Ratios, Rates, Unit Rates

A ratio is a comparison of two numbers. Ratios are used often in everyday life to compare amounts of different things. In sports, you might hear someone talk about the win to loss record of a team, or the baseball pitcher’s win to loss record, or a quarterback’s ratio of completed passes to total attempts. In architecture and art, the golden ratio is the “perfect” relationship of the length and width of a rectangle. In cooking a cake, there is a certain ratio of the amount of sugar to the amount of flour that is used.

There are several ways to write a ratio. In a classroom, if there are 2 boys and 4 girls, the ratio of boys to girls can be written as 2 to 4, or 2:4, or 2/4. You would read all of these as “two to four”. Notice that, in the expression “boys to girls“, “boys” is first. It is very important to know which one comes first. The number of the first one must be written first, or in the numerator, of the ratio. If the problem was written as “girls to boys”, the ratio would use the number of girls first, like 4:2 or 4/2.


To compare two ratios, write them as fractions and reduce the fractions to lowest terms. If the fractions are the same, the ratios are equal. If one ratio is 6/8 and the other is 12/16, you would need to reduce both fractions, using the Greatest Common Factor (GCF) 4, to see that they are both equal to 3/4. To reduce a fraction to lowest terms, the numerator and denominator must be divided by the Greatest Common Factor.

A rate is a ratio.   A ratio is a comparison of two numbers.   A ratio can be expressed three ways:

  1. Using the fraction bar as in 2/3.
  2. Using a colon symbol as in 2:3 .
  3. Using the word “to” as in 2 to 3.

Write 1/2 and 4 to 5 each in two different ways.

Answers (lesson 11)

When the denominator of a rate is 1, we call the rate a unit rate. We usually use the key word “per” or the division symbol ( /) to indicate a unit rate. For example: If a student earns $7.65 per hour, it is the same as $7.65 per hour or $7.65/hour.   This means $7.65 for every hour of work.   Unit rates can also be used to solve problems.

Watch the video to see an example. Whenever there is an example problem being solved, you should write it down and solve it too so that you get the practice.

Here’s another example.