Changing subject of equation

For example, amount of substance $n$ is measured in moles (mol), mass $m$ in grams (g), and molar mass $M$ in grams per mole (g mol⁻¹). They are related by

$n=\frac{m}{M}$

OCR also writes this relationship as ‘number of moles = mass of substance ÷ relative formula mass’. The molar mass has the same numerical value as the relative formula mass, but its units are g mol⁻¹.

Keep both sides equal

Think of an equation as a balance: if you change one side, you must make the same change to the other. To make $m$ the subject of $n=m/M$, undo the division by $M$ by multiplying both sides by $M$:

$nM=\frac{m}{M}\times M$

The $M$ on the right cancels, giving

$m=nM$

This form lets you find a mass when you know the amount in moles and the molar mass. Its units check: mol × g mol⁻¹ = g.

When the subject is below the fraction line

Suppose instead that you know $m$ and $n$ and need $M$. Start again from $n=m/M$. First multiply both sides by $M$, giving $nM=m$. Then divide both sides by $n$:

$M=\frac{m}{n}$

Dividing g by mol gives g mol⁻¹, as expected for molar mass. The important method is to reverse the operations acting on the variable, one at a time, while preserving the equality. It works for other mathematical equations used in chemistry too.