basic stuff on how percentages work

7/26/2019 Basic Stuff on How Percentages Work

1/21

BASIC STUFF ON HOW PERCENTAGES WORK

WHAT IS A PERCENTAGE?

A percentage is the top part of a fraction whose bottom part is 100.

So 50% means 'half of' and 25% means 'a quarter of'. 100% means thecomplete quantity.

WHY BOTHER WITH THEM?

ercentages are useful because they ma!e it "ery easy to compare things.

#or e$ample suppose the mar!s in two successi"e tests are &()0 and 51(&0.*t is not "ery easy to say which of these was best.

ercentages use our ordinary number system of 10's 100's etc and becausethey are out of 100 rather than 10 we a"oid a lot of the decimal points whichma!e some people twitchy.


2/21

CHANGING A FRACTION TO A PERCENTAGE

+a!ing the e$ample of the test mar! of & out of )0

,ultiplying both sides of this equation by 100 gi"es us

RULE:- to chang a !"act#on to a $"cntag% &'(t#$() #t *) +,,

.'/t#on:--hat is the second test mar! of 51(&0 as a % +ry this yourselfbefore loo!ing.

An/0"

so the mar! in the second test was higher.

*'"e had some emails as!ing for help to turn a single number into apercentage. *t can't be done/ ou ha"e to !now as a percentage of what.

#or e$ample a drin!s bill of 20 for a party costing )0 in total means that thedrin!s cost 20()0 or 1( or 25% of the total. +he 20 on its own can't beturned into a percentage.


3/21

CHANGING A PERCENTAGE TO A FRACTION

RULE:- Yo' /#&$() t'"n #t #nto a !"act#on *) 0"#t#ng #t o1" +,,Thn canc( 2o0n #! $o//#*(

3$ample4 -hat is 65% as a fraction

cancelling down to the simplest form by di"iding the top and bottom by 5 inthis instance.

7uestion4 -hat is 5.5% as a fraction

3338emember that the "alue of a fraction remains unchanged when youmultiply or di"ide both the top and the bottomby the same number. 333


4/21

CHANGING A 4ECIMAL TO A PERCENTAGE

9ead easy this one/

Suppose we want to write 0.2 as a %. Since a decimal is a !ind of fraction

all we ha"e to do is to multiply by 100. ou :ust need to remember that eachtime you multiply by 10 the number becomes larger by a factor of 10 so thedecimal point mo"es one place to the right. ,ultiplying by 100 mo"es it 2places to the right. +his neat rule is because decimals are fractions in ourbase ten number system.

So we find that 0.2 is the same as ;0.2 $ 100


5/21

CHANGING A PERCENTAGE TO A 4ECIMAL

;Again dead easy/ere are 6 e$amples to show you how to deal with all possible snags.

E8a&$( 9+-hat is 6% as a decimal

Answer4 6% is the same as 0.6.

E8a&$( 97-hat is 25.5% as a decimal

Answer4 25.5% is the same as 0.255.

;?otice that the percentage had a decimal point in here too.ow much did it costbefore the sale


13/21

+he wor!ing is "ery similar to the pre"ious e$ample. -e !now that 120 is)0% of the original selling price since 20% has been ta!en off this price. +histime we'll sa"e some writing in the equations by calling the original sellingprice . +hen we ha"e

?ow multiplying both sides of this equation by 100 and di"iding both sides by)0 we ha"e

So the original selling price was 12 000()0 = 150.

A little bit of algebra sa"es a lot of writing/


14/21

E8a&$( 9eople ha"e found difficulty here when they needed to wor! bac!wards froma bill whose total includes GA+ ;"alue added ta$< at 1.5% to find out what thebill would ha"e been before the GA+ was added.

+he easiest way to e$plain how this is done is to ta!e an actual e$ample.Suppose that a bill which includes GA+ comes to 1&02.0. -e want to !nowwhat the amount was before GA+ was added.

4ANGER ou can't wor! out this answer by finding 1.5% of 1&02.0 andthen ta!ing it off. +he reason for this is that the 1.5% is of the original amountof the bill and not the final 1&02.0.

-e'll sa"e writing by calling the amount before GA+ was added E.+hen wor!ing in we !now that

+he total of the bill before GA+ was added was 16&.

-e can ma!e a general rule for this if we let stand for the total of the billincluding GA+ at 1.5%.

-e want to find E the amount of the bill before GA+ was added.

Hsing the same argument as abo"e we get

RULE:- To !#n2 th a&o'nt o! a *#(( *!o" AT at +>5 0a/ a222%&'(t#$() th a&o'nt #nc('2#ng AT *) +,, an2 2#1#2 th "/'(t *) ++>

+he wor!ing here is similar to 3$ample ;5< abo"e but GA+ seems to createspecial difficulties.


15/21

ou can practise all the percentage rules now by wor!ing out the answers tosome problems yourself.

>ere are some questions for you to ha"e a go at. +ry to do them without

loo!ing bac! at the indi"idual rules. ;>a"e a quic! chec! through before youstart if you want.owe"er a recentsur"ey in a large city has re"ealed that the proportion of 1& yearolds whosmo!e daily has :umped )% since 1CC2 to 22% in 1CCC. +ragically in this cityalone this means that in 1CCC there were an estimated 6 600 daily smo!ers inthis age group.

9ecide which of the following statements are true based on the abo"einformation.

;1< +he number of 1& yearolds in this city in 1CCC was about

;A


20/21

E8a&$( 9=

Ehocblo$ plc ha"e recently brought out two new sorts of chocolate bar the?utcho$ and the #ruticho$.

+hey sell ?utcho$ bars wholesale in bo$es of 100 bars at 2 a bo$ and#ruticho$ bars wholesale in bo$es of 120 bars at 62 a bo$.

+he launch was at the beginning of anuary 1CCC and the sales figures for thefirst & months are shown on the graph below. Hse this graph to answer thequestions below it about the sales. ;*'"e put the graph in again at the end ofthe questions to sa"e you some scrolling.

basic stuff on how percentages work

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