Units of Capacity
LEARNING outcomes
- Define units of capacity and convert from one to another.
- Perform arithmetic calculations on units of capacity.
- Solve application problems involving units of capacity.
| Fluid Ounce A unit of capacity equal to [latex] \displaystyle \frac{1}{8}[/latex] of a cup. One fluid ounce of water at 62°F weighs about one ounce. The amount of liquid medicine is often measured in fluid ounces. |
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| Cup A unit equal to 8 fluid ounces. The capacity of a standard measuring cup is one cup. |
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| Pint A unit equal to 16 fluid ounces, or 2 cups. The capacity of a carton of ice cream is often measured in pints. |
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| Quart A unit equal to 32 fluid ounces, or 4 cups. You often see quarts of milk being sold in the supermarket. |
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| Gallon A unit equal to 4 quarts, or 128 fluid ounces. When you fill up your car with gasoline, the price of gas is often listed in dollars per gallon. |
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Try It
[ohm_question]18868[/ohm_question]|
Unit Equivalents |
Conversion Factors (heavier to lighter units of measurement) |
Conversion Factors (lighter to heavier units of measurement) |
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1 cup = 8 fluid ounces |
[latex] \displaystyle \frac{\text{1 cup}}{\text{8 fluid ounces}}[/latex] |
[latex] \displaystyle \frac{\text{8 fluid ounces}}{\text{1 cup}}[/latex] |
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1 pint = 2 cups |
[latex] \displaystyle \frac{\text{1 pint}}{2\text{ cups}}[/latex] |
[latex] \displaystyle \frac{2\text{ cups}}{1\text{ pint}}[/latex] |
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1 quart = 2 pints |
[latex] \displaystyle \frac{\text{1 quart}}{2\text{ pints}}[/latex] |
[latex] \displaystyle \frac{2\text{ pints}}{\text{1 quart}}[/latex] |
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1 quart = 4 cups |
[latex] \displaystyle \frac{\text{1 quart}}{4\text{ cups}}[/latex] |
[latex] \displaystyle \frac{4\text{ cups}}{\text{1 quart}}[/latex] |
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1 gallon = 4 quarts |
[latex] \displaystyle \frac{\text{1 gallon}}{4\text{ quarts}}[/latex] |
[latex] \displaystyle \frac{4\text{ quarts}}{\text{1 gallon}}[/latex] |
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1 gallon = 16 cups |
[latex] \displaystyle \frac{1\text{ gallon}}{\text{16 cups}}[/latex] |
[latex] \displaystyle \frac{\text{16 cups}}{1\text{ gallon}}[/latex] |
Converting Between Units of Capacity
As with converting units of length and weight, you can use the factor label method to convert from one unit of capacity to another. An example of this method is shown below.Converting between fractions, mixed numbers, and decimals
The methods to convert between different forms of numbers were explained in detail in previous sections in this module. Here's a quick synopsis. Mixed number to fraction: Multiply the whole number to the denominator, add the numerator and place the result over the denominator. Ex. [latex] 7\dfrac{3}{4} = \dfrac{7\cdot4+3}{4} = \dfrac{31}{4}.[/latex] Fraction to mixed number: Since a fraction is a division problem, the mixed number will be made of the quotient and the remainder over the divisor. Ex. [latex]\dfrac{17}{3}=17\div3=5\dfrac{2}{3}[/latex] Fraction to decimal: Since a fraction is a division problem, divide the numerator by the denominator using a calculator to obtain the fraction's decimal form. Ex. [latex]\dfrac{11}{8}=1.375[/latex] Decimal to mixed number: The whole number part will be the number to the left of the decimal. The fraction part will be the translation of the decimal part to a fraction such as in, [latex]0.7 = \dfrac{7}{10} \text{ , } 0.25 = \dfrac{25}{100}=\dfrac{1}{4} \text{ , and } 0.057 = \dfrac{57}{1000}[/latex]. Ex. [latex]7.25 = 7\dfrac{1}{4} \text{ , } 3.5 = 3\dfrac{1}{2} \text{ , } 1.057 = 1\dfrac{57}{1000} \text{ , etc.}[/latex]Example
How many pints is [latex] \displaystyle 2\frac{3}{4}[/latex] gallons?Answer: Begin by reasoning about your answer. Since a gallon is larger than a pint, expect the answer in pints to be a number greater than [latex] \displaystyle 2\frac{3}{4}[/latex].
[latex]2\frac{3}{4}\text{ gallons}=\text{___ pints}[/latex]
The table above does not contain a conversion factor for gallons and pints, so you cannot convert it in one step. However, you can use quarts as an intermediate unit, as shown here. Set up the equation so that two sets of labels cancel: gallons and quarts.[latex]\frac{11\text{ gallons}}{4}\cdot\frac{4\text{ quarts}}{1\text{ gallon}}\cdot\frac{2\text{ pints}}{1\text{ quart}}=\text{___ pints}[/latex]
[latex]\frac{11\cancel{\text{ gallons}}}{4}\cdot\frac{4\cancel{\text{ quarts}}}{1\cancel{\text{ gallon}}}\cdot\frac{2\text{ pints}}{1\cancel{\text{ quart}}}=\text{___ pints}[/latex]
[latex]\frac{11}{4}\cdot{4}{1}\cdot\frac{2\text{ pints}}{1}=\text{___ pints}[/latex]
Multiply and simplify.[latex]\frac{11\cdot4\cdot2\text{ pints}}{4\cdot1\cdot1}=\text{___ pints}[/latex]
[latex]\frac{88\text{ pints}}{4}=22\text{ pints}[/latex]
[latex] \displaystyle 2\frac{3}{4}[/latex] gallons is 22 pints.Example
How many gallons is 32 fluid ounces?Answer: Begin by reasoning about your answer. Since gallons is a larger unit than fluid ounces, expect the answer to be less than 32.
[latex]32\text{ fluid ounces}=\text{___ gallons}[/latex]
The table above does not contain a conversion factor for gallons and fluid ounces, so you cannot convert it in one step. Use a series of intermediate units, as shown here.[latex]\frac{32\text{ fl oz}}{1}\cdot\frac{1\text{ cup}}{8\text{ fl oz}}\cdot\frac{1\text{ qt}}{2\text{ pt}}\cdot\frac{1\text{ gal}}{4\text{ qt}}=\text{___ gal}[/latex]
Cancel units that appear in both the numerator and denominator.[latex]\frac{32\cancel{\text{ fl oz}}}{1}\cdot\frac{1\cancel{\text{ cup}}}{8\cancel{\text{ fl oz}}}\cdot\frac{1\cancel{\text{ qt}}}{2\cancel{\text{ pt}}}\cdot\frac{1\text{ gal}}{4\cancel{\text{ qt}}}=\text{___ gal}[/latex]
[latex]\frac{32}{1}\cdot\frac{1}{8}\cdot\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1\text{ gal}}{4}=\text{____ gal}[/latex]
Multiply and simplify.[latex]\frac{32\cdot1\cdot1\cdot1\cdot1\text{ gal}}{1\cdot8\cdot2\cdot2\cdot4}=\text{___ gal}[/latex]
[latex] \displaystyle \frac{32\text{ gal}}{\text{128}}=\frac{1}{4}\text{ gal}[/latex]
32 fluid ounces is the same as [latex]\frac{1}{4}[/latex] gallon.Try It
Find the sum of 4 gallons and 2 pints. Express your answer in cups.Answer: 4 gallons + 2 pints = 64 cups + 4 cups = 68 cups
[ohm_question]989-23258[/ohm_question]Applying Unit Conversions
There are times when you will need to combine measurements that are given in different units. In order to do this, you need to convert first so that the units are the same. Consider the situation posed earlier in this topic.Exercises
Sven and Johanna were hosting a potluck dinner. They did not ask their guests to tell them what they would be bringing, and three people ended up bringing soup. Erin brought 1 quart, Richard brought 3 pints, and LeVar brought 9 cups. How much soup did they have total?Answer: Since the problem asks for the total amount of soup, you must add the three quantities. Before adding, you must convert the quantities to the same unit. The problem does not require a particular unit, so you can choose. Cups might be the easiest computation.
[latex]1\text{ quart}+3\text{ pints}+9\text{ cups}[/latex]
This is given in the table of equivalents.[latex]1\text{ quart}=4\text{ cups}[/latex]
Use the factor label method to convert pints to cups.[latex]\frac{3\text{ pints}}{1}\cdot\frac{2\text{ cups}}{1\text{ pint}}=\text{___ cups}[/latex]
[latex]\frac{3\cancel{\text{ pints}}}{1}\cdot\frac{2\text{ cups}}{1\cancel{\text{ pint}}}=\text{6 cups}[/latex]
Add the 3 quantities.[latex]4\text{ cups}+6\text{ cups}+9\text{ cups}=19\text{ cups}[/latex]
There are 19 cups of soup for the dinner.Exercises
Natasha is making lemonade to bring to the beach. She has two containers. One holds one gallon and the other holds 2 quarts. If she fills both containers, how many cups of lemonade will she have?Answer: This problem requires you to find the sum of the capacity of each container and then convert that sum to cups.
[latex]1\text{ gallon}+2\text{ quarts}=\text{___ cups}[/latex]
First, find the sum in quarts. 1 gallon is equal to 4 quarts.[latex]4\text{ quarts}+2\text{ quarts}=6\text{ quarts}[/latex]
Since the problem asks for the capacity in cups, convert 6 quarts to cups. Cancel units that appear in both the numerator and denominator. Multiply.[latex]\frac{6\text{ quarts}}{1}\cdot\frac{2\text{ pints}}{1\text{ quart}}\cdot\frac{2\text{ cups}}{1\text{ pint}}=\text{____ cups}[/latex]
[latex]\frac{6\cancel{\text{ quarts}}}{1}\cdot\frac{2\cancel{\text{ pints}}}{1\cancel{\text{ quart}}}\cdot\frac{2\text{ cups}}{1\cancel{\text{ pint}}}=\text{____ cups}[/latex]
[latex]6\times2\times2=24\text{ cups}[/latex]
Natasha will have 24 cups of lemonade.Try It
Alan is making chili. He is using a recipe that makes 24 cups of chili. He has a 5-quart pot and a 2-gallon pot and is trying to determine whether the chili will all fit in one of these pots. Which of the pots will fit the chili?Answer: The chili will only fit in the 2 gallon pot
Summary
There are five basic units for measuring capacity in the U.S. customary measurement system. These are the fluid ounce, cup, pint, quart, and gallon. These measurement units are related to one another, and capacity can be described using any of the units. Typically, people use gallons to describe larger quantities and fluid ounces, cups, pints, or quarts to describe smaller quantities. Often, in order to compare or to solve problems involving the amount of liquid in a container, you need to convert from one unit of measurement to another.Licenses & Attributions
CC licensed content, Original
- Question ID 126635, 126782. Authored by: Day, Alyson. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.
- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- Question ID 989, 18868. Authored by: Lippman, David. License: CC BY: Attribution. License terms: iMathAS Community License CC-BY + GPL.
- Unit Conversion Application - Number of Lemons for a Lemon Pie. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
- American Unit Conversion . Authored by: James Sousa (Mathispower4u.com) . License: CC BY: Attribution.
