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# How To Solve Proportions

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In this page we are going to discuss about solving proportion .The proportion is the way of expressing the ratio between the part and the whole. A proportion is an equation in which two ratios are set equal to each other. In this concept, cross product can be used to find the unknown number. Here we use letter x in place of unknown number. The condition for proportion is, if four quantities, a, b, c, d, are said to be in proportion if [a/b] = [c/d] . Now let us going to see some of the example problems for solving proportion in this article. Proportion is also defined as equivalent of two fractions. When we are going to write equivalent fractions, we need to create a proportion For example :­ [2/6] = [4/12] This is called as proportion 2 x 12 = 24, 6 x 4 = 24 So The two cross products are equal.
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HowToSolveProportions
expressingtheratiobetweenthepartandthewhole.Aproportionisanequationinwhichtwo
ratiosaresetequaltoeachother.Inthisconcept,crossproductcanbeusedtofindtheunknown
number.Hereweuseletterxinplaceofunknownnumber.Theconditionforproportionis,iffour
quantities,a,b,c,d,aresaidtobeinproportionif[a/b]=[c/d].Nowletusgoingtoseesomeof
theexampleproblemsforsolvingproportioninthisarticle.
Proportionisalsodefinedasequivalentoftwofractions.Whenwearegoingtowriteequivalent
fractions,weneedtocreateaproportion
Forexample:[2/6]=[4/12]
Thisiscalledasproportion
2x12=24,6x4=24
SoThetwocrossproductsareequal.

Ifanyoneofthefournumberisunknown,crossproductcanbeusedtofindtheunknownnumber.
Thisprocessisknownassolvingproportions.HereweuseletterXinplaceofunknownnumber.
HowtoSolveaProportion
Proportioncanbeexpressedinthreeforms,
[a/b][c/d](or)a:b=c:d(or)a:b::c:d
Importantproperty:Productofextremes=Productofmeans
Note:(i)Thefirstandfourthtermsarecalledextremesand
(ii)Thesecondandthirdtermsarecalledmiddletermsormeans.
Example:Verify3:4=9:12isaproportionornot.
Solution:Productofextremes=3*12=36
Productofmeans=4*9=36
36=36

Thesetwoproductsareequal.
Therefore3:4=9:12isaproportion.
StepsforSolvingSimpleProportion
Tosolvetheproportion,wehavethreesteps.
Step1:Applyingcrossmultiplication
Step2:Makeanequation
Step3:Solveforxvariable
SolvedExamples
Example1:[11/13]=[55/x]Solvethisproportion:
Solution:Thegivenproportion:
=[11/13]=[55/x]
Step1:ApplyingCrossmultiply.

11*X=13*55

Step2:Makeanequation.
11X=715
Step3:SolvingforXvariable.
Divideby11eachside.
=[(11X)/(11)]=[715/11]
Simplifyit,X=65.
Example2:If2:3=14:xisaproportion,solveforx.
Solution:Productofextremes=2xx
Productofmeans=3x14
Sinceitaproportion,2xx=42
2x=42
Divide2onbothsides,

=[(2x)/2]=[42/2]

x=21
Example3:Samistypingapaperthatis420wordslong.Hecantype35wordsin1minute.
Howlongwillittakehimtotypethepaper?
Solution:Wecansolvethisproblembyusingproportionality.
Samistyping35words=1minute
420words=xminute
Therefore,[(35words)/(1mins)]=[(420words)/(xmins)]
Nowusingthecrossmultipliestoget
35(xmin)=420(1min)
35x=420,x=[420/35]
=12,x=12min
So,Samcantype420wordsin12minutes.

Example4:Solvethefollowingproportion(x+3):8=(x+2):10andfindthevalueofx.

Sol:(x+3):8=(x+2):10
Writetheproportionas,
(x+3)/8=(x+2)/10
Takingcrossproduct,
10(x+3)=8(x+2)
10x+30=8x+16
Subtract8xonbothsides,
10x8x+30=8x8x+16
2x+30=16
Combineconstantterm,2x=1630
2x=14
Divideby2onbothsides,x=7
H
encethevalueofxintheproportionis7.

ThankYou
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How To Solve Proportions

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