24 Finding percentages of quantities

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1 24 Finding percentages f quantities We are learning t calculate percentages f whle number amunts using benchmark percentages. NUMBER KNOWLEDGE Numeracy Bk 4 Reading Decimal Fractins Mre Reading f Decimal Fractins The Same but Different In AM1 and this bk Fractins and decimals... page 172 (AM1) Equivalent fractins... page 18 Fractins, decimals and percentages... page 190 Yu can use sme percentages that are easy t wrk with t calculate ther percentages. 10%, 25% and 50% are easy percentages t find. 10% f 0 = 10 / 1 tenth ( 100) 1 f % f 0 = half f 10% f 0 = half f = 3 30% f 0 = 3 times 10% f 0 = 3 = % f 0 = (30% + 5%) f 0 = = 21 We call these srts f percentages benchmarks. Example Abut 35% f the 0 peple at a riding schl were left-handed. Hw many were left-handed? Yu culd use a mind map t help 10% = 5% = 3 If 100% = 0 30% = 18 r Yu culd use a duble number line. It is easy t see frm this that 35 / f 0 (30 / 5 / ) f number 0 5% 10% 30% 50% 100% percentage r All f these strategies use benchmarks like finding 10 / first t help wrk ut the answer % 5% 30% 100% = 0 s 10% = s 5% = 3 s 30% = 18 35% = 30% + 5% = = R a t i s a n d P r p r t i n s Cnvert fractins t decimals, and percentages and vice versa. Estimating Percentages Bk 8

2 Activity 1 1 Discuss hw benchmarks culd be used t slve these and find the answers. There were 80 peple at a restaurant ne evening. a 15% rdered the chicken dish. Hw many rdered the chicken dish. b 95% f them had left by 10 p.m. Hw many had left? c 45% f them were female. Hw many were female? 2 Find the answers t these using an efficient strategy. a There are 180 pupils at Jamie s schl. 30% f them went n camp. Hw many went n camp? b Sudi sells cmputers. She gets 5% f the value f each ne she sells. What des she get if she sells a cmputer fr $840? c David s family went ut fr dinner. The cst f the meal was $140. They gave a 15% tip. Hw much did they tip? d The femur (thighbne) is a lng bne. Its length is abut 25% f a persn s height. Ann is 1. m tall. Abut hw lng is her femur? 3 Find these. Remember \45/ a 70% f 0 kg b 40% f 30 ml c 15% f 240 m d 11% f 3200 km e 5% f 14 cm f 5% f 1200 g g 95% f $4580 h 45% f 2. 4 m 50/ - 5 /? 1. m 4 Challenge A jeweller tk 10 / ff all gld rings ne week. At the end f the week she added 10 / I m ging t d the calculatins fr a ring that riginally cst 100. f the sale price back again. These new prices were nt the same as the ld prices. Explain t a partner why nt. R A T I O S A N D P R O P O R T I O N S 129

3 We are using fractins equivalent t percentages t estimate percentages f given numbers. Activity 2 1 Cpy this table and fill in the missing fractins and percentages. Percentage 10% 50% 20% Fractin Last year there were 750 whales stranded arund the wrld. I read that there were 4. 8 / mre whales stranded this year than last. Hw can I estimate abut hw many mre there were this year? Well 4. 8 / is clse t 5 / and 5 / is half. f 10 / Discuss with a classmate hw Millee culd make an estimate using Sam s suggestin. What wuld Millee s estimate be? Millee wrked ut the answer using a calculatr and gt 3. Is the estimate acceptable? Check using an estimate whether the red numbers given in questins 3 t 9 are reasnable. Justify yur answer. 3 Katrina s bank accunt earns interest f 8. 9% per year. Katrina thught that she wuld earn $ interest this year n the $325 she has in her savings accunt. 4 Last year 120 lambs were brn n Blair s farm. This year 31. % mre lambs were brn. Blair wrked ut that there were 488 mre lambs brn this year. 130 R a t i s a n d P r p r t i n s Cnvert fractins t decimals, and percentages and vice versa. Estimating Percentages Bk 8

4 5 Sam s baby sister weighed 8. 2 kg when she was eight mnths ld. When she was weighed three mnths later her weight had increased by 15. %. Her weight had increased by 1. 3 kg It was fund in the 200 census that 74. 2% f New Zealand husehlds have access t a cell phne. In a twn f 80 husehlds, 38 f them wuld have access t a cell phne. 7 The Fire Service reprted that during a bush fire 44. 3% f land in a natinal park was burnt. The natinal park cvered 353 hectares s hectares f the park was burnt. Pic here f smething t d with either, 7 r 8. 8 Mumbai in India has mm f rain in the mnsn seasn. This is 9. 4% f the annual rainfall f 2707 mm. 9 Every week Akram dnates 0. 89% f his wages t charity. a He earned $48 ne week and dnated $ b He gt a pay rise t $ a week. Nw he will dnate $ Estimate which is greater, Challenge a 59 / b 19. / f r 80. / f 5889 r 5. 8 / f f Shw hw yu estimated these. Designer hmes Design a flr plan fr a huse that has abut 40% fr the bedrms, 40% fr the lunge, dining rm and any ther living rms, 20% fr the kitchen, bathrms and hallways. This infrmatin might help yu. A typical huse will have between 100 m 2 in ttal (small huse) up t 300 m 2 (large huse). Yu culd take sme measurements frm yu wn hme t see what typical rm sizes are. Yu culd use the squares in yur maths bk t help yu draw the plan. R A T I O S A N D P R O P O R T I O N S 131

5 At the fair Sam and Millee went t a lcal fair. 1 There was a very large market at the fair. Millee had a cupn fr ne f the stalls that gave her 10% discunt n items up t $50 and 15% discunt fr items ver $50. She bught a garden statue and three packets f seeds fr her mther fr Mther s Day. $3.80 $4. 00 a Hw much did Millee save n the garden statue? b Hw much did she pay fr it? c Hw much did she save n the packets f seeds? d Hw much did she spend altgether? $3.80 $3.80 Estimate first. Rund sensibly. 2 There was a rides sectin at the fair and there were sme special discunts ffered n the rides. Helispinner Ride $ % discunt Tday nly Ride in the Dark adults $10 children $8 Family f up t 5 $28 Tday nly 35% discunt See the Wrld Big Wheel $8 per persn r save 20% by filling a capsule $40 (a capsule hlds up t peple) a Hw much d yu save n the Helispinner ride tday? b Hw much is each ride n the Helispinner? c Hw much des each adult, child and family save n the Ride in the Dark ride tday? d Hw much des each srt f ticket fr Ride in the Dark cst tday? 132 R a t i s a n d P r p r t i n s Cnvert fractins t decimals, and percentages and vice versa. Estimating Percentages Bk 8

6 e Wuld it be cheaper fr tw adults and ne child t buy a family ticket r individual tickets fr Ride in the Dark tday? f Is the advertisement fr the See the Wrld Big Wheel crrect in saying that yu save 20% if yu pay $40 fr a whle capsule and fill it with peple? Justify yur answer. 3 A stall selling sprts gear and sprts wear had the fllwing items n sale. 20% when yu buy ne $ $ $ Buy tw and get 25% Amazing 40% Tday nly 15% Tday nly 45% $ $ Bargain 25% a Sam bught a sprts singlet and a rugby ball. Hw much did he save? b Hw much change did he get frm $50? c Make a table shwing the items, their riginal price, the saving made and the sale price. d Millee spent almst $50 at this stall. What might she have bught? Give three different pssibilities. e Millee s mum spent between $25 and $40. Give an example f what she might have bught. f What is the ttal saving that yu wuld make if yu bught ne f each item n sale? R A T I O S A N D P R O P O R T I O N S 133