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Kaushiki from Delhi Public School, asked a question
Subject: Math , asked on 2/4/15

 explain componendo and dividendo....

Gunjan From Fergusson College, added an answer, on 26/2/11
166 helpful votes in Math

  Componendo and dividendo is a method of simplification in mathematics.

According to it,

 text{if } frac{a}{b} = frac{c}{d} text{ and } a neq b text{, then } frac{a+b}{a-b} = frac{c+d}{c-d}.

This proof is invalid for a=b and c=d because if

 frac{a}{b} = frac{c}{d}  such that  a = b  &  d = c

then by application of componendo and dividendo we get  frac{a+b}{a-b} = frac{c+d}{c-d} = frac{a+b}{0} = frac{c+d}{0}  {a=b,c=d} and since division by zero is not defined : a neq b

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Gunjan From Fergusson College, added an answer, on 26/2/11
166 helpful votes in Math

  omponendo and dividendo is a fundamental concept in mathematics. It helps in solving complex problems.

if a / b = c / d ,  then by applying componendo and dividendo , we  get  

                   (a + b) / ( a - b ) = (c + d ) / ( c - d ), where a is not equal to b.

  This proof is invalid for a = b and c= d .

  because if a/b = c/d and a = b and c= d / then ( a+ b ) / ( a - b ) = ( c + d ) / ( c- d )

  (a+b ) / 0 = ( c+d) / 0

  which is not defined.

  componendo and dividendo is a combination of componendo and dividendo.

Proof of Componendo and Dividendo Rule

componendo rule proof

 If  a / b = c / d,

then by using componendo , we get ,

( a + b ) / b = ( c + d ) / d 

Proof: 

adding 1 both side , we get 

  a / b + 1 = c / d + 1

( a + b ) / b = ( c + d ) / d 

hence proved.

Proof of dividendo rule

If a / b = c / d , then ( a - b ) / b = ( c - d ) / d

proof: 

subtracting 1 from both side , we get

a / b - 1 = c / d - 1 

( a - b ) / b = ( c - d ) / d 

hence proved.

Proof of Componendo and Dividendo

if a / b = c / d , then ( a + b ) / ( a  - b ) = ( c + d ) / ( c - d ) 

proof : 

Taking L. H . S, we get ( a + b ) / ( a - b ) = ( a / b + 1 ) / ( a / b - 1 ) = ( c / d + 1 ) / ( c / d - 1 ) 

                                                                      = ( c + d ) / ( c - d ) 

            Hence proved.

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Gunjan From Fergusson College, added an answer, on 26/2/11
166 helpful votes in Math

 plzzzzzzzzzzzzz thumbs up

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Gunjan From Fergusson College, added an answer, on 26/2/11
166 helpful votes in Math

 plzzzzzzzz thumbs up 

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EXPERT ANSWER

Priyanka Kedia , Meritnation Expert added an answer, on 2/4/15

This conversation is already closed by Expert

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nats.arora... , added an answer, on 15/11/12
1 helpful votes in Math

 its all copy paste from wikipedia. we can go on it u knw

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Shubham Kumar , added an answer, on 26/3/14

thanks

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Kenny Singh From Vidhya Bharti English School, added an answer, on 21/2/13

 according to divindo and componendo rule

a/b=c/d converts into a+b/a-b=c+d/c-d

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Pradeep Chauhan From Kendriya Vidyalaya No. 1 Vasco, added an answer, on 27/8/12

 k

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Arshi , added an answer, on 8/9/12
1 helpful votes in Math

ur effort is really appreciable.

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Ghanavi , added an answer, on 3/2/13
1 unhelpful votes in Math

3a + 2x=2a+ 9x

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