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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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.

**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.

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.

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.

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?

The word per also tells me I can divide to find the answer, so if I take $80 dollars, and divide it by 8, what do I get?

$80 divided by 8 = _____ or remember you can multiply too, 8 times _____ = $80

If you guessed $10, then you now know how to calculate unit rates.

We drove the car 200 miles in 8 hours to the coast. I wonder how many miles that was per hour?

Let's figure it out:

Step One - Make a ratio... 200 miles:8 hours, or 200:8, or (200 miles for every 8 hours)

Step Two - Change it to a fraction... 200:8 is the same as 200/8

Step Three - Compare it to 1 unit rate... 200/8 = / 1

Step Four - Reduce the denominators to equal 1... 8/8 = 1

Step Five- Whatever number is divided in the denominator, must also be used to divide the numerator... 200/8 = 25

Final Answer:

200/8 = 25/1, which means if I had driven 200 miles in 8 hours. I would only go 25 miles in 1 hour.

To help remember how to calculate **unit rates**, you must first understand a **ratio**, which is a comparison in value of two or more objects. Once the ratio is discovered, turning it into a fraction will help you to set up the problem.

Remember, when solving for a unit, you are solving to find one, since unit means one. Use the **fraction** created by the ratio, and set it up beside a fraction with the number one as the denominator.

Finally, divide the denominator on the left by a number that will equal 1 to match the denominator of the fraction on the right.

Whatever number you divided the denominator by, you must use to divide out of the numerator on the left. The answer to that division problem will tell how much of something fits into one unit.

If you follow these steps, you will understand how to calculate unit rates.

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Ratios & Rates: Definitions & Examples 6:37
- How to Find the Unit Rate 3:57
- How to Solve a One-Step Problem Involving Ratios 4:32
- How to Solve a One-Step Problem Involving Rates 5:06
- How to Solve Problems with Money 8:29
- Proportion: Definition, Application & Examples 6:05
- Calculations with Ratios and Proportions 5:35
- How to Solve Problems with Time 6:18
- Distance Formulas: Calculations & Examples 6:31
- How to Find an Unknown in a Proportion
- Calculating Unit Rates Associated with Ratios of Fractions
- Identifying the Constant of Proportionality 6:10
- Representing Proportional Relationships by Equations
- Graphing Proportional Relationships
- Proportional Relationships in Multistep Ratio & Percent Problems
- Constructing Proportions to Solve Real World Problems
- Go to 6th-8th Grade Math: Rates, Ratios & Proportions

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