Rates, Unit Rates, and Ratios

What are they and how do you solve them?

What are ratios?

A ratio is a comparison of two numbers or measurements. The numbers or measurements being compared are called the terms of the ratio.


Ratios have 3 main forms:

1. N to N

2. N : N

3. N / N


There can be "Part to Part" ratios and "Part to Whole" ratios.




For example, a family could be made up of 2 boys and 3 girls.


These two are examples of "Part to Part" ratios.


The ratio of boys to girls is 2:3, 2/3, or 2 to 3.


The ratio of girls to boys is 3:2, 3/2, or 3 to 2.


These are two examples of "Part to Whole" ratios.


The ratio of boys to the entire family is 2:5, 2/5, or 2 to 5.


The ratio of girls to the entire family is is 3:5, 3/5 or 3 to 5.



You can simplify or increase ratios.



For example, we can use the ratio 3:9.


You can simplify the ratio by dividing both numbers by 3.


If you divide them both by 3, you get 1:3.


You can also increase the ratio by multiplying it by 2, for example.


Then you would get 6:18.

What are rates?

A rate is a special ratio in which the two terms are in different units.


A few examples of rates are:

1. 69¢ for 12 ounces

2. 16 feet per 4 seconds

3. $5.50 for 5 pounds of potatoes

What are unit rates?

Unit rates are basically simplified rates.


Unit rates always have a denominator of 1.


If you wanted to find the unit rate of 16 feet per 4 seconds, you'd divide 16 by 4 and get 4 feet per second.


If you wanted to find out the unit rate of $5.50 for 5 pounds of potatoes, you would divide 5.50 by 5. The unit rate would be $1.10 per pound of potatoes.