CAN YOU EXPLAIN IN DEATAIL ABOUT COMPONENDO AND DIVIDENDO RULE AND INVERTENDO RULE WITH  EXAMPLES IN SOLVING QUESTIONS?

Asked by abinash.gupta003 | 11th May, 2017, 03:25: PM

Expert Answer:

begin mathsize 16px style Componendo colon
If space straight a over straight b equals straight c over straight d
Applying space componendo space means space Adding space denominator space to space numertor space and space denominator space unchanged
rightwards double arrow fraction numerator straight a plus straight b over denominator straight b end fraction equals fraction numerator straight c plus straight d over denominator straight d end fraction
Dividendo colon
If space straight a over straight b equals straight c over straight d
Applying space dividendo space means space Subtracting space denominator space from space numertorand space denominator space unchanged
rightwards double arrow fraction numerator straight a minus straight b over denominator straight b end fraction equals fraction numerator straight c minus straight d over denominator straight d end fraction
Componendo minus Dividendo colon
If space straight a over straight b equals straight c over straight d
Applying space componendo minus dividendo space means
fraction numerator straight a plus straight b over denominator straight a minus straight b end fraction equals fraction numerator straight c plus straight d over denominator straight c minus straight d end fraction

Alternendo colon
If space straight a over straight b equals straight c over straight d
Applying space alternendo space means space cross space multiplication
rightwards double arrow straight a cross times straight d equals straight b cross times straight c

Example colon
If space fraction numerator 8 straight a minus 5 straight b over denominator 8 straight c minus 5 straight d end fraction equals fraction numerator 8 straight a plus 5 straight b over denominator 8 straight c plus 5 straight d end fraction comma space prove space that space straight a over straight b equals straight c over straight d
Solution colon
Given comma fraction numerator 8 straight a minus 5 straight b over denominator 8 straight c minus 5 straight d end fraction equals fraction numerator 8 straight a plus 5 straight b over denominator 8 straight c plus 5 straight d end fraction
rightwards double arrow fraction numerator 8 straight a minus 5 straight b over denominator 8 straight a plus 5 straight b end fraction equals fraction numerator 8 straight c minus 5 straight d over denominator 8 straight c plus 5 straight d end fraction space space space space space space space space space left parenthesis Applying space alternendo right parenthesis
rightwards double arrow fraction numerator 8 straight a minus 5 straight b plus 8 straight a plus 5 straight b over denominator 8 straight a minus 5 straight b minus 8 straight a minus 5 straight b end fraction equals fraction numerator 8 straight c minus 5 straight d plus 8 straight c plus 5 straight d over denominator 8 straight c minus 5 straight d minus 8 straight c minus 5 straight d end fraction space space space space space space space space space left parenthesis Applying space componendo minus dividendo right parenthesis
rightwards double arrow fraction numerator 16 straight a over denominator negative 10 straight b end fraction equals fraction numerator 16 straight c over denominator negative 10 straight d end fraction
rightwards double arrow straight a over straight b equals straight c over straight d
end style

Answered by Rashmi Khot | 12th May, 2017, 09:45: AM