# 3.3.2: Multiply or Divide to Convert between Customary Units of Length, Weight, and Capacity

- Page ID
- 8744

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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 by Multiplying

Michaela is planning a party. She buys 5 pounds of shrimp for 10 people. She guesses that each person will eat about 7 ounces of shrimp. Will Michaela have enough shrimp for everyone?

In this concept, you will convert customary units of measure using multiplication.

**Converting Customary Units by Multiplying**

When converting customary units of measure from a larger unit to a smaller unit, multiply the the larger unit by its smaller **equivalent** unit. You may already be wondering why you need to multiply as opposed to some other operation. Here is an example to demonstrate this.

1 dollar = 100 pennies

There are 100 pennies in one dollar. The dollar is a larger unit than the penny. You need many pennies to equal one dollar. The same is true when working with units of **length**, **weight** and **capacity**. You need more of a smaller unit to equal a larger unit.

Think back to all of the units of length* ,* weight and capacity that you have previously learned about.

Here are some equivalence tables.

#### Customary Units of Length

inch (in.) |
foot (ft) |
yard (yd) |
mile (mi) |

12 | 1 | ||

3 | 1 | ||

1,760 | 1 |

#### Customary Units of Weight

ounces (oz) |
pounds (lb) |
tons (T) |

16 | 1 | |

2,000 | 1 |

#### Customary Units of Capacity

fluid ounces (fl oz) |
cups (c) |
pints (pt) |
quarts (qt) |
gallon (gal) |

8 | 1 | |||

16 | 2 | 1 | ||

32 | 4 | 2 | 1 | |

128 | 16 | 8 | 4 |
1 |

Let's look at a conversion problem.

John has a rope that is 10 feet long. How long is his rope in inches?

Notice, you are converting from feet to inches. A foot is a larger unit than an inch.

10 feet = _____ inches

To solve this problem, multiply the number of feet by the unit equivalence. This will give you the measurement in inches.

1 foot = 12 inches

10 × 12 = 120

The answer is 10 feet is equivalent to 120 inches.

**Examples**

Example 3.3.2.1

Earlier, you were given a problem about Michaela and her party.

Michaela has 5 pounds of shrimp and is wondering if she will have enough for 10 people if each person eats 7 ounces of shrimp. Convert the 5 pounds to ounces to see if Michaela will have enough for everyone.

**Solution**

5 pounds = _____ ounces

First, check if she will multiply or divide. A pound is larger than an ounce. Multiply when converting a larger unit to a smaller unit.

Then, find the unit equivalence.

1 pound = 16 ounces

Next, multiply the number of pounds by the unit equivalence.

5 × 16 = 80

5 pounds = 80 ounces

If 10 people eat 7 ounces of shrimp each, then Michaela will need at least 70 ounces of shrimp. Michaela will have enough shrimp for the party.

Example 3.3.2.2

Convert the unit of measure: Jason’s baby brother drank 3 cups of milk. How many fluid ounces did he drink?

**Solution**

Once again, you are going from a larger unit to a smaller unit.

3 cups = _____ fl oz

Multiply the number of cups by the unit equivalence.

1 cup = 8 fl oz.

3 × 8 = 24

The answer is 3 cups is equivalent to 24 fluid ounces.

Convert the following units of measure.

Example 3.3.2.3

Convert the following unit of measure: 4 tons = ____ pounds.

**Solution**

Multiply the number of tons by the unit equivalence.

1 ton = 2,000 pounds.

4 × 2,000 = 8,000

The answer is 4 tons is equivalent to 8,000 pounds

Example 3.3.2.4

Convert the following unit of measure: 5 feet = ____ inches.

**Solution**

Multiply the number of feet by the unit equivalence.

1 foot = 12 inches

5 × 12 = 60

The answer is 5 feet is equivalent to 60 inches

Example 3.3.2.5

Convert the following unit of measure: 8 pints = ____ cups.

**Solution**

Multiply the number of tons by the unit equivalence.

1 pint = 2 cups

8 × 2 = 16

The answer is 8 pints is equivalent to 16 cups.

**Review**

Convert the following units of measure.

- 5 tons = ____ pounds
- 6 feet = ____ inches
- 9 tons = ____ pounds
- 8 pounds = ____ ounces
- 2.5 feet = ____ inches
- 3.5 tons = ____ pounds
- 2.25 pounds = ____ ounces
- 9 cups = ____ fl oz
- 5 pints = ____ cups
- 7 pints = ____ cups
- 8 quarts = ____ pints
- 1 quart = ____ pints
- 6 gallons = ____ quarts
- 7.75 gallons = ____ quarts
- 8 miles = _____ feet
- 3 feet = _____ inches
- 12 miles = _____ feet

### Review (Answers)

To see the Review answers, open this PDF file and look for section 7.16.

### Vocabulary

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

Capacity |
The volume of liquid an object or item can hold. Customary units of capacity include fluid ounces, cups, pints, quarts and gallons. |

Equivalent |
Equivalent means equal in value or meaning. |

Length |
Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles. |

Weight |
Weight is a measurement of the heaviness or mass of someone or something. The customary units of weight included ounces, pounds, and tons. |

### Additional Resources

Video:

PLIX Interactive: **The Price of a Unit**

Practice: **Multiply or Divide to Convert between Customary Units of **(...)