Question

please describe me about compodendo and dividendo​

Answer 1

Componendo Dividendo

• Comonendo Dividendendo is a theorem used for proportion to solve the problems easily

• If a/d = c/d then ( a + b) / ( a - b) = ( c + d) /( a - d)

Given :

a/b = c/d

To prove :

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

Proof :

a/b = c/d

Adding 1 on both sides

=> a/b + 1 = c/d + 1

=> ( a + b ) / b = ( c + d ) / d --- Eq( 1 )

a/b = c/d

Subtracting 1 on both sides

=> a/b - 1 = c/d - 1

=> ( a - b ) / b = ( c - d ) / d --- Eq( 2)

Dividing Eq( 1 ) by Eq( 2 )

=> ( a + b) / b ÷ ( a - b ) / b = ( c + d) / d ÷ ( c - d) / d

=> ( a + b ) / b × b / ( a - b) = ( c + d) / d × d / ( c - d)

=> ( a + b ) / ( a - b ) = ( c + d ) / ( c - d )

Hence proved

Answer 2

Answer:

Componendo and Dividendo is a theorem on proportions that allows for a quick way to perform calculations and reduce the number of expansions needed. It is particularly useful when dealing with equations involving fractions or rational functions in mathematical Olympiads, especially when you see fractions.

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