Question

Define componendo and dividendo along with their applications in mathematics.

Answer 1

Step I: Definition of componendo and dividendo.

Componendo and dividendo is a rule on ratio and proportions that is used to perform calculations and reduce the number of steps. This rule is generally used to solve equations and fractions.

Step II: Componendo and Dividendo Rule.

In the concept of componendo, the fundamental rule is if $a:b::c:d$ then $(a+b):b::(c+d):d$. It can be observed that it is required to add the denominator to the numerator in the given ratios and then they are equated. If the rule is used on the left side, then it should be used on the right side too.

In the dividendo rule, if $a:b::c:d$ then $(a–b):b::(c–d):d$. It can be observed that it is required to subtract the denominator from the numerator in the given ratios. Everything else is the same as the componendo rule.

In the componendo and dividendo rule, if $a:b::c:d$ then $(a+b):(a–b)::(c+d):(c–d)$. If this rule is applied, then componendo and dividendo are used together.

Also, If $\frac{u}{v}=\frac{x}{y}$, then $\frac{(u+v)}{\left(u-v\right)}=\frac{(x+y)}{\left(x-y\right)}$, which is known as componendo -Dividendo Rule.