# CLASS-6PROPORTION

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 =  1st Term  x  4th Term

Product of Means = 2nd Term  x  3rd 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 = 1st Term x 4th Term = 21 x 15 = 315

And, Product Means = 2nd Term x 3rd 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 3rd Term, whether 1st, 2nd , and 4th Term are respectively 20, 25 , 35.

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

So, as per the rules we can -

1st Term       3rd Term       20           X

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

2nd Term       4th Term       25          35

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

20 X 35

X = --------------   =  28

25

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