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 (...)