# SOLVE PROPORTIONS

## About "Solve proportions"

Solve proportions :

When two ratios expressed in its simplest form are equal they are said to be in proportion.

Proportion is represented by the symbol ‘ = ‘ or ‘:: ‘

If the ratio a: b is equal to the ratio c : d then a,b,c,d are said to be in proportion.

If a : b and c : d are in proportion then a x d = b x c

The proportion is written as a : b :: c : d

In a proportion, the product of extremes is equal to the product of means. ## Solve proportions - Examples

Example  1 :

Find the missing term in 3 : 4 = 12 : ____

Solution :

Let "x" be the missing term

3 : 4 = 12 : x

Since the ratios 3 : 4 is equal to 12 : x, 3, 4, 12 and x are said to be in proportion.

That is,

Product of extremes  = Product of means

3 x  = 4 (12)

x  =  48/3  =  16

Hence the missing term is 16.

Example  2 :

Using 3 and 12 as means, write any two proportions

Solution :

Given 3 and 12 are means

So, __: 3 = 12 : __

Let "a" and "b" be the missing terms

The product of the means 3 x 12 = 36

The product of Extremes (a x b) must be 36

36 can be written as 2 x 18 or 4 x 9 etc,

2 : 3 = 12 : 18

4 : 3 = 12 : 9

Two proportions are 2 : 3 :: 12 : 18 and 4 : 3 :: 12 : 9.

Example  3 :

Using 4 and 20 as means, write two proportions.

Solution :

Given 3 and 12 are means

So, __: 4 = 20 : __

Let "a" and "b" be the missing terms

The product of the means 4 x 20 = 80

The product of Extremes (a x b) must be 80

80 can be written as 16 x 5 or 10 x 8 etc,

16 : 4 = 20 : 5

10 : 4 = 20 : 8

Two proportions are 16 : 4 = 20 : 5 and 10 : 4 = 20 : 8.

Example 4 :

Show that 12 : 9, 4 : 3 are in proportion.

Solution :

The product of the extremes = 12 x 3 = 36

The product of the means = 9 x 4 = 36

12 : 9, 4 : 3 are in proportion

(i.e.) 12 : 9 :: 4 : 3

Example 5 :

Solve 5/3  =  x/48

Solution :

5/3  =  x/48

5(48)  =  x (3)

3x = 5(48)

x = 240/3

x = 80

Example 6 :

Solve 18/a  =  9/50

Solution :

18/a  =  9/50

18(50)  =  a (9)

9a  =  18(50)

a  =  18(50)/9

a = 900/9  =  100 After having gone through the stuff given above, we hope that the students would have understood "Solve proportions".

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