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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. Prereqnisites:
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 ‘lL 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 wculd
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 P._@
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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 Spring '11
 DR.MCDONALD

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