### 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: \begin{align*}\frac{3 \ feet}{1 \ yard}\end{align*}.

**Now write the second ratio.**

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

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

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

\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 \begin{align*}\frac{1 \ pound}{16 \ ounces}\end{align*}.

The proportion is: \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.**

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

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

\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.

\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.

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

**This is our answer.**

### Video Review

### Practice

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

- 102 inches = ______ feet
- 25 pounds = ______ ounces
- 160 cups = ______ gallons
- 150 pounds = ______ tons
- 6 feet = ______ inches
- 360 inches = ______ feet
- 5.5 feet = ______ inches
- 900 inches = ______ feet
- 32 ounces = ______ pounds
- 320 ounces = ______ pounds
- 6 pounds = ______ ounces
- 15 pounds = ______ ounces
- 6 cups = ______ pints
- 3 gallons = ______ quarts
- 8 quarts = ______ pints
- 24 pints = ______ quarts