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# Conversion of Customary Units of Measurement

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

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Convert Customary Units of Measurement

Karen is making cookies for a school fundraiser. The recipe she uses calls for 20 ounces of liquid. How many cups does this represent?

In this concept, you will learn to convert customary units of measurement.

### Customary and Metric Systems

In the United States, you often use the customary system of measurement. The customary system is made up of units such as inches, feet, cups, gallons and pounds and is often referred to as Imperial measure.

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

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

#### Customary Units of Measurement

Now let’s look at how you convert among customary units of measurement. Because there is a relationship between different units of measure, you can use proportions to help you convert between customary units of measurement.

Let’s look at an example.

How many feet are in 5 yards?

First, set up a proportion.

1 yard3 feet=5 yardx feet\begin{align*}\frac{1 \text{ yard}}{3 \text{ feet}} = \frac{5 \text{ yard}}{x \text{ feet}}\end{align*}

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

131xx===5x3×515\begin{align*}\begin{array}{rcl} \frac{1}{3} &=& \frac{5}{x} \\ 1x &=& 3 \times 5 \\ x &=& 15 \end{array}\end{align*}

Therefore, 5 yards is equal to 15 feet.

Here is another example.

How many ounces are there in 20 pounds?

First, set up a proportion.

1 pound6 ounces=20 poundsx ounces\begin{align*}\frac{1 \text{ pound}}{6 \text{ ounces}} = \frac{20 \text{ pounds}}{x \text{ ounces}}\end{align*}

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

1161xx===20x16×20320\begin{align*}\begin{array}{rcl} \frac{1}{16} &=& \frac{20}{x} \\ 1x &=& 16 \times 20 \\ x &=& 320 \end{array}\end{align*}

Therefore, 20 pounds is equal to 320 ounces.

### Examples

#### Example 1

Earlier, you were given a problem about Karen’s cooking measurements.

Karen needs to convert 20 ounces into cups.

First, set up a proportion.

1 cup8 ounces=x cups20 ounces\begin{align*}\frac{1 \text{ cup}}{8 \text{ ounces}} = \frac{x \text{ cups}}{20 \text{ ounces}}\end{align*}

Next, cross multiply.

\begin{align*}\begin{array}{rcl} \frac{1}{8} &=& \frac{x}{20} \\ 8x &=& 1 \times 20 \\ 8x &=& 20 \end{array}\end{align*}

Then, cross multiply to solve for \begin{align*}x\end{align*}.

\begin{align*}\begin{array}{rcl} 8x &=& 20 \\ \frac{8x}{8} &=& \frac{20}{8} \\ x &=& 2.5 \\ \end{array}\end{align*}

Therefore, 20 ounces is equal to 2.5 cups.

#### Example 2

Eight pints is equal to how many gallons?

Set up a proportion to convert pints to gallons.

\begin{align*}\frac{1 \text{ gallon}}{4 \text{ quarts}} \times \frac{1 \text{ quart}}{2 \text{ pints}} = \frac{1 \text{ gallon}}{8 \text{ pints}}\end{align*}

Therefore, 8 pints is equal to 1 gallon.

#### Example 3

Convert 6 tons to pounds.

First, set up a proportion.

\begin{align*}\frac{1 \text{ ton}}{2000 \text{ pounds}} = \frac{6 \text{ tons}}{x \text{ pounds}}\end{align*}

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

\begin{align*}\begin{array}{rcl} \frac{1}{2000} &=& \frac{6}{x} \\ 1x &=& 6 \times 2000 \\ x &=& 12000 \end{array}\end{align*}

Therefore, 6 tons is equal to 12,000 pounds.

#### Example 4

Convert 3 yards to feet.

First, set up a proportion.

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

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

\begin{align*}\begin{array}{rcl} \frac{1}{3} &=& \frac{3}{x} \\ 1x &=& 3 \times 3 \\ x &=& 9 \end{array}\end{align*}

Therefore, 3 yards is equal to 9 feet.

#### Example 5

Convert 18 gallons to quarts.

First, set up a proportion.

\begin{align*}\frac{1 \text{ gallon}}{4 \text{ quarts}} = \frac{18 \text{ gallons}}{x \text{ quarts}}\end{align*}

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

\begin{align*}\begin{array}{rcl} \frac{1}{4} &=& \frac{18}{x} \\ 1x &=& 4 \times 18 \\ x &=& 72 \end{array}\end{align*}

Therefore, 18 gallons is equal to 72 quarts.

### Review

Solve each problem by converting among customary units of measurement.

1. \begin{align*}102 \text{ inches} = \underline{\;\;\;\;\;\;\;} \text{ feet}\end{align*}
2. \begin{align*}25 \ \text{pounds} = \underline{\;\;\;\;\;\;\;} \ \text{ounces}\end{align*}
3.  \begin{align*}160 \ \text{cups} = \underline{\;\;\;\;\;\;\;}\ \text{gallons}\end{align*}
4.  \begin{align*}150 \ \text{pounds} = \underline{\;\;\;\;\;\;\;} \ \text{tons}\end{align*}
5.  \begin{align*}6 \ \text{feet} = \underline{\;\;\;\;\;\;\;} \ \text{inches}\end{align*}
6.  \begin{align*}360 \ \text{inches} = \underline{\;\;\;\;\;\;\;} \ \text{feet}\end{align*}
7.  \begin{align*}5.5 \ \text{feet} = \underline{\;\;\;\;\;\;\;} \ \text{inches}\end{align*}
8.  \begin{align*}900 \ \text{inches} = \underline{\;\;\;\;\;\;\;} \ \text{feet}\end{align*}
9.  \begin{align*}32 \ \text{ounces} = \underline{\;\;\;\;\;\;\;} \ \text{pounds}\end{align*}
10.  \begin{align*}320 \ \text{ounces} = \underline{\;\;\;\;\;\;\;} \ \text{pounds}\end{align*}
11.  \begin{align*}6 \ \text{pounds} = \underline{\;\;\;\;\;\;\;} \ \text{ounces}\end{align*}
12.  \begin{align*}15 \ \text{pounds} = \underline{\;\;\;\;\;\;\;} \ \text{ounces}\end{align*}
13.  \begin{align*}6 \ \text{cups} = \underline{\;\;\;\;\;\;\;} \ \text{pints}\end{align*}
14.  \begin{align*}3 \ \text{gallons} = \underline{\;\;\;\;\;\;\;} \ \text{quarts}\end{align*}
15.  \begin{align*}8 \ \text{quarts} = \underline{\;\;\;\;\;\;\;} \ \text{pints}\end{align*}
16.  \begin{align*}24 \ \text{pints} = \underline{\;\;\;\;\;\;\;} \ \text{quarts}\end{align*}

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### Vocabulary Language: English

Customary System

The customary system is the measurement system commonly used in the United States, including: feet, inches, pounds, cups, gallons, etc.

Proportion

A proportion is an equation that shows two equivalent ratios.

Ratio

A ratio is a comparison of two quantities that can be written in fraction form, with a colon or with the word “to”.