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# Conversion of Customary Units of Measurement

## Convert between customary units for length, mass and volume.

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MCC6.RP.3d - Customary Units of Measurement

“You keep telling me that Mount Everest is 29,035 feet high, but how many miles is that?” Teiyisha asked Josh during geography class.

“Well, you don’t need to know the miles because you are climbing it. Doesn’t it make more sense to measure it in feet?” Josh asked while working on his map.

“It might, but if I wanted to know how many miles, how could I figure this out?” Teiyisha asked.

Josh thought about it for a minute.

“You would have to do a conversion. You would have to change feet to miles, and we can do that if we know how many feet are in 1 mile. It still makes more sense to use feet though. Think about it, you can’t exactly draw a straight line up Mount Everest. Miles would be very hard to measure.”

“I get that, but I still want to know how many miles high it is,” Teiyisha explained.

“Alright, first let’s think about miles and feet. There are 5,280 feet in 1 mile.”

Let’s stop there. To accomplish Teiyisha’s task, we will need to create a proportion and convert feet to miles. We can do this by converting among customary units of measurement. Pay attention to this Concept and you will have it figured out by the end.

### Guidance

When we measure in the United States, we often use the customary system of measurement.

The customary system is made up of units such as inches, feet, cups, gallons and pounds.

You may have also heard of the Metric System of measurement. The metric system is often used in countries outside of the United States or in science measurements. Here, you will learn how to convert between different customary units of measurement.

But first, let’s look at some of the units in the customary system of measurement.

Customary Units of Measurement

Take a few minutes to copy all of these units of measurement down in your notebook.

Now let’s look at how we convert among customary units of measurement.

While you may be able to complete some of the mathematics in your head, it may make more sense to use a proportion. Because there is a relationship between different units of measure, you can use proportions to help you convert between customary units of measurement.

First, set up the proportion in the same way you used to find actual measurements from scale drawings. Use the conversion factor as the first ratio, and the known and unknown units in the second ratio.

How many feet are in 5 yards?

Set up a proportion.

The conversion factor is the number of feet in 1 yard: 3 feet1 yard\begin{align*}\frac{3 \ feet}{1 \ yard}\end{align*}.

Now write the second ratio.

The known unit is 5 yards. The unknown unit is x\begin{align*}x\end{align*} feet. Make sure that the second ratio follows the form of the first ratio: feet over yards.

3 feet1 yard=x feet5 yards\begin{align*}\frac{3 \ feet}{1 \ yard}=\frac{x \ feet}{5 \ yards}\end{align*}

Next cross-multiply to solve for x\begin{align*}x\end{align*}.

(1)xx=3(5)=15\begin{align*}(1)x &= 3(5)\\ x &= 15\end{align*}

There are 15 feet in 5 yards.

Here is another one.

How many ounces are there is 20 pounds?

First, set up a proportion.

The scale of measurement is 1 pound16 ounces\begin{align*}\frac{1 \ pound}{16 \ ounces}\end{align*}.

The proportion is: 116=20x\begin{align*}\frac{1}{16}= \frac{20}{x}\end{align*}

Next, we cross multiply and solve for the number of ounces.

There are 320 ounces in 20 pounds.

Convert among customary units of measurement.

#### Example A

Convert 6 tons to pounds

Solution: 12,000 pounds

#### Example B

Convert 3 yards to feet

Solution: 9 feet

#### Example C

Convert 18 gallons to quarts.

Solution: 72 quarts

Now let's go back to the dilemma from the beginning of the Concept.

First, we need to write a proportion to convert feet to miles. We know that there are 5,280 feet in 1 mile. This is the first part of the proportion. The second part of the proportion contains the unknown miles in a variable and the number of feet in Everest.

52801=29035x\begin{align*}\frac{5280}{1}=\frac{29035}{x}\end{align*}

Next, we cross multiply and divide to solve for the variable.

5280xx=29035=5.5 miles\begin{align*}5280x &= 29035\\ x &= 5.5 \ miles\end{align*}This is our answer.

### Vocabulary

Customary System
the system of measurement that includes inches, feet, miles, pounds, tons, cups, quarts, gallons, etc.

### Guided Practice

Here is one for you to try on your own.

Eight pints is equal to how many gallons?

Solution

To figure this out, we can first convert pints to quarts.

Two pintsEight pints=1 quart=4 quarts\begin{align*}\text{Two pints} &= 1~\text{quart} \\ \text{Eight pints} &= 4~\text{quarts}\end{align*}

There are 4 quarts in 1 gallon, so eight pints equals 1 gallon.

8 pints=1 gallon\begin{align*}8~\text{pints} = 1~\text{gallon}\end{align*}

### Practice

Directions: Solve each problem by converting among customary units of measurement.

1. 102 inches = ______ feet
2. 25 pounds = ______ ounces
3. 160 cups = ______ gallons
4. 150 pounds = ______ tons
5. 6 feet = ______ inches
6. 360 inches = ______ feet
7. 5.5 feet = ______ inches
8. 900 inches = ______ feet
9. 32 ounces = ______ pounds
10. 320 ounces = ______ pounds
11. 6 pounds = ______ ounces
12. 15 pounds = ______ ounces
13. 6 cups = ______ pints
14. 3 gallons = ______ quarts
15. 8 quarts = ______ pints
16. 24 pints = ______ quarts

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