Solving a Proportion

A proportion is a statement that two ratios are equal, like $\frac{3}{5} = \frac{9}{15}$. When one of the four numbers is missing, the proportion tells you what it must be. Take $\frac{n}{4} = \frac{21}{28}$.

Look for the pair of matching numbers you know completely: here the two bottoms, 4 and 28. 28 is 4 times 7, so the right ratio is the left one scaled up by 7. Going from the right side back to the left divides by 7, so divide the top as well: 21 divided by 7 is 3, and $n = 3$.

The scale factor can come from the bottoms or the tops, whichever pair is complete, and it may be a multiplication or a division depending on which side the missing number sits. Check your claim by simplifying: $\frac{3}{4}$ and $\frac{21}{28}$ are the same ratio.