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Calculating Unit Rates Associated with Ratios of Fractions

Instructor: Lynne Hampson

Lynne Hampson has a Masters in Instr. Design & Bach. in Elem./Spec. Educ. She taught 8 years in Elem. Core, Science, Coding, Microsoft, Internet Safety, and Life Skills.

This lesson demonstrates a few different ways to calculate unit rates. We use them to solve problem such as how many beats per minute, or how many miles per hour. To master this lesson, you must understand how ratios and fractions will help to find the unit rate based off of a higher ratio of values.

Unit Rate Vocabulary

Ratios compare two or more types of objects in a group by their value.

For example, if Tom had a bundle of fruit with 4 strawberries and 8 bananas, and he was asked to show how many strawberries there were as compared to bananas, he would use this ratio:

For every 4 strawberries, there are 8 bananas.

This is also expressed in number form, 4:8 (four to eight), or it can be expressed as a fraction, 4/8.

Fractions are a part of a whole, whether it is a whole number, or a whole pizza, it is a whole of something.

To say something is in a fraction, is to say that it is broken up, or no longer one piece or group. We express fractions in numbers such as this: 1/2.

The bottom number of the fraction 1/2 is the denominator. The 2 means the whole object is broken into 2 parts. Together, those two parts would make a whole.

The top number of the fraction 1/2 is the numerator. The 1 means you now only have, or are concerned with 1 out of those 2 parts.

A unit rate consists of one unit, since the word unit actually means one.

We use unit rates to decide how much of something it would take to go into one thing. We use words like 'per' or 'in' when we speak of unit rates.

For example: If a person were to go on a bike trip, and rode 6 miles 'per' hour to get to their destination, then the unit rate would be 1 hour. For every 1 hour, they can go 6 miles.

Why Calculate Unit Rates?

When calculating a unit rate, you are trying to find how many of something it would take to fit into one unit. We use ratios of fractions to solve for the problem. Reminder: You will see the word 'per' a lot when you are solving for unit rates.

A few examples would be money per hour, breathes per minute, miles per gallon, miles per hour, and minutes per hour.

Problem Solving with Unit Rates

Let's use this example below to show how to calculate unit rate with ratios of fractions.

Word Problem:

Andy took a new job in Boston. Andy was told he would make $80.00 per 8 hours of work. How much will Andy make per hour?

Step One - Make a ratio out of the problem. We know that for every $80 dollars Andy gets paid, he works 8 hours.

So that looks like this: $80:8 ($80 to 8 hours)

Step Two - Turn the ratio into a fraction. Take the numbers we see in the ratio. Put the first number on top, as the numerator, and put the second number on the bottom, as the denominator. $80/8

Step Three - Realize that we are solving to find 1 unit, which, in this case, is one hour. To solve, we set the problem up to look like this: $80/8 = /1.

The number on the bottom stands for the one unit rate we are trying to find. The blank number on the top will be our answer. It will tell us how much Andy will make per hour.

Step Four - Look at the two bottom numbers of the fraction. We have 8, and we have 1. Since we are trying to find the one unit, we need to reduce 8 down to 1. We reduce fractions by dividing. So, what number can we divide by 8 to equal 1?

We could also ask the question, what times one equals 8, since division is the opposite of multiplication. In either scenario, the answer is 8. 1 x 8= 8, or 8/8= 1.

Step Five - Now that we divided on the bottom part of the fraction, you must divide by 8 on the top of the same fraction. This keeps the ratio or fraction balanced. The top number is $80. If I divide by 8, I get $10.

Final Answer:

$80/8 = $10/1, which means if I had received $80 dollars for every 8 hours per work. I would make $10 dollars per hour.

Another Way to Find the Answer

Let's use the same problem, and do quick division to find the answer.

Andy took a new job in Boston. Andy was told he would make $80.00 per 8 hours of work. How much will Andy make in one hour?

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