Using Proportions and Cross-Multiplication
Ratios are a powerful tool in science and math. But in order to take full advantage of
them, we have to do more than just calculate ratiosâ€”we have to put them to work! For
example, if you have three bacteria specimens for every student in your class, you know
that you will have a ratio of 3 to 1,
, or 3:1. But this ratio does not tell you the total
number of specimens. To find that, you need to use a proportion.
A proportion is a statement of equality between two ratios. This means that the
ratios are equal. It also means that the numerator of one ratio multiplied by the
denominator of the other ratio is equal to the product of the other numerator and
denominator. An example looks like this:
Notice that you are multiplying across the equal sign in your proportion. This process is
called cross-multiplication. Cross-multiplication is useful because if you know three of the
quantities in a proportion, you can find the fourth.
PROCEDURE: To find an unknown quantity in a proportion, set up the numbers
you know in equal ratios. Leave the place for the quantity you do not know
empty for now. Then cross-multiply the known numerator of one ratio with the
known denominator of the other. Then divide this product by your remaining
known quantity. The quotient is your answer.
SAMPLE PROBLEM: Find the missing number in this proportion:
Step 1: Cross-multiply the known numerator of one ratio with the known
denominator of the other ratio.
Step 2: Divide this product with your remaining known quantity.
The missing number in the proportion is 25;