Study Mathematics notes on Changing the subject of the formula for Secondary. Useful for revision, homework, and exam preparation in Zimbabwe.
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Changing the subject of the formula
What do we mean by changing the subject of the formula ?
Consider the formula for the circumference of a circle.
\[
C=\pi d
\]
If we are given the diameter then we can use this formula to calculate the circumference.
However, if we are given the circumference, and need to calculate the diameter, then it would make more sense to have a formula of the form:
\[
d=\ldots \ldots .
\]
We will look at how we can change around formulae, to make using them easier.
Terminology
In the formula
The variable on the left, is known as the subject: What you are trying to find.
The formula on the right, is the rule, that tells you how to calculate the subject.
So, if you want to have a formula or rule that lets you calculate $d$, you need to make $d$, the subject of the formula.
This is changing the subject of the formula from $C$ to $d$.
So clearly in the case above where
\[
C=\pi d
\]
We get $C$ by multiplying $\pi$ by the diameter
To calculate $d$, we need to divide the Circumference $C$ by $\pi$
So
\[
d=\frac{C}{\pi}
\]
and now we have $d$ as the subject of the formula.