## 22.4 Working with formulas

In science and in many other fields of work, we need to be able to work with formulas. For example, if you know the area of a square and need to find its side length, you can rearrange the formula to make the side length the subject of the formula. In other words, you solve the equation for the variable that you need.

The formula for the area of a square is:

\[A = s^{2}\]where \(A\) is the area of the square and \(s\) is the side of the square.

We need to solve this equation for \(s\). To find \(s\), we use the inverse operation, which is the square root:

\[\begin{align} \sqrt{A} &= \sqrt{s^{2}} \\ &= s \\ \therefore s &= \sqrt{A} \end{align}\]So if the area of a square is \(25 \text{ cm}^2\), then the side length is \(s = \sqrt{25} = 5 \text{ cm}\).

## Worked Example 22.4 Working with formulas

Use this equation to find a formula for \(a\).

\[F = ma\]We need to rearrange the given equation in order to have just \(a\) on its own.

### Use inverse operations to rearrange the equation.

Divide both sides by \(m\).

\[\frac{F}{m} = \frac{ma}{m}\]### Simplify.

\[\frac{F}{m} = a\]### Switch the two sides around.

\[a = \frac{F}{m}\]You now have a formula that you can solve to find values for \(a\).

## Worked Example 22.5 Working with formulas

Find a formula for \(V\).

\[C = \frac{n}{V}\]We need to rearrange the given equation in order to have \(V\) on its own.

### Use inverse operations to rearrange the equation.

Multiply both sides by \(V\) and simplify.

\[\begin{align} CV &= \left( \frac{n}{V} \right)V \\ &= n \end{align}\]### Divide both sides by \(C\) and simplify.

\[\begin{align} \frac{CV}{C} &= \frac{n}{C} \\ V &= \frac{n}{C} \end{align}\]You now have a formula for \(V\).