# decimal p3 - Maths Study Sheet 6 d e c i m a I s dealing...

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Unformatted text preview: Maths Study Sheet 6 d e c i m a I s dealing with percentages part 3 — When ven have werked Lhrengh this Part , ven will i have defined special fractiens knewn as percentages - be able te write a tractien in decimal er percentage term and vice versa - find a percentage ef a given quantity 1' express ene arneunt as a percentage ef anether I knew hew te increase er decrease an amennt by a given percentage. Pre-reqnisites: Yen shenld be familiar with Part 1 ef this UNIT. The cencepts ef Katie and Preperiien {UNIT 3) are need in the later examples ef this Part. Yen will require a calcnlater. Percentages A fractien which has a denerninater IUD is eften written with a special symhnl and referred tn as a percentage. 5 - . Fer example: ﬂ is written 5% and this is read as “five per cent”. Te read a decimal as a percentage . . 4 LLU-‘l = — = 4Ii’e i0“ 15 [115 = — = 15% Rig 3 l 2 3.12 = "u—H = 312% 100 125 1'2. 5 1 0.125 = —' — — 12—%, 12.5% 1000' 100 _ 2 Te change a fractien in a percentage 100 multiply by 100% [Nate tliiaie the same as —— = l] {00 l — = - >< 100% = 25% 4 4 3 3 j = — a: lﬂﬂ% = 60% a 5 Tu change a percentage ta a decimal replace the ‘l-L ajarnbcil by the preceaa crf “ciii'ieinn by 1:10”. _ 7 are = — =03? HJU 3_ 25 place 3 in hundrcdtlia pneitinn 5 {it —— — = 0.0325 4 100 T Equivalence Table ﬂf ccin'uncln fracticms, decimals and percentages Fractien Decimal Percentage l — 0.5 SEW: 2 l —- 0.25 2525?} 4 3 A _ _ 1 1 — 0.125 I? 7‘?” 8 ._ 3 8 I 10 1 ICE} ._ — 203’}: 0.9 — Percentage of a quantity — 0.0? — 1 a 3 1 3 a G 2 -_ 2 — Ella—Te 3 '3 _ _ 4H1: Fill the gaps in the table abexe. Percentages enable us tn cempare the prnpnrtinns ef cempenent parts in am: quantity. Fer example, mest taxpayers will pay 25% ef their taxable mceme in tax and be allewecl te retain F511}. Se we keep three times what we give tn the gtwernment. The ether helpful cencept is that in 101] parts 135% is 25 parts. In the case ef the taxpayer it might be in ever}! £100, £25 will be tax. Example {1) Find 3%941 ef rises 3.5 3 ef £1000: ——x 1000 = as {s}. * lUU Example (2} Express 30 m as a percentage nf 1 km. Since 1km = 1000 m, the fractien is 30 3 — = --——= 3% 1000 100 Tn increase er decrease an ameunl by a percentage. Example (3} Membership eta swimming club is 275. If there is a decrease at Silt}, what will be the new membership? 8 'l'he decrease:—— >5. '2??? : 22 100 New membership is 253. Anether wa},r te- appreach this calculatien is in use the idea nf ratie. A decrease et 8% means that fer ever}! 10D members at present, there wc-uld be 100 — 3, i.e. 92 members in the future. The ratie ef new membership : elcl membership -= 92 : 1tltl new lll‘llb- ' ' 1 Using the essticiated fractiens: = £— eld membership liltl _ 92 Then, new memberstup = is eld membership 92 = —-— 2a: 2??) It'll] — 253 Example {4} A Inﬁnitth insurance premium increased frnm £11.10 if £12.50. What is the percentage increase? Increase = £12.50 — £11.10 = £1.40. We have te express this increase as a percentage ef the eriginal premium. As a fractien ef the eriginal premium this is 1.40 11.10 ll Increase As a percentage this becemes 1.4ﬂ 11.10 Increase : X 100% 5:: gull Example (5} A whelesaler sells an item te a retailer fer a pref it ef 20”“. The retailer eventu— all)»r manages te sell it be a custerner in a sale fer £57,. but makes a small less el 5‘12}. What was the eriginal price charged by the whulesaler? The diagram beltiw describes the situatien. We want te fincl q, then p. Whulesaler Retailer IClusteiner Ep 4.: Eq —> £5? Zﬁ‘ﬁm 5% prefit less Use the ratie Inethed te deal with the 5% less between Retailer and Custeiner. A less ef 5% means IUU units {E} beeernes 95 units (E). Se ratie q : 57 = 100 : 95 and i = ﬂ 5? 95 i q = >1 57 = {30 95 New leek at the EDEEJ prefit between Whelesaler and Retailer. A prefit ef 20% rneans 1UU units (E) beeeines 120 units {E}. Se ratie p : q z 100 : 120 [email protected] q 120 100 _ p : — “5*: 6f} : St} 120 The eriginal prirga Charged by the whalesaler was £59. 1. Express — as a decimal and as a percentage. 8 Exercise Solutions re W'hat is 6% of £32.50? 1 Ableed dener gives — litre ef his eriginal 5 litres ef blend. 1“that is his 2 mementary percentage less ef bleed? The sales fer a greup’s latest disc were 11400 cempared with 15,000 ier their previens single release. What is the percentage increase in sales? In a 1U year peried the pepulatien ef a tewn increased by 3% te T3332. What was the pepnlatien it} years age? A hemeewner whe beught his hense fer Eilﬂﬂtltl in 1988 is warned by a heuse agent that, if he sells it new, he must espect te make a less ef 15%. Wat price can he espect te realise? A jeweller whe buys rings at an auctien fer £91”) each puts a “marked” price en them in his shep, but actually sells them at a disceLmt et IU'irl: eff this “marked” price. If he still makes a prefit ef 350:1” find the actual selling price and the “marked” price. H ex re |_. “s3 1.3 L = U. 625 8 £1.95 Fl. 10% Grigmal pepnlatien was 372,900 Ratie is Original pepnlatien : Newpepnlatien = 10U:1UE5 He can espect te sell at £313,500 RatieefSelling price 1 lfest price = 135:1{310 SP. 2 £121.50 Katie ef Marked price : Sellmgprice = IUU : ‘91:} Marked price = £135 ...
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decimal p3 - Maths Study Sheet 6 d e c i m a I s dealing...

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