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Often, it plays a key role in solving the problems quickly. In this session we will show how Componendo dividendo plays a key role in solving hard algebra problems in only a few steps. We will use three examples. After a recap we will start problem solving. If you are familiar with the concept, you may skip the recap section. Componendo dividendoâ€”What it is and Why it is powerful Componendo dividendo is powerful because, It simplifies an apparently complex expression greatly and quickly. Because of the special form of expression on which Componendo dividendo can be applied, it is easy to identify where it can be applied, It is easy to understand and use in application.

It is just a three-step simple method, Due to its simplicity, the three step process can be done in mind and so we can consider the ability to apply Componendo dividendo under mental math skills. At the basic level, Componendo dividendo is applied in two ways. We will explain with examples. This is a standard form of expression where immediate application of Componendo dividendo will give you the answer in a few seconds without need to write any calculation steps on paper.

We can arrive at the same result and verify whether our result is correct by conventional method of cross-multiplication. In this form, at the second step, you need to subtract the two sides of the equation from 1, instead of subtracting 1 from two sides of the equation.

If it is in the numerator, you need to subtract the two sides of the equation from 1 at the second step, so that the resultant numerator stays positive. Instead of a single variable, the expression to be simplified can appear in two variables.

Let us consider the third general form. In this case we have one equation and two variables. At most we may get the ratio. That is the simplest result we usually need under the circumstances.

Step 1. Step 3. Even in this simple form, Componendo dividendo is the preferred and quicker way to reach the result for us. To show how this highly popular three-step simple method can help to solve relatively more complex problems quickly, we will use three problem examples from Algebra.

Problem example 1.

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## Componendo dividendo explained

Often it plays a key role in solving the problem quickly. Componendo dividendo is powerful because, It simplifies an apparently complex expression greatly. Because of the special form of expression on which Componendo dividendo can be applied, it is easy to identify where it can be applied, It is easy to understand and use in application. It is just a three-step simple method, Due to its simplicity, the three step process can be done in mind and so we can consider the ability to apply Componendo dividendo under mental math skills. At the basic level, Componendo dividendo is applied in two ways. We will explain with examples.

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## Componendo and Dividendo Rule

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## Componendo dividendo in Algebra

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