CLASS-6
PROPORTION

PROPORTION

Equality of the two ratio is called ‘PROPORTION’

If there are four quantity such as  w, x, y, z and if  w: x and y: z then as per the condition ‘Proportion’ can be described as w : x =  y : z on the other way we can describe as w : x : :  y : z, here  : :  stands for ‘is as’

We read  w : x : :  y : z  as  =>  ( w is to x ) as ( y is to z )   

We call a) First and Fourth quantity is called extreme terms or ‘Extremes’, and b) Second and Third quantity is called middle terms ‘Means’.

So, Product of Extreme =  1^st Term  x  4^th Term

Product of Means = 2^nd Term  x  3^rd Term

In a proportion we have, Products of Extreme = Product of Means

So,     w : x : :  y : z                                              

    =>  (w : x)  =  (y : z)    

             w                 y                                                                       

    =>  ---------   =  ---------                                                                     

             x                  z                                                                                                                                                                                                             

    =>      wz  =  yx        (Cross Multiplication Rules)       

   Here, Product of Extreme = wz,  Product of Means =  yx  

So, when ever wz = yx  then we can say w, x, y, z are in proportion and if  wz & yx are not equal then w, x, y, z are not in proportion.

Q1) Check whether the ratio 36 : 144  and  17 : 68  form proportion or not?

Ans.)  first take 36 : 144

Now find the H.C.F of 36 and 144.

     36 )  144  (  4        36           36 ÷  36         1

           144            -------  = ----------- = ------  =  1 : 4

       ---------          144          144 ÷ 36         4

             0        

  Now find the H.C.F of 17 and 68.

     17 )  68  (  4        17        17 ÷ 17       1

           68            ------ = --------- = -----  =  1 : 4

       ---------         68        68 ÷ 17       4

            0                       

   Thus   36 : 144  =  17 :  68  ;   1 : 4 = 1 : 4

So, 36 : 144  =  17 : 68, we can conclude that  36 : 144  and  17 :  68 are  form a proportion.        (Ans.)

Q2.) Show whether the numbers 21, 25, 35, 15 form proportionate or not.

Ans.) There are another way we will describe to prove whether all given numbers are forming Proportion or not.

The given terms are  21, 25, 35, & 15.

So, Product extremes = 1^st Term x 4^th Term = 21 x 15 = 315

And, Product Means = 2^nd Term x 3^rd Term = 25 x 35 = 875

As per the rules, the condition for satisfying proportion, Product extremes, and Product Means must be equal.

But in that case we can observe that, Product extremes = Product (Not Equal) Means ( 315 = 875) (Not Equal).

So, we can conclude that, given numbers 21, 25, 35, & 15 does not form the proportion.          (Ans.)

Q.3) Find the value of 3^rd Term, whether 1^st, 2^nd , and 4^th Term are respectively 20, 25 , 35.

Ans.)  Let the 3^rd term of proportion will be X.

So, as per the rules we can -

         1^st Term       3^rd Term       20           X

       ---------- = ---------- ; ------- = -------    

         2^nd Term       4^th Term       25          35  

        =>  20 x 35  = 25 x X   (Via Cross Multiplication rules)

                 20 X 35

       X = --------------   =  28

                    25         

So, where X is the 3^rd Term, then the 3^rd Term is 28.        (Ans.)