# 3.3.1: Conversion between Customary Units of Length, Weight, and Capacity

- Page ID
- 8743

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)## Conversion of Customary Units of Measurement

Leslie is trying to decide which yogurt to buy at the grocery store. There are two yogurts she is considering. The first kind of yogurt is in a 2 pound container and costs $6. The second kind of yogurt is in a 6 ounce container and is being sold in packs of 5 for $6. She sees that both options cost $6 so she figures she should choose whichever option will give her more yogurt. How can Leslie figure out which option will give her more yogurt?

In this concept, you will learn how to convert and compare customary units of measure.

### Converting Customary Units of Measure

The ** customary system of measurement** is the system of measurement primarily used in the United States. The tables below show some of the most common U.S. customary units and how they are related.

inch (in) |

foot (ft) = 12 inches |

yard (yd) = 3 feet |

mile (mi) = 5,280 feet |

ounce (oz) |

pound (lb) = 16 ounces |

fluid ounce (oz) |

cup (c) = 8 ounces |

pint (pt) = 2 cups = 16 ounces |

quart (qt) = 4 cups = 2 pints = 32 ounces |

gallon (gal) = 4 quarts |

teaspoon (tsp) |

tablespoon (tbsp) = 3 teaspoons |

cup (c) = 16 tablespoons |

To move between different U.S. customary units of length, mass, and capacity, you will multiply or divide by a conversion factor.

- Any time you are going from a smaller unit of measure to a larger unit of measure you will need to divide by the conversion factor.
- Any time you are going from a larger unit of measure to a smaller unit of measure you will need to multiply by the conversion factor.

Here is an example.

Convert 374 inches to feet.

First, notice that inches are smaller than feet. You are moving from a smaller unit of measure to a larger unit of measure. This means you will need to divide. There are 12 inches in a foot, so your conversion factor is 12.

Now, divide. Take the given number of inches and divide by 12.

374÷12=374/12=187/6=31(1/6)

The answer is 374 inches=31(1/6) feet.

Once you know how to convert between different units of measurements, you can compare measurements. The best way to compare two measurements is to first make sure they are in the same unit. Then, you can more easily see which measurement is larger and which is smaller.

Let's look at an example.

Compare 4(1/2) pounds and 74 ounces.

First, notice that you have two different units of mass. In order to compare these measurements, convert one of them so that both units are the same. Let's convert 4(1/2) pounds to ounces.

Now, when converting pounds to ounces you are moving from a larger unit of measure to a smaller unit of measure. This means you will need to multiply. There are 16 ounces in a pound, so your conversion factor is 16.

Next, multiply. Take the given number of pounds and multiply by 16.

4(1/2)×16=(9/2)×(16/1)=144/2=72

4(1/2) pounds=72 ounces

Now you are looking to compare 72 ounces and 74 ounces. 72 ounces is less than 74 ounces, so 4(1/2) pounds is less than 74 ounces.

The answer is 4(1/2) pounds<74 ounces.

### Examples

Example 3.3.1.1

Earlier, you were given a problem about Leslie, who is trying to buy yogurt.

She has two options. Her first option is a 2 pound container. Her second option is five 6-ounce containers. Both options will cost her $6. She wants to choose the option that will give her more yogurt.

**Solution**

First Leslie should realize that five 6-ounce containers is 30 ounces of yogurt. Leslie needs to compare 2 pounds and 30 ounces. Since Leslie has two different units of mass, in order to compare these measurements she should convert one of them so that both units are the same. She can convert pounds to ounces.

Now, when converting pounds to ounces she is moving from a larger unit of measure to a smaller unit of measure. This means she will need to multiply. There are 16 ounces in a pound, so her conversion factor is 16.

Next, she should multiply. Take the given number of pounds and multiply by 16.

2×16=32

2 pounds=32 ounces

Now Leslie is looking to compare 32 ounces and 30 ounces. 32 ounces is more than 30 ounces, so 2 pounds is greater than 30 ounces.

The answer is Leslie should buy the 2 pound container of yogurt.

Example 3.3.1.2

Henrietta is having her 7 best friends over for a luncheon. She wants to prepare salads in which she uses exactly 7 tablespoons of Romano cheese. If she is preparing 8 salads, how many cups of Romano cheese does Henrietta require?

**Solution**

First, figure out how many tablespoons of Romano cheese Henrietta will need. She is making 8 salads and each salad requires 7 tablespoons of cheese.

8×7=56

Henrietta will need 56 tablespoons of Romano cheese.

Now, convert 56 tablespoons to cups. You are moving from a smaller unit of measure to a larger unit of measure. This means you will need to divide. There are 16 tablespoons in a cup, so your conversion factor is 16.

Now, divide.

56÷16=3(1/2)

The answer is Henrietta will need 3(1/2) cups of Romano cheese.

Example 3.3.1.3

Convert 82 pints to quarts.

**Solution**

First, notice that pints are smaller than quarts. You are moving from a smaller unit of measure to a larger unit of measure. This means you will need to divide. There are 2 pints in a quart, so your conversion factor is 2.

Now, divide. Take the given number of pints and divide by 2.

82÷2=41

The answer is 82 pints=41 quarts.

Example 3.3.1.4

Compare 80 ounces and 3 quarts.

**Solution**

First, notice that you have two different units of capacity. In order to compare these measurements, convert one of them so that both units are the same. Let's convert 3 quarts to ounces.

Now, when converting quarts to ounces you are moving from a larger unit of measure to a smaller unit of measure. This means you will need to multiply. There are 32 ounces in a quart, so your conversion factor is 32.

Next, multiply. Take the given number of quarts and multiply by 32.

3×32=96

3 quarts=96 ounces

Now you are looking to compare 80 ounces and 96 ounces. 80 ounces is less than 96 ounces, so 80 ounces is less than 3 quarts.

The answer is 80 ounces<3 quarts.

Example 3.3.1.5

Convert 8(1/2) gallons to quarts.

**Solution**

Convert 8(1/2) gallons to quarts.

First, notice that gallons are larger than quarts. You are moving from a larger unit of measure to a smaller unit of measure. This means you will need to multiply. There are 4 quarts in a gallon, so your conversion factor is 4.

Now, multiply. Take the given number of gallons and multiply by 4.

8(1/2)×4=(17/2)×(4/1)=68/2=34

The answer is 8(1/2) gallons=34 quarts.

### Review

Convert the following measurements into yards. Round to the nearest tenth when necessary.

- 195 inches
- 0.2 miles
- 88 feet
- 90 feet
- 900 feet

Convert the following measurements into pounds.

- 2,104 ounces
- 96 ounces
- 3 tons
- 15 tons

Convert the following measurements into pints.

- 102 quarts
- 57 ounces
- 9.5 gallons
- 4 quarts
- 18 quarts
- 67 gallons

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.21.

### Vocabulary

Term | Definition |
---|---|

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

Metric System |
The metric system is a system of measurement commonly used outside of the United States. It contains units such as meters, liters, and grams, all in multiples of ten. |

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”. |

### Additional Resources

PLIX Interactive: **United States Customary Units: Gelato Pint**

Video:

Practice: **Conversion between Customary Units of Length, Weight, and **(...)

Real World Application: **You Can Cook**