Video Transcript

Rates are an important type of ratio because they often measure something important. Unit rates are particularly important because you can use a unit rate to measure any value based on that rate.

In this video we look at unit rates and how they can be used to solve problems.

Let's look at an example.

Three pounds of bananas cost $2.25. Find the unit rate for the cost of bananas.

Use the unit rate to find what the cost of 10 pounds of bananas would be.

We know what three pounds of bananas cost, but how do we determine how much one pound costs? For that we need a unit ratio.

A unit ratio is simply a ratio when, in fraction form, has a denominator of 1. And the simplest way to get to a unit rate is to divide numerator by the denominator.

Take the ratio 2.25/3 and divide 2.25 by 3. We get 0.75 dollars/pound. In other words, the unit rate is 75 cents a pound.

With this unit rate, we can calculate the cost for any amount. So the cost of 10 pounds of bananas is 10 times the unit rate or 10 times 0.75 dollars/pound, for a total of $7.50.

Unit rates are an important part of our everyday use of mathematics. Let's look at another example.

A barista earned $150 for a 7 1/2-hour shift. What was the hourly rate, expressed as a unit rate?

How much does the barista earn in a 40-hour work week?

Take the numerical ratio 150/7.5 to find the unit rate. Also, make a note of the units, dollars/hour.

We get a unit rate of $20/hour.

For 40 hours, we multiply $20/hr times 40 hours.

So, the barista earns $800 in a 40-hour week.

Notice when multiplying $20/hr times 40 hours, the hours units cancel out and you’re left with dollars.

We can also use unit rates to convert from one type of unit to another. Let's look at an example.

What is the unit conversion rate to convert miles to kilometers?

Use that unit rate to convert 29.5 miles to kilometers.

The unit conversion rate to go from miles to kilometers is 1.60934 kilometers/mile

To convert x miles to kilometers, multiply by this unit rate.

So let's convert 29.5 miles to kilometers:

29.5 miles x 1.60934 kilometers/mile

What we get is 47.47553 kilometers.

Unit conversion rates are used quite a lot. They allow for converting measurement, amounts of money, and many other applications.