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What is componendo and dividendo, how do we apply this in different fields of mathematics?

What is componendo and dividendo, how do we apply this in different fields of mathematics?

Grade:11

2 Answers

Himanshu
103 Points
4 years ago
Componendo and dividendo are just a part of the mathematics calculation.
Componendo and dividendo are greek words. According to it,
If a/b = c/d , then (a+b) / (a-b) = (c+d) / (c-d).
Let me give you proof for the above statement.
Add 1 to both sides of the equation i.e., a/b + 1 = c/d + 1
(a+b) / b = (c+d) / d                      ….i)
Now, Subtract 1 from both sides of the equation i.e., a/b - 1 = c/d - 1
(a-b) / b = (c-d) / d                        ….ii)
Dividing eq. i) by ii). We get,
(a+b) / (a-b) = (c+d) / (c-d)
We use componendo and dividendo just to speed up the calculation part of the mathematics.
 
Kartik pandey
21 Points
3 years ago
If a/b=c/d then we can say that a:b=c:d=k(universally recognised as costant).If a/b=c/d then a+b/a-b=c+d/c-d.By tranfering b on the other side we can say that a=kb,c=kd.A.T.Q kb+b/kb-b=kd+d/kd-dLets take LHS first:Lets take b common now we can say that b(k+1)/b(k-1) cancel out b fron numerator and denominator we obtain (k+1)/(k-1)RHS:kd+d/kd-d take d as common we can say that d(k+1)/d(k-1) .Cancel out d fron both numerator and denominator we obtain (k+1)/(k-1).LHS = (k+1)/(k-1)= RHS =(k+1)/(k-1).We conclude that LHS=RHS QED.

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