{"id":622,"date":"2016-11-30T21:55:00","date_gmt":"2016-11-30T21:55:00","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&p=622"},"modified":"2021-02-05T23:48:13","modified_gmt":"2021-02-05T23:48:13","slug":"units-of-capacity","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/units-of-capacity\/","title":{"raw":"Units of Capacity","rendered":"Units of Capacity"},"content":{"raw":"
\r\n

LEARNING outcomes<\/h3>\r\n
\r\n
    \r\n \t
  • Define units of capacity and convert from one to another.<\/li>\r\n \t
  • Perform arithmetic calculations on units of capacity.<\/li>\r\n \t
  • Solve application problems involving units of capacity.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\nCapacity<\/b> is the amount of liquid (or other pourable substance) that an object can hold when it's full. When a liquid, such as milk, is being described in gallons or quarts, this is a measure of capacity.\r\n\r\nUnderstanding units of capacity can help you solve problems like this: 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 many cups of soup did they have all together?\r\n\r\nThere are five main units for measuring capacity in the U.S. customary measurement system. The smallest unit of measurement is a fluid ounce<\/b>. The word\u00a0ounce<\/em>\u00a0is also used as a measure of weight, so it is important to use the word fluid<\/em> with ounce<\/em> when you are talking about capacity. Sometimes the prefix fluid<\/em>\u00a0is not used when it is clear from the context that the measurement is capacity, not weight.\r\n\r\nThe other units of capacity in the customary system are the cup<\/b>, pint<\/b>, quart<\/b>, and gallon<\/b>. The table below describes each unit of capacity and provides an example to illustrate the size of the unit of measurement.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Fluid Ounce\u00a0\u00a0<\/b>A unit of capacity equal to [latex] \\displaystyle \\frac{1}{8}[\/latex] of a cup. One fluid ounce of water at 62\u00b0F weighs about one ounce. The amount of liquid medicine is often measured in fluid ounces.<\/td>\r\n\r\n

    \"Pipette<\/b><\/p>\r\n<\/td>\r\n<\/tr>\r\n

    Cup\u00a0\u00a0<\/b>A unit equal to 8 fluid ounces. The capacity of a standard measuring cup is one cup.<\/td>\r\n\r\n

    \"A<\/p>\r\n<\/td>\r\n<\/tr>\r\n

    Pint\u00a0\u00a0<\/b>A unit equal to 16 fluid ounces, or 2 cups. The capacity of a carton of ice cream is often measured in pints.<\/td>\r\n\r\n

    \"A<\/p>\r\n<\/td>\r\n<\/tr>\r\n

    Quart\u00a0\u00a0<\/b>A unit equal to 32 fluid ounces, or 4 cups. You often see quarts of milk being sold in the supermarket.<\/td>\r\n\r\n

    \"A<\/p>\r\n<\/td>\r\n<\/tr>\r\n

    Gallon\u00a0\u00a0<\/b>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.<\/td>\r\n\r\n

    \"A<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nYou can use any of these five measurement units to describe the capacity of an object, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the capacity of a swimming pool in gallons and the capacity of an expensive perfume in fluid ounces.\r\n

    \r\n

    Try It<\/h3>\r\n[ohm_question]18868[\/ohm_question]\r\n\r\n<\/div>\r\nSometimes you will need to convert between units of measurement. For example, you might want to express 5 gallons of lemonade in cups if you are trying to determine how many 8-fluid ounce servings the amount of lemonade would yield.\r\n\r\nThe table below shows some of the most common equivalents and conversion factors for the five customary units of measurement of capacity.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \r\n

    Unit Equivalents<\/b><\/p>\r\n<\/td>\r\n

    		\r\n

    Conversion Factors (heavier to lighter units of measurement)<\/b><\/p>\r\n<\/td>\r\n

    		\r\n

    Conversion Factors<\/b><\/p>\r\n

    (lighter to heavier units of measurement)<\/b><\/p>\r\n<\/td>\r\n<\/tr>\r\n

    \r\n

    1 cup = 8 fluid ounces<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{\\text{1 cup}}{\\text{8 fluid ounces}}[\/latex]<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{\\text{8 fluid ounces}}{\\text{1 cup}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

    \r\n

    1 pint = 2 cups<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{\\text{1 pint}}{2\\text{ cups}}[\/latex]<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{2\\text{ cups}}{1\\text{ pint}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

    \r\n

    1 quart = 2 pints<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{\\text{1 quart}}{2\\text{ pints}}[\/latex]<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{2\\text{ pints}}{\\text{1 quart}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

    \r\n

    1 quart = 4 cups<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{\\text{1 quart}}{4\\text{ cups}}[\/latex]<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{4\\text{ cups}}{\\text{1 quart}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

    \r\n

    1 gallon = 4 quarts<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{\\text{1 gallon}}{4\\text{ quarts}}[\/latex]<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{4\\text{ quarts}}{\\text{1 gallon}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n

    \r\n

    1 gallon = 16 cups<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{1\\text{ gallon}}{\\text{16 cups}}[\/latex]<\/p>\r\n<\/td>\r\n

    		\r\n

    [latex] \\displaystyle \\frac{\\text{16 cups}}{1\\text{ gallon}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Converting Between Units of Capacity<\/h2>\r\nAs 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.\r\n
    \r\n

    Converting between fractions, mixed numbers, and decimals<\/h3>\r\nThe methods to convert between different forms of numbers were explained in detail in previous sections in this module. Here's a quick synopsis.\r\n\r\nMixed number to fraction<\/strong>: Multiply the whole number to the denominator, add the numerator and place the result over the denominator.\r\n\r\nEx. [latex] 7\\dfrac{3}{4} = \\dfrac{7\\cdot4+3}{4} = \\dfrac{31}{4}.[\/latex]\r\n\r\nFraction to mixed number<\/strong>: Since a fraction is a division problem, the mixed number will be made of the quotient and the remainder over the divisor.\r\n\r\nEx. [latex]\\dfrac{17}{3}=17\\div3=5\\dfrac{2}{3}[\/latex]\r\n\r\nFraction to decimal<\/strong>: Since a fraction is a division problem, divide the numerator by the denominator using a calculator to obtain the fraction's decimal form.\r\n\r\nEx. [latex]\\dfrac{11}{8}=1.375[\/latex]\r\n\r\nDecimal to mixed number<\/strong>: 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].\r\n\r\nEx. [latex]7.25 = 7\\dfrac{1}{4} \\text{ , } 3.5 = 3\\dfrac{1}{2} \\text{ , } 1.057 = 1\\dfrac{57}{1000} \\text{ , etc.}[\/latex]\r\n\r\n<\/div>\r\n \r\n
    \r\n

    Example<\/h3>\r\nHow many pints is [latex] \\displaystyle 2\\frac{3}{4}[\/latex] gallons?\r\n[reveal-answer q=\"442206\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"442206\"]\r\n\r\nBegin 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].\r\n

    [latex]2\\frac{3}{4}\\text{ gallons}=\\text{___ pints}[\/latex]<\/p>\r\nThe 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.\r\n\r\nSet up the equation so that two sets of labels cancel: gallons and quarts.\r\n

    [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]<\/p>\r\n

    [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]<\/p>\r\n

    \u00a0[latex]\\frac{11}{4}\\cdot{4}{1}\\cdot\\frac{2\\text{ pints}}{1}=\\text{___ pints}[\/latex]<\/p>\r\nMultiply and simplify.\r\n

    [latex]\\frac{11\\cdot4\\cdot2\\text{ pints}}{4\\cdot1\\cdot1}=\\text{___ pints}[\/latex]<\/p>\r\n

    [latex]\\frac{88\\text{ pints}}{4}=22\\text{ pints}[\/latex]<\/p>\r\n[latex] \\displaystyle 2\\frac{3}{4}[\/latex] gallons is 22 pints.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n

    \r\n

    Example<\/h3>\r\nHow many gallons is 32 fluid ounces?\r\n[reveal-answer q=\"49180\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"49180\"]\r\n\r\nBegin by reasoning about your answer. Since gallons is a larger unit than fluid ounces, expect the answer to be less than 32.\r\n

    [latex]32\\text{ fluid ounces}=\\text{___ gallons}[\/latex]<\/p>\r\nThe 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.\r\n

    [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]<\/p>\r\nCancel units that appear in both the numerator and denominator.\r\n

    [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]<\/p>\r\n

    [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]<\/p>\r\nMultiply and simplify.\r\n

    [latex]\\frac{32\\cdot1\\cdot1\\cdot1\\cdot1\\text{ gal}}{1\\cdot8\\cdot2\\cdot2\\cdot4}=\\text{___ gal}[\/latex]<\/p>\r\n

    [latex] \\displaystyle \\frac{32\\text{ gal}}{\\text{128}}=\\frac{1}{4}\\text{ gal}[\/latex]<\/p>\r\n32 fluid ounces is the same as [latex]\\frac{1}{4}[\/latex] gallon.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n

    \r\n

    Try It<\/h3>\r\nFind the sum of 4 gallons and 2 pints. Express your answer in cups.\r\n[reveal-answer q=\"69640\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"69640\"]4 gallons + 2 pints = 64 cups + 4 cups = 68 cups[\/hidden-answer]\r\n\r\n[ohm_question]989-23258[\/ohm_question]\r\n\r\n<\/div>\r\n

    Applying Unit Conversions<\/h2>\r\nThere 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.\r\n\r\nConsider the situation posed earlier in this topic.\r\n
    \r\n

    Exercises<\/h3>\r\nSven 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?[reveal-answer q=\"749363\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"749363\"]\r\n\r\nSince 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.\r\n\r\nThe problem does not require a particular unit, so you can choose. Cups might be the easiest computation.\r\n

    [latex]1\\text{ quart}+3\\text{ pints}+9\\text{ cups}[\/latex]<\/p>\r\nThis is given in the table of equivalents.\r\n

    [latex]1\\text{ quart}=4\\text{ cups}[\/latex]<\/p>\r\nUse the factor label method to convert pints to cups.\r\n

    [latex]\\frac{3\\text{ pints}}{1}\\cdot\\frac{2\\text{ cups}}{1\\text{ pint}}=\\text{___ cups}[\/latex]<\/p>\r\n

    [latex]\\frac{3\\cancel{\\text{ pints}}}{1}\\cdot\\frac{2\\text{ cups}}{1\\cancel{\\text{ pint}}}=\\text{6 cups}[\/latex]<\/p>\r\n \r\n\r\nAdd the 3 quantities.\r\n

    [latex]4\\text{ cups}+6\\text{ cups}+9\\text{ cups}=19\\text{ cups}[\/latex]<\/p>\r\nThere are 19 cups of soup for the dinner.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n

    \r\n

    Exercises<\/h3>\r\nNatasha 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?\r\n[reveal-answer q=\"50819\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"50819\"]\r\n\r\nThis problem requires you to find the sum of the capacity of each container and then convert that sum to cups.\r\n

    [latex]1\\text{ gallon}+2\\text{ quarts}=\\text{___ cups}[\/latex]<\/p>\r\nFirst, find the sum in quarts. 1 gallon is equal to 4 quarts.\r\n

    [latex]4\\text{ quarts}+2\\text{ quarts}=6\\text{ quarts}[\/latex]<\/p>\r\nSince the problem asks for the capacity in cups, convert 6 quarts to cups.\r\n\r\nCancel units that appear in both the numerator and denominator.\r\n\r\nMultiply.\r\n

    [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]<\/p>\r\n

    [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]<\/p>\r\n

    [latex]6\\times2\\times2=24\\text{ cups}[\/latex]<\/p>\r\nNatasha will have 24 cups of lemonade.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nAnother way to work the problem above would be to first change 1 gallon to 16 cups and change 2 quarts to 8 cups. Then add: [latex]16+8=24[\/latex] cups.\r\n\r\nWatch the following video for another example of using unit conversions to solve a problem. \u00a0It shows how to find the number of lemons needed to make a pie, given that each lemon yields about 4 tablespoons of juice.\r\n\r\nhttps:\/\/youtu.be\/4NJ6oqXflbE\r\n

    \r\n

    Try It<\/h3>\r\nAlan 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?\r\n[reveal-answer q=\"193631\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"193631\"]\r\n\r\nThe chili will only fit in the 2 gallon pot\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following video covers US measurements for length, weight, and capacity, and how to convert between larger and smaller units for each type. It's a little long, at 9:44, but it's a good summary of the concepts covered in the US Units of Measurement section of this module.\r\n\r\nhttps:\/\/youtu.be\/ozSnWr4do5o\r\n

    Summary<\/h2>\r\nThere 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.","rendered":"
    \n

    LEARNING outcomes<\/h3>\n
    \n
      \n
    • Define units of capacity and convert from one to another.<\/li>\n
    • Perform arithmetic calculations on units of capacity.<\/li>\n
    • Solve application problems involving units of capacity.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n

      Capacity<\/b> is the amount of liquid (or other pourable substance) that an object can hold when it’s full. When a liquid, such as milk, is being described in gallons or quarts, this is a measure of capacity.<\/p>\n

      Understanding units of capacity can help you solve problems like this: 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 many cups of soup did they have all together?<\/p>\n

      There are five main units for measuring capacity in the U.S. customary measurement system. The smallest unit of measurement is a fluid ounce<\/b>. The word\u00a0ounce<\/em>\u00a0is also used as a measure of weight, so it is important to use the word fluid<\/em> with ounce<\/em> when you are talking about capacity. Sometimes the prefix fluid<\/em>\u00a0is not used when it is clear from the context that the measurement is capacity, not weight.<\/p>\n

      The other units of capacity in the customary system are the cup<\/b>, pint<\/b>, quart<\/b>, and gallon<\/b>. The table below describes each unit of capacity and provides an example to illustrate the size of the unit of measurement.<\/p>\n\n\n\n\n\n\n\n
      Fluid Ounce\u00a0\u00a0<\/b>A unit of capacity equal to [latex]\\displaystyle \\frac{1}{8}[\/latex] of a cup. One fluid ounce of water at 62\u00b0F weighs about one ounce. The amount of liquid medicine is often measured in fluid ounces.<\/td>\n\n

      \"Pipette<\/b><\/p>\n<\/td>\n<\/tr>\n

      Cup\u00a0\u00a0<\/b>A unit equal to 8 fluid ounces. The capacity of a standard measuring cup is one cup.<\/td>\n\n

      \"A<\/p>\n<\/td>\n<\/tr>\n

      Pint\u00a0\u00a0<\/b>A unit equal to 16 fluid ounces, or 2 cups. The capacity of a carton of ice cream is often measured in pints.<\/td>\n\n

      \"A<\/p>\n<\/td>\n<\/tr>\n

      Quart\u00a0\u00a0<\/b>A unit equal to 32 fluid ounces, or 4 cups. You often see quarts of milk being sold in the supermarket.<\/td>\n\n

      \"A<\/p>\n<\/td>\n<\/tr>\n

      Gallon\u00a0\u00a0<\/b>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.<\/td>\n\n

      \"A<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      You can use any of these five measurement units to describe the capacity of an object, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the capacity of a swimming pool in gallons and the capacity of an expensive perfume in fluid ounces.<\/p>\n

      \n

      Try It<\/h3>\n