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How is a given variable made the subject of the formula ?
A formula is an equation that shows the general relation between two or more variables. If a particular variable appears by itself on the left-hand side of the equation, it is called the subject of the formula.
The statement 'Perimeter (P) of a rectangle equals twice the sum of the length (L) and the breadth (B)' may be expressed by the following formula :
P = 2(L + B)
In the above formula, P is the subject of the formula. In other words, P can be easily calculated when the values of L and B are given.
But, what if the values of P and L are given, and B needs to be calculated?
Then, it is better to change the subject of the formula to B. This is done by following the same method used to solve equations. The basic principle in solving any equation is to do the same thing to both sides of the equation. In other words, the same number may be added to both sides, the same number may be subtracted from both sides, both sides may be multiplied or divided by the same number (except 0), both sides may be squared, or the reciprocal of both sides taken.
Now P = 2(L + B) and to change the subject of the formula to B, the following steps are followed:
P = 2L + 2B on eliminating the parenthesis
P - 2L = 2B on subtracting 2L from both sides of the equation
(P - 2L)/2 = B on dividing both sides of the equation by 2
B = (P - 2L)/2 on interchanging the two sides of the equation.
The final formula in terms of B may also be written as B = P/2 - L.
This could have been directly obtained from P = 2(L + B) by dividing both sides by 2 and then subtracting L from both sides of the equation.
Practice Exercise for Algebra Module on Subject of the Formulae