit/loss (to.p.) of the ost n sle pries for these: Cost prie $0.0 Sle prie $. Profit Loss Cost prie $9.0 Sle prie $8.9 Profit Loss Differene Differene % Profit of the ost prie Loss of the ost prie % Profit of the ost prie Loss of the ost prie % Profit of the ost prie Loss of the ost prie % Profit of the ost prie Loss of the ost prie SERES 0 TOPC Mthletis Pssport P Lerning

37 Wht else n you o? Profit n loss Clulte the mrke prie for these items fter the given perentge mrkups. Cost prie $ Mrkup % Cost prie $.0 Mrkup 6% Cost prie $0.00 Mrkup.% Mrke prie $ Mrke prie $ Mrke prie $ 6 A store isplye the sign elow in its winow. Clulte the isounte prie for these items: Mrke prie $7.00 Mrke prie $78.0 Disounte prie $ Disounte prie $ 7 A store purhses 0 ining tles for $0 per tle. The mrkup put on eh tle y the store ws 0%. Five tles were suessfully sol for the mrke prie. Clulte the profit me from the sle of these five tles. Write the profit me s perentge of the ost prie for the five tles sol. The store isounte the mrke prie of the five remining tles y 0% to mke room for new stok. Clulte the new isounte prie for eh tle. Clulte the profit/loss me on the sle of ll ten tles. Mthletis Pssport P Lerning SERES 0 TOPC

38 Wht else n you o? Profit n loss The unitry metho is helpful for these profit n loss questions: 8 A store hel speil letter tg sle. Any item in the store lele with n S, A, L or E tg ws isounte y the perentges shown elow (-70% mens isount of 70%). Use the given informtion to lulte the mrke prie for the items tgge elow: Television Pirte ht Disounte prie $0 Disounte prie $.80 Perentge isount Perentge isount ` Mrke prie ` Mrke prie Megphone Golf lus Disounte prie $97.0 Disounte prie $.60 Perentge isount Perentge isount ` Mrke prie ` Mrke prie 9 An item osting $0 is given mrk up of 0%. f the item ws then given % isount when sol, i retiler mke profit or loss? Show the lultions use to get your nswer. SERES 6 0 TOPC Mthletis Pssport P Lerning

39 Wht else n you o? Profit n loss PROFT AND LOSS * PROFT AND LOSS * 0 When n item is sol for the sme mount s the ost prie, it is lle reking even (or the retiler sys they roke even on the sle ). A set of rystl glsses were ought y retiler for $00 n given mrkup of %. Clulte the mrke prie on the rystl glsses in the retil store..../.../ 0... Wht perentge isount (to.p.) ws given to uyer if the retiler roke even on the sle? The ost prie of forml ress ws.% more thn the sle prie of $890. How muh money i the seller lose on the sle of this ress? Wht ws the lele prie of the ress if the ost prie ws given mrkup of 0%? Clulte the isount given to this ress t the time of its sle s perentge of the ost prie (to the nerest whole perent). A retiler eies tht 7.% profit is neee on new rnge of prouts if it is going to ontinue selling them. The new prouts were purhse t ost prie of $7.0 eh. The prouts re mrke up y 6. o %. Wht is the mrke prie for these prouts to.p.? Wht is the minimum prie (to the nerest whole ollr) the items must e sol for so the retiler will ontinue selling them? Clulte the mximum perentge isount tht n e given to the mrke prie to ensure the retiler ontinues to sell the prout (to nerest whole perent)? Mthletis Pssport P Lerning SERES 0 TOPC 7

40 Wht else n you o? More pplitions of perentge lultions Look t this nutritionl informtion for pket of foo. Nutritionl nformtion Serving size: g Avg Qty per Serve Avg Qty per 00g Energy 78 kj 0 kj Protein 0. g 8.0 g Ft, totl 0. g. g -sturte 0.0 g 0. g Crohyrte.8 g 7.0 g -sugrs. g.9 g Soium 8 mg 6 mg Vitmin C 7 mg 00 mg Vitmin A 9 U 890 U Clulte your minimum ily requirement of protein. Psst: rememer, perent men per 00!! The stnr metho use y nutritionists to estimte our minimum ily grms of protein neee is to multiply the oy weight in kilogrms y 0.8. Use the formul to lulte the mss of protein reommene for n ult who weighs 70 kg. How mny servings of this foo will give this person their reommene ily soure of protein? f 70 kg ult ets just enough servings to get their require ily soure of protein, how mny grms of rohyrtes will lso e eten? e An expert reommens splitting your totl ily foo into 0% rohyrtes, % proteins n 8% helthy fts for helthy lifestyle. Use perentge lultions to show whether or not this foo is helthy option y ompring the mount of protein n rohyrte eten y this ult..../.../ 0... MORE APPLCATONS OF PERCENTAGE CALCULATONS * Plnet X orits its sun every ys. This is. 6 % of the time tken for Plnet G to orit the sme sun. How long oes it tke for Plnet G to omplete orits to the nerest whole y? Psst: orits is like 00%! SERES 8 0 TOPC Mthletis Pssport P Lerning

41 Wht else n you o? More pplitions of perentge lultions Every yer, the height of pine tree in renewle forestry plnttion inreses y 0 % of the height it rehe the yer efore. The height of one prtiulr tree now is m. How high will this tree e one yer from now? How muh further will the grow etween one n two yers from now to eiml ples? By wht overll perentge will the tree hve grown y two yers from now to eiml ple? One the tree rehes height of m, it is ut own n use for timer prouts. Will this tree e ut own three yers from now? Show working to k up your nswer. e f llowe to ontinue growing, four yers from now the tree will e more thn oule the urrent height. Explin how this is possile if it hs only grown y 0 eh yer. This one eserves n wesome pssport stmp one omplete. While flying 0 m ove the groun, hot ir lloon is fille with hot ir so its height ove the groun inrese y %. After 0 minutes, the lloon h lrey lowere 7 m efore more hot ir is put into the lloon, rising the height ove the groun t tht time y 8. 8 o %. Clulte the perentge hnge in height from the initil 0 m ove groun to nerest whole perent. AWESOME AWESOME AWESOME Mthletis Pssport P Lerning SERES 0 TOPC 9

42 LESS, REDUCE, SHRNK, SHORTEN, QUCKER, DECREASE, LOSS, LOSS,LOSS, LOSS, LOSS, LOSS, Chet Sheet Here is summry of some importnt things to rememer for perentge lultions Perentge of n mount Clulte 0% of 0 'of' mens # 0 00 # 0 or 0. # 0 Using the equivlent frtion Using the equivlent eiml One mount s perentge of nother Sore of 6 out of 0 Frtion # 00 0 B or 6 ^6 ' 0h# 00@ % 80% perentge Complementry perentges Like omplementry frtions. f 0% of the ingreients is flour, then the rest of the ingreient is 00% - 0% 80%. Perentge hnge NCREASE, MORE, GROW, LARGER, FURTHER, NFLATE, Perentge inrese A the perentge mount to 00% Perentge erese Sutrt the perentge mount from 00% Profit n Loss PROFT, PROFT, PROFT, PROFT, Profit wht you gin from sle Sle prie Cost prie Loss wht you lose from sle Sle prie Cost prie ` Sle prie - Cost prie Positive nswer ` Sle prie - Cost prie Negtive nswer Both n e expresse s perentges of the ost prie or sle prie. ost prie: The prie retilers py for the items they re going to sell. mrke prie: The prie retilers put on the items they re selling to ustomers. sle prie: The prie retilers tully sell the items for. mrk up: The perentge vlue e to the ost prie for selling. isount: The perentge vlue eute from the mrke prie for selling. Unitry Metho Divie the mount y the perentge vlue to fin the mount % represents. Multiply the mount % y the new perentge vlue require. Quik metho using lultor: Newperentge nitil perentge # nitil perentge mount SERES 0 0 TOPC Mthletis Pssport P Lerning

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