Sometimes we are interested in percentages of an amount other than 100 or 1. For example, what is 30% of 50 pounds? We can use a double number line diagram to solve problems about percentages.

Because we are looking for a percentage of 50 pounds, 100% is aligned to 50 pounds on the double number line diagram, like this:

We divide the distance between 0% and 100% and that between 0 and 50 pounds into ten equal parts. The tick marks on the top line can be labeled by counting by 5s ($50\div10=5$). Those on the bottom line can be labeled by counting by 10% ($100\div10=10$). We can see that 30% of 50 pounds is 15 pounds.

Double number line diagrams can also help us find the value of 100% when we know the value of another percentage.

Suppose Mai read for 90 minutes on Monday and this was 125% as much time as she spent reading on Sunday. How long did she read on Sunday?

In this case, the value we’re looking for is 100% of the number of reading minutes on Sunday. On a double number line diagram, we can align 90 minutes and 125%. Then, we can divide the interval between 0 and 90 and between 0 and 125% into five equal parts.

Each part on the top line represents 18 minutes ($90\div 5=18$) and each part on the bottom line represents 25% ($125 \div 5 = 25$).

From the diagram, we can see that 72 minutes corresponds to 100%, so Mai read for 72 minutes on Sunday.