Question

$\huge\pink\bigstar{question :}$ EXPLAIN DIVIDENDO & COMPONENDO $\huge{No.spam}$​

Answer 1

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.

Hence, if the ratio of any two numbers is equal to the ratio of another two numbers, then the ratio of the sum of numerator and denominetor to the difference of numerator and denomenetor of both rational numbers.

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Answer 2

Componendo :-

It is a type of a property of proportion .

Here if,

⇒ a : b : : c : d

which implies,

⇒ a/b = c/d

Here the given proportional can be written as,

⇒ (a + b) : b : : (c + d) : d

which implies,

⇒ (a + b)/b = (c + d)/d

The above relationship is termed as " componendo ".

Now , let's take an example of componendo of property for better understanding,

If,

⇒ 2 : 5 : : 6 : 15

which implies,

⇒ 2/5 = 6/15

Now by the componendo property we have,

⇒ (2 + 5) : 5 : : (6 + 15) : 15

which implies,

⇒ (2 + 5)/5 = (6 + 15)/15

⇒ 7/5 = 21/15

⇒ 1.4 = 1.4

Dividendo :-

It is a type of a property of proportion .

Here if,

⇒ a : b : : c : d

which implies,

⇒ a/b = c/d

Here the given proportional can be written as,

⇒ (a - b) : b : : (c - d) : d

which implies,

⇒ (a - b)/b = (c - d)/d

The above relationship is termed as " Dividendo ".

Now , let's take an example of componendo of property for better understanding,

If,

⇒ 2 : 5 : : 6 : 15

which implies,

⇒ 2/5 = 6/15

Now by the dividendo property we have,

⇒ (2 - 5) : 5 : : (6 - 15) : 15

which implies,

⇒ (2 - 5)/5 = (6 - 15)/15

⇒ -3/5 = -9/15

⇒ -0.6 = -0.6