Proportion

Proportion
The equality of two ratio is called Proportion.
If a/b = c/d or a : b = c : d then we say a, b, c and d are proportional. It is denoted by : : symbol. In simple words, a : b : : c : d denotes the four numbers are proportional.
Types of Proportion

Mean Proportion:- Mean proportion between a and b is √ab
Example: - Find the mean proportion of 4 and 9
Solution:- Mean Proportion = √4 x 9 = √36 = 9

Third Proportion: - If a : b : : b : c then c is called the third proportion to a and b.
Formula to find Third Proportion: - c = b^2 / a
Example: - Find the third proportion of 4 : 6
Solution: - Third proportion = 6^2 / 4 = 9

Fourth Proportion:- If a : b : : c : d then d is called the fourth proportion to a, b , c and d. Fourth proportion = b c /a
Example: Find the fourth proportion to 3, 7 and 9
Solution: - Here, 3 : 7 : : 9 : x then the fourth proportion = bc / a = 7 x 9 /3 = 21

Basic Rule involved in Proportion

 Invertendo:- For a : b :: c : d the invertendo = b : a : : d : c

 Alternando : - For a : b :: c : d the alterando = a : c :: b : d

 Componendo :- For a : b :: c : d the componendo = a + b : b : : c +d : d

 Dividendo : For a : b :: c : d the dividendo = a – b : b : : c – d : d

 Componendo and Dividendo :- For a : b :: c : d the componendo and dividendo = a + b : a = b = c + d : c – d

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Dr Rajesh Kumar Thakur