# How to Perform Basic Operations with Measurements

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• 0:02 Measurements Are Like…
• 3:05 Subtracting Measurements
• 4:29 Multiplying Measurements
• 6:45 Dividing Measurements
• 8:04 Lesson Summary

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will learn how measurements are very much like variables when it comes to adding, subtracting, multiplying, and dividing them. You will also see examples of how they are done.

## Measurements Are Like Variables

In this video lesson, we are going to talk about performing operations such as adding and multiplying, on measurements. Why is this important? It is important because in real life many problems deal with measurements where you will need to perform these operations to get your answer.

For example, restaurant owners need to add and subtract measurements to find out how many tables and chairs will fit inside their restaurant. They need to add the length and width of the tables and chairs together to make sure there is enough room for them.

When you need to perform your basic operations on your measurements, treat them like variables, a symbol for something we don't know. As we go in this video lesson, we will see how to subtract, add, multiply, and divide our measurements. You will see that it is a lot like adding, subtracting, multiplying, and dividing variables. So, let's get going.

We first talk about adding measurements. So, say you are a restaurant owner. You want to put two tables together to create a longer table. But, you need to add the lengths of the tables to make sure that you have enough room in your restaurant to do this. One table measures 3 feet and the other table measures 4 feet. How do you add them together?

First, we see that both measurements are in feet, so that tells us that we can go ahead with our addition without any changes. We can go ahead and add 3 feet and 4 feet together. What do we get? We get 7 feet.

Notice that I still have my measurement unit of feet attached to my number 7. If we thought about this as adding variables, we can change our feet to x. Our problem then becomes 3x + 4x.

Because both terms have an x as the variable, they are like terms so we can go ahead and add to get 7x. We can switch out the x for feet again and we would have our answer of 7 feet as well.

We just talked about adding when our measurement units are the same. But what do we do when our measurement units are similar, but not exactly the same? For example, what if one table measured 3 feet and the other table measured 36 inches? What would we do then?

Well, we see that our measurement units are not the same so that tells us that we can't go ahead with addition. But we see that we can convert our measurement units. We need our measurement units to be the same before adding. We see that one measurement is in feet and the other is in inches. We can go about it two ways. We can either change our feet measurement into inches or our inches measurement into feet.

I'm going to change our inches measurement into feet. How do you choose? If you are doing multiple choice problems, pick the unit that is in the answers. To change the inches measurement into feet, we need to use what we know about converting measurements. We know that there are 12 inches in a foot. So, I can divide my inches measurement by 12 to convert it into feet. Doing that, I get 36 inches / 12 = 3 feet. So, now I have 3 feet + 3 feet. My measurement units are the same so I can go ahead with the addition to get 6 feet.

## Subtracting Measurements

We also need to make sure our measurement units are the same when subtracting. If they are the same, we can go ahead with our subtraction. If they are not, then we need to convert the measurement so that the measurement units are the same.

For example, say you, as the restaurant owner, wanted to install a fish tank inside your restaurant. The fish tank measures 7 feet in length. The space where you want to install the fish tank is 10 feet in length. Will the fish tank fit? We can find out by subtracting the length of the fish tank from the length of the restaurant space.

We see that both measurement units are the same so we can go ahead with our subtraction of 10 feet - 7 feet. What do we get? We get 3 feet. That means that you will have 3 extra feet and the fish tank will fit. Turning this into a variable problem, we have 10x - 7x, which equals 3x, or 3 feet.

Again, if our measurement units are different, we need to convert them so that they are the same before proceeding. So, if our fish tank measured 120 inches and our restaurant space measured 10 feet, we need to either convert the 120 inches into feet or the 10 feet into inches.

This time we are going to convert the feet into inches. To do this, I multiply my 10 feet by 12 to get 120 inches. Hey, look at that. The measurements are exactly the same and 120 - 120 is 0. That means the fish tank just fits!

## Multiplying Measurements

Now that you've got the fish tank covered, it's time to look at the floor covering. Your floor looks pretty bad. Customers would probably get grossed out looking at it. So, you decide to tile your restaurant floor.

You call a flooring company and the company asks you how many square feet of tile you need for your restaurant. What they are asking you is the area of your restaurant. To find your area, you need to multiply the length of your restaurant by its width since your restaurant is a rectangle. Your restaurant measures 7 feet 6 inches in width and 10 feet in length. So, we need to multiply these two numbers together.

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