8.1.10 Which Percent is It?

You probably agree that comparing percentages can be easier than comparing fractions. When we have a certain quantity, how do we write it as a percent of another, usually larger, number?

For example, if 42 people out of a group of 70 people agree to participate in a new community project, what percentage of the group is this?

Whenever you have a part of a group and the whole of the entire group, you can calculate percent by setting up the ratio of “part over whole.” You can then turn this fraction successfully into a percentage.

So in this case, turn 42 divided by 70 into a percent, first by multiplying by 100% and then by reducing by 10 and then by 7:

42 divided by 70 multiplication 100 percent equation left hand side equals right hand side 42 divided by 70 sub seven multiplication 100 super 10 divided by one percent equation left hand side equals right hand side 42 super six divided by seven sub one multiplication 10 divided by one percent equation sequence equals six multiplication 10 divided by one multiplication one equals 60 percent

(Note: You also could have reduced 42 divided by 70 to three divided by five first and then turned it into a percent.)

These calculations show us that 60% of the group agree to participate in the community project.

As you know, the calculation 42 division 70 multiplication 100 can be performed even quicker with a calculator, as can the other percent calculations.

Summary

To express one number as a percentage of another, divide the first number by the second and convert the result into percent by multiplying by 100%.

8.1.11 Calculator Exploration: Using Percentages