Rates and Ratios

Working with rates and ratios can sometimes be confusing because these terms are often regarded as having the same meaning. In actuality, these two terms are referring to a similar concept, but have different applications. A ratio is a comparison of two numbers or measurements, while a rate is a special kind of ratio in which the two things being compared have different units. Rates are often used when dealing with word problems and real life examples. In order to better understand these concepts and their applications, let’s look at a couple examples.

Ratios

First, let’s look at how to correctly write a ratio when comparing two different numbers:

 

Now, let’s take a look at a real world situation in which we would need to use a ratio. For example, assume you are having a slumber party with your friends and want to make cupcakes. The cupcake recipe calls for 4 cups of flour and 1 cup of sugar, but if we wanted to double that recipe we could use a ratio to figure out how much of each ingredient we would need.

Rates

When dealing with rates, you are now dealing with a situation where there are two different units of measurement. A lot of problems will ask for the unit rate, which is the rate when the second term is equal to 1. The most common rate has to do with distance per time. Let’s look at an example where we find the unit rate:

 

As you can see, rates and ratios have very similar applications and methods of solving; however, ratios have the same unit of measure, while rates have different units of measure. With practice, your child will get better at determining the differences between these two terms and being able to quickly solve these types of equations. Be sure to help your child master rates and ratios because they have many real world applications and will be used in every day life.

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