{"id":1058,"date":"2017-01-11T00:18:41","date_gmt":"2017-01-11T00:18:41","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=1058"},"modified":"2019-10-03T21:03:19","modified_gmt":"2019-10-03T21:03:19","slug":"introduction-units-of-measurement","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wmopen-mathforliberalarts\/chapter\/introduction-units-of-measurement\/","title":{"raw":"US Units of Measurement","rendered":"US Units of Measurement"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<div>\r\n<ul>\r\n \t<li>Define units of length and convert from one to another.<\/li>\r\n \t<li>Perform arithmetic calculations on units of length.<\/li>\r\n \t<li>Solve application problems involving units of length.<\/li>\r\n \t<li>Define units of weight and convert from one to another.<\/li>\r\n \t<li>Perform arithmetic calculations on units of weight.<\/li>\r\n \t<li>Solve application problems involving units of weight.<\/li>\r\n \t<li>Describe the general relationship between the U.S. customary units and metric units of length, weight\/mass, and volume.<\/li>\r\n \t<li>Define the metric prefixes and use them to perform basic conversions among metric units.<\/li>\r\n \t<li>Solve application problems involving metric units of length, mass, and volume.<\/li>\r\n \t<li>State the freezing and boiling points of water on the Celsius and Fahrenheit temperature scales.<\/li>\r\n \t<li>Convert from one temperature scale to the other, using conversion formulas.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<strong>Measurement<\/strong> is a number that describes the size or amount of something. You can measure many things like length, area, capacity, weight, temperature and time. In the United States, two main systems of measurement are used: the <strong>metric system<\/strong> and the <strong>U.S. customary measurement system<\/strong>.\r\n\r\nIn this section we will explore units for length, weight, and capacity, as well as solve problems that involve converting between different units of length, weight or capacity.\r\n<h2>Units of Length<\/h2>\r\nThis topic addresses the measurement of length using the U.S. customary measurement system.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21220507\/meter-512181_1280.jpg\"><img class=\"aligncenter wp-image-942\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21220507\/meter-512181_1280-1024x1024.jpg\" alt=\"coiled measuring tape spiraling against a red background\" width=\"600\" height=\"600\" \/><\/a>\r\n\r\nSuppose you want to purchase tubing for a project, and you see two signs in a hardware store: <i>$1.88 for 2 feet<\/i> of tubing and <i>$5.49 for 3 yards<\/i> of tubing. If both types of tubing will work equally well for your project, which is the better price? You need to know about two <b>units of measurement<\/b>, yards and feet, in order to determine the answer.\r\n\r\n<b>Length<\/b> is the distance from one end of an object to the other end, or from one object to another. For example, the length of a letter-sized piece of paper is 11 inches. The system for measuring length in the United States is based on the four customary units of length: <b>inch<\/b>, <b>foot<\/b>, <b>yard<\/b>, and <b>mile<\/b>. Below are examples to show measurement in each of these units.\r\n<table border=\"1\" width=\"613\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td><b>Unit<\/b><\/td>\r\n<td><b>Description<\/b><\/td>\r\n<td><b>Image<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Inch\/Inches<\/td>\r\n<td>Some people donate their hair to be made into wigs for cancer patients who have lost hair as a result of treatment. One company requires hair donations to be at least 8 inches long.<\/td>\r\n<td><img id=\"Picture 1\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200906\/image049.jpg\" width=\"64\" height=\"132\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>Frame size of a bike: the distance from the center of the crank to the top of the seat tube. Frame size is usually measured in inches. This frame is 16 inches.<\/td>\r\n<td><img id=\"Picture 2\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200907\/image050.jpg\" width=\"264\" height=\"157\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Foot\/Feet<\/td>\r\n<td>Rugs are typically sold in standard lengths. One typical size is a rug that is 8 feet wide and 11 feet long. This is often described as an 8 by 11 rug.<\/td>\r\n<td><img id=\"Picture 3\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200909\/image051.jpg\" width=\"116\" height=\"174\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yard\/Yards<\/td>\r\n<td>Soccer fields vary some in their size. An official field can be any length between 100 and 130 yards.<\/td>\r\n<td><img id=\"Picture 4\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200910\/image052.gif\" width=\"255\" height=\"153\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Mile\/Miles<\/td>\r\n<td>A marathon is 26.2 miles long. One marathon route is shown in the map to the right.<\/td>\r\n<td><img id=\"Picture 5\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200911\/image053.jpg\" width=\"192\" height=\"323\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nYou can use any of these four U.S. customary measurement units to describe the length of something, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the length of a rug in feet rather than miles, and to describe a marathon in miles rather than inches.\r\n\r\nYou may need to convert between units of measurement. For example, you might want to express your height using feet and inches (5 feet 4 inches) or using only inches (64 inches). You need to know the unit equivalents in order to make these conversions between units.\r\n\r\nThe table below shows equivalents and conversion factors for the four customary units of measurement of length.\r\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td><b>Unit Equivalents<\/b><\/td>\r\n<td><b>Conversion Factors <\/b>\r\n\r\n<b>(longer to shorter units of measurement)<\/b><\/td>\r\n<td><b>Conversion Factors<\/b>\r\n\r\n<b>(shorter to longer units of measurement)<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 foot = 12 inches<\/td>\r\n<td>[latex] \\displaystyle \\frac{12\\ \\text{inches}}{1\\ \\text{foot}}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{1\\text{ foot}}{12\\text{ inches}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 yard = 3 feet<\/td>\r\n<td>[latex] \\displaystyle \\frac{3\\text{ feet}}{1\\text{ yard}}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{\\text{1 yard}}{\\text{3 feet}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1 mile = 5,280 feet<\/td>\r\n<td>[latex] \\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex]<\/td>\r\n<td>[latex] \\displaystyle \\frac{\\text{1 mile}}{\\text{5,280 feet}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNote that each of these conversion factors is a ratio of equal values, so each conversion factor equals 1. Multiplying a measurement by a conversion factor does not change the size of the measurement at all since it is the same as multiplying by 1; it just changes the units that you are using to measure.\r\n<h3>Convert Between Different Units of Length<\/h3>\r\nYou can use the conversion factors to convert a measurement, such as feet, to another type of measurement, such as inches.\r\n\r\nNote that there are many more inches for a measurement than there are feet for the same measurement, as feet is a longer unit of measurement. You could use the conversion factor [latex] \\displaystyle \\frac{\\text{12 inches}}{\\text{1 foot}}[\/latex].\r\n\r\nIf a length is measured in feet, and you\u0092d like to convert the length to yards, you can think, \u0093I am converting from a shorter unit to a longer one, so the length in yards will be less than the length in feet.\u0094 You could use the conversion factor [latex] \\displaystyle \\frac{\\text{1 yard}}{\\text{3 feet}}[\/latex].\r\n\r\nIf a distance is measured in miles, and you want to know how many feet it is, you can think, \u0093I am converting from a longer unit of measurement to a shorter one, so the number of feet would be greater than the number of miles.\u0094 You could use the conversion factor [latex] \\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex].\r\n\r\nYou can use the <b>factor<\/b> <b>label<\/b> <b>method<\/b> (also known as <b>dimensional analysis<\/b>) to convert a length from one unit of measure to another using the conversion factors. In the factor label method, you multiply by unit fractions to convert a measurement from one unit to another. Study the example below to see how the factor label method can be used to convert [latex] \\displaystyle 3\\frac{1}{2}[\/latex] feet into an equivalent number of inches.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nHow many inches are in [latex] \\displaystyle 3\\frac{1}{2}[\/latex] feet?\r\n[reveal-answer q=\"284681\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"284681\"]\r\n\r\nBegin by reasoning about your answer. Since a foot is longer than an inch, this means the answer would be greater than [latex] \\displaystyle 3\\frac{1}{2}[\/latex].\r\n\r\nFind the conversion factor that compares inches and feet, with \u0093inches\u0094 in the numerator, and multiply.\r\n<p style=\"text-align: center;\">[latex]3\\frac{1}{2}\\text{feet}\\cdot\\frac{12\\text{ inches}}{1\\text{foot}}=\\text{? inches}[\/latex]<\/p>\r\nRewrite the mixed number as an improper fraction before multiplying.\r\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\text{feet}\\cdot\\frac{12\\text{ inches}}{1\\text{foot}}=\\text{? inches}[\/latex]<\/p>\r\nYou can cancel similar units when they appear in the numerator <i>and<\/i> the denominator. So here, cancel the similar units \u0093feet\u0094 and \u0093foot.\u0094 This eliminates this unit from the problem.\r\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\cancel{\\text{feet}}\\cdot\\frac{12\\text{ inches}}{\\cancel{1\\text{foot}}}=\\text{? inches}[\/latex]<\/p>\r\nRewrite as multiplication of numerators and denominators.\r\n<p style=\"text-align: center;\">[latex]\\frac{7\\cdot12\\text{ inches}}{2}=\\frac{84\\text{ inches}}{2}=42\\text{ inches}[\/latex]<\/p>\r\nThere are 42 inches in [latex] \\displaystyle 3\\frac{1}{2}[\/latex] feet.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNotice that by using the factor label method you can cancel the units out of the problem, just as if they were numbers. You can only cancel if the unit being cancelled is in both the numerator and denominator of the fractions you are multiplying.\r\n\r\nIn the problem above, you cancelled <i>feet<\/i> and <i>foot<\/i> leaving you with <i>inches<\/i>, which is what you were trying to find.\r\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\cancel{\\text{feet}}\\cdot\\frac{12\\text{ inches}}{\\cancel{1\\text{foot}}}=\\text{? inches}[\/latex]<\/p>\r\nWhat if you had used the wrong conversion factor?\r\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\text{feet}\\cdot\\frac{1\\text{foor}}{12\\text{ inches}}=\\text{? inches}[\/latex]?<\/p>\r\nYou could not cancel the feet because the unit is not the same in <i>both <\/i>the numerator and the denominator. So if you complete the computation, you would still have both feet and inches in the answer and no conversion would take place.\r\n\r\nHere is another example of a length conversion using the factor label method.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nHow many yards is 7 feet?\r\n[reveal-answer q=\"571283\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"571283\"]\r\n\r\nStart by reasoning about the size of your answer. Since a yard is longer than a foot, there will be fewer yards. So your answer will be less than 7.\r\n\r\nFind the conversion factor that compares feet and yards, with yards in the numerator.\r\n<p style=\"text-align: center;\">[latex]7\\text{ feet}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}=\\text{? yards}[\/latex]<\/p>\r\nCancel the similar units \u0093feet\u0094 and \u0093feet\u0094 leaving only yards.\r\n<p style=\"text-align: center;\">[latex]7\\cancel{\\text{ feet}}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}=\\text{? yards}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]7\\cdot\\frac{1\\text{ yard}}{3}=\\text{? yards}[\/latex]<\/p>\r\n7 feet equals [latex] \\displaystyle 2\\frac{1}{3}[\/latex] yards.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=117507&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=986&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"250\"><\/iframe>\r\n<iframe id=\"mom10\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=992&amp;theme=oea&amp;iframe_resize_id=mom10\" width=\"100%\" height=\"250\"><\/iframe>\r\n<iframe id=\"mom15\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=993&amp;theme=oea&amp;iframe_resize_id=mom15\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\n<h3>Apply Unit Conversions With Length<\/h3>\r\nThere are times when you will need to perform computations on measurements that are given in different units. For example, consider the tubing problem given earlier. You must decide which of the two options is a better price, and you have to compare prices given in different unit measurements.\r\n\r\nIn order to compare, you need to convert the measurements into one single, common unit of measurement. To be sure you have made the computation accurately, think about whether the unit you are converting to is smaller or larger than the number you have. Its relative size will tell you whether the number you are trying to find is greater or lesser than the given number.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAn interior decorator needs border trim for a home she is wallpapering. She needs 15 feet of border trim for the living room, 30 feet of border trim for the bedroom, and 26 feet of border trim for the dining room. How many yards of border trim does she need?\r\n\r\n[reveal-answer q=\"483916\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"483916\"]\r\n\r\nYou need to find the total length of border trim that is needed for all three rooms in the house. Since the measurements for each room are given in feet, you can add the numbers.\r\n<p style=\"text-align: center;\">[latex]15\\text{ feet}+30\\text{ feet}+26\\text{ feet}=71\\text{ feet}[\/latex]<\/p>\r\nHow many yards is 71 feet?\r\n\r\nReason about the size of your answer. Since a yard is longer than a foot, there will be fewer yards. Expect your answer to be less than 71. Use the conversion factor [latex]\\frac{1\\text{ yard}}{3\\text{ feet}}[\/latex]\r\n<p style=\"text-align: center;\">[latex]\\frac{71\\text{ feet}}{1}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}=\\text{? yards}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{71\\cancel{\\text{ feet}}}{1}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}={23}\\frac{2}{3}\\text{ yards}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom3\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=126605&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<\/div>\r\nThe next example uses the factor label method to solve a problem that requires converting from miles to feet.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTwo runners were comparing how much they had trained earlier that day. Jo said, \u0093According to my pedometer, I ran 8.3 miles.\u0094 Alex said, \u0093That\u0092s a little more than what I ran. I ran 8.1 miles.\u0094 How many more feet did Jo run than Alex?\r\n[reveal-answer q=\"508168\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"508168\"]\r\n\r\nYou need to find the difference between the distance Jo ran and the distance Alex ran. Since both distances are given in the same unit, you can subtract and keep the unit the same.\r\n<p style=\"text-align: center;\">[latex]8.3\\text{ miles}-8.1\\text{ miles}=0.2\\text{ mile}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]0.2\\text{ mile}=\\frac{2}{10}\\text{ mile}[\/latex]<\/p>\r\nSince the problem asks for the difference in <i>feet<\/i>, you must convert from miles to feet. How many feet is 0.2 mile? Reason about the size of your answer. Since a mile is longer than a foot, the distance when expressed as feet will be a number greater than 0.2.\r\n<p style=\"text-align: center;\">[latex]\\frac{2}{10}\\text{ mile}=[\/latex] ___ feet<\/p>\r\nUse the conversion factor [latex] \\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\frac{2\\text{mile}}{10}\\cdot\\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex] = ___ feet<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{2\\cancel{\\text{mile}}}{10}\\cdot\\frac{5,280\\text{ feet}}{1\\cancel{\\text{ mile}}}[\/latex] = ___ feet<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{2}{10}\\cdot\\frac{5,280\\text{ feet}}{1}[\/latex] = ___ feet<\/p>\r\nMultiply. Divide.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{2\\bullet \\text{5,280 feet}}{10\\bullet 1}[\/latex]= ___ feet<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{10,560\\text{ feet}}{10}[\/latex]= ___ feet<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{\\text{10,560 feet}}{\\text{10}}[\/latex]= 1,056 feet<\/p>\r\nJo ran 1,056 feet further than Alex.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the next example we show how to compare the price of two different kinds of tubing for a project you are making. One\u00a0type of tubing is given in cost per yards, and the other is given in cost per feet. It is easier to make a comparison when the units are the same, so we convert one price into the same units as the other. For problems like this, it doesn't matter which cost you convert, either one will work.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nYou are walking through a hardware store and notice two sales on tubing.\r\n\r\n3 yards of Tubing A costs $5.49.\r\n\r\nTubing B sells for $1.88 for 2 feet.\r\n\r\nEither tubing is acceptable for your project. Which tubing is less expensive?\r\n[reveal-answer q=\"468145\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"468145\"]\r\nFind the unit price for each tubing. This will make it easier to compare.\r\n<h4>Tubing A<\/h4>\r\nFind the cost per yard of Tubing A by dividing the cost of 3 yards of the tubing by 3.\r\n<p style=\"text-align: center;\">3 yards = $5.49<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{5.49\\div3}{3\\text{ yards}\\div3}=\\frac{\\$1.83}{1\\text{ yard}}[\/latex]<\/p>\r\nTubing B is sold by the foot. Find the cost per foot by dividing $1.88 by 2 feet.\r\n<h4>Tubing B<\/h4>\r\n<p style=\"text-align: center;\">2 feet = $1.88<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{1.88\\div2}{2\\text{ feet}\\div2}=\\frac{\\$0.94}{1\\text{ foot}}[\/latex]<\/p>\r\nTo compare the prices, you need to have the same unit of measure.\r\n\r\nUse the conversion factor [latex] \\displaystyle \\frac{3\\text{ feet}}{1\\text{ yard}}[\/latex], cancel and multiply.\r\n<p style=\"text-align: center;\">[latex]\\frac{\\$0.94}{1\\text{ foot}}\\cdot\\frac{3\\text{ feet}}{1\\text{ yard}}=\\frac{\\$\\text{____}}{\\text{____ yard}}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{\\$0.94}{1\\cancel{\\text{ foot}}}\\cdot\\frac{3\\cancel{\\text{ feet}}}{1\\text{ yard}}=\\frac{\\$2.82}{1\\text{ yard}}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\$2.82\\text{ per yard}[\/latex]<\/p>\r\nCompare prices for 1 yard of each tubing.\r\n\r\nTubing A: $1.83 per yard\r\n\r\nTubing B: $2.82 per yard\r\n\r\nTubing A is less expensive than Tubing B.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the problem above, you could also have found the price per foot for each kind of tubing and compared the unit prices of each per foot.\r\n\r\nYou need to convert from one unit of measure to another if you are solving problems that include measurements involving more than one type of measurement. Each of the units can be converted to one of the other units using the table of equivalents, the conversion factors, and\/or the factor label method shown in this topic.The four basic units of measurement that are used in the U.S. customary measurement system are: inch, foot, yard, and mile. Typically, people use yards, miles, and sometimes feet to describe long distances. Measurement in inches is common for shorter objects or lengths.\r\n<h2>Units of Weight<\/h2>\r\nWhen you mention how heavy or light an object is, you are referring to its weight. In the U.S. customary system of measurement, weight is measured in ounces, pounds, and tons. These measurements actually refer to how much the gravitational force of the Earth pulls on the object. Like other units of measurement, you can convert between these units and you sometimes need to do this to solve problems.\r\n\r\nThe grocery store sells a 36 ounce canister of ground coffee for $14, and sells bulk coffee for $9 per pound. Which is the better deal? To answer this question, you need to understand the relationship between ounces and pounds.\r\n\r\nYou often use the word <b>weight<\/b> to describe how heavy or light an object or person is. Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An <b>ounce<\/b> is the smallest unit for measuring weight, a <b>pound<\/b> is a larger unit, and a <b>ton<\/b> is the largest unit.\r\n<table width=\"560\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td>Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that\u0092s equal to 400,000 pounds.<\/td>\r\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/14211333\/Mother_and_baby_sperm_whale.jpg\"><img class=\"alignnone size-medium wp-image-1534\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/14211333\/Mother_and_baby_sperm_whale-300x169.jpg\" alt=\"Sperm whale mother and baby off the coast of Mauritius. The calf has remoras attached to it.\" width=\"300\" height=\"169\" \/><\/a><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Meat is a product that is typically sold by the pound. One pound of ground beef makes about four hamburger patties.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200932\/image072.gif\" width=\"186\" height=\"136\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Ounces are used to measure lighter objects. A stack of 11 pennies is equal to about one ounce.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200933\/image073.jpg\" width=\"76\" height=\"116\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nYou can use any of the customary measurement units to describe the weight of something, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the weight of a human being in pounds rather than tons. It makes more sense to describe the weight of a car in tons rather than ounces.\r\n<p style=\"text-align: center;\">1 pound = 16 ounces<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{16\\text{ ounces}}{1\\text{ pound}}[\/latex]<\/p>\r\n\r\n<h3>Converting Between Units of Weight<\/h3>\r\nFour ounces is a typical serving size of meat. Since meat is sold by the pound, you might want to convert the weight of a package of meat from pounds to ounces in order to determine how many servings are contained in a package of meat.\r\n\r\nThe weight capacity of a truck is often provided in tons. You might need to convert pounds into tons if you are trying to determine whether a truck can safely transport a big shipment of heavy materials.\r\n\r\nThe table below shows the unit conversions and conversion factors that are used to make conversions between customary units of weight.\r\n<table cellspacing=\"0\" cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th>Unit Equivalents<\/th>\r\n<th>Conversion Factors (heavier to lighter units of measurement)<\/th>\r\n<th>Conversion Factors(lighter to heavier units of measurement)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>\r\n<p align=\"center\">1 pound = 16 ounces<\/p>\r\n<\/td>\r\n<td>[latex]\\frac{16\\text{ ounces}}{1\\text{ pound}}[\/latex]<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{\\text{1 pound}}{\\text{16 ounces}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\r\n<p align=\"center\">1 ton = 2000 pounds<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex]\\frac{2000\\text{ pounds}}{1\\text{ ton}}[\/latex]<\/p>\r\n<p align=\"center\"><\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{\\text{1 ton}}{\\text{2000 pounds}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nYou can use the <i>factor label method<\/i> to convert one customary unit of weight to another customary unit of weight. This method uses conversion factors, which allow you to \u0093cancel\u0094 units to end up with your desired unit of measurement.\r\n\r\nEach of these conversion factors is a ratio of equal values, so each conversion factor equals 1. Multiplying a measurement by a conversion factor does not change the size of the measurement at all, since it is the same as multiplying by 1. It just changes the units that you are using to measure it in.\r\n\r\nTwo examples illustrating the factor label method are shown below.\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nHow many ounces are in [latex] \\displaystyle 2\\frac{1}{4}[\/latex]<b> pounds?<\/b>\r\n\r\n[reveal-answer q=\"56269\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"56269\"]\r\n\r\nBegin by reasoning about your answer. Since a pound is heavier than an ounce, expect your answer to be a number greater than [latex] \\displaystyle 2\\tfrac{1}{4}[\/latex].\r\n<p style=\"text-align: center;\">[latex]2\\frac{1}{4}\\text{ pounds}=\\text{___ ounces}[\/latex]<\/p>\r\nMultiply by the conversion factor that relates ounces and pounds: [latex] \\displaystyle \\frac{16\\text{ ounces}}{1\\text{ pound}}[\/latex].\r\n<p style=\"text-align: center;\">[latex]2\\frac{1}{4}\\text{ pounds}\\cdot\\frac{16\\text{ ounces}}{1\\text{ pound}}=\\text{____ ounces}[\/latex]<\/p>\r\nWrite the mixed number as an improper fraction.\r\n\r\nThe common unit \u0093pound\u0094 can be cancelled because it appears in both the numerator and denominator.\r\n<p style=\"text-align: center;\">[latex]\\frac{9\\text{ pounds}}{4}\\cdot\\frac{16\\text{ ounces}}{1\\text{ pound}}=\\text{____ ounces}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{9\\cancel{\\text{ pounds}}}{4}\\cdot\\frac{16\\text{ ounces}}{1\\cancel{\\text{ pound}}}=\\text{____ ounces}[\/latex]<\/p>\r\nMultiply and simplify.\r\n<p style=\"text-align: center;\">[latex]\\frac{9}{4}\\cdot\\frac{16\\text{ ounces}}{1}=\\text{____ ounces}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{9\\cdot16\\text{ ounces}}{4\\cdot1}=\\text{___ ounces}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{144\\text{ ounces}}{4}=\\text{____ ounces}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{144\\text{ ounces}}{4}=\\text{36 ounces}[\/latex]<\/p>\r\n&nbsp;\r\n\r\nThere are 36 ounces in [latex] \\displaystyle 2\\frac{1}{4}[\/latex] pounds.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT NOW<\/h3>\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=988&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"180\"><\/iframe>\r\n\r\n<iframe id=\"mom20\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=108209&amp;theme=oea&amp;iframe_resize_id=mom20\" width=\"100%\" height=\"230\"><\/iframe>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nHow many tons is 6,500 pounds?\r\n\r\n[reveal-answer q=\"565442\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"565442\"]\r\n\r\nBegin by reasoning about your answer. Since a ton is heavier than a pound, expect your answer to be a number less than 6,500.\r\n<p style=\"text-align: center;\">[latex]6,500\\text{ pounds}=\\text{___ tons}[\/latex]<\/p>\r\nMultiply by the conversion factor that relates tons to pounds: [latex] \\displaystyle \\frac{\\text{1 ton}}{\\text{2,000 pounds}}[\/latex].\r\n\r\nApply the Factor Label method.\r\n\r\nMultiply and simplify.\r\n<p style=\"text-align: center;\">[latex]6,500\\text{ pounds}\\cdot\\frac{1\\text{ ton}}{2,000\\text{ pounds}}=\\text{____ tons}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{6,500\\text{ pounds}}{1}\\cdot\\frac{1\\text{ ton}}{2,000\\text{ pounds}}=\\text{____ tons}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{6,500\\cancel{\\text{ pounds}}}{1}\\cdot\\frac{1\\text{ ton}}{2,000\\cancel{\\text{ pounds}}}=\\text{____ tons}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{6,500}{1}\\cdot\\frac{1\\text{ ton}}{2,000}=\\text{____ tons}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{6,500\\text{ pounds}}{\\text{2,000}}\\text{= 3}\\frac{1}{4}\\text{ tons}[\/latex]<\/p>\r\n&nbsp;\r\n\r\n6,500 pounds is equal to [latex] \\displaystyle 3\\frac{1}{4}[\/latex] tons.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT NOW<\/h3>\r\n<iframe id=\"mom5\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=23259&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"200\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Applications of Unit Conversions With Weight<\/h3>\r\nThere are times when you need to perform calculations on measurements that are given in different units. To solve these problems, you need to convert one of the measurements to the same unit of measurement as the other measurement.\r\n\r\nThink about whether the unit you are converting to is smaller or larger than the unit you are converting from. This will help you be sure that you are making the right computation. You can use the factor label method to make the conversion from one unit to another.\r\n\r\nHere is an example of a problem that requires converting between units.\r\n<div class=\"exercises textbox\">\r\n<h3>Example<\/h3>\r\nA municipal trash facility allows a person to throw away a maximum of 30 pounds of trash per week. Last week, 140 people threw away the maximum allowable trash. How many tons of trash did this equal?\r\n\r\n[reveal-answer q=\"198853\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"198853\"]\r\n\r\n&nbsp;\r\n\r\nDetermine the total trash for the week expressed in pounds.\r\n\r\nIf 140 people each throw away 30 pounds, you can find the total by multiplying.\r\n<p style=\"text-align: center;\">[latex]140\\cdot30\\text{ pounds}=4,200\\text{ pounds}[\/latex]<\/p>\r\nThen convert 4,200 pounds to tons. Reason about your answer. Since a ton is heavier than a pound, expect your answer to be a number less than 4,200.\r\n<p style=\"text-align: center;\">[latex]4,200\\text{ pounds}=\\text{___ tons}[\/latex]<\/p>\r\nFind the conversion factor appropriate for the situation:\r\n<p style=\"text-align: center;\">[latex] \\displaystyle \\frac{1\\text{ ton}}{2,000\\text{ pounds}}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\text{ pounds}}{1}\\cdot\\frac{1\\text{ ton}}{2,000\\text{ pounds}}=\\text{___ tons}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\cancel{\\text{ pounds}}}{1}\\cdot\\frac{1\\text{ ton}}{2,000\\cancel{\\text{ pounds}}}=\\text{___ tons}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{4,200}{1}\\cdot\\frac{1\\text{ ton}}{2,000}=\\text{___ tons}[\/latex]<\/p>\r\nMultiply and simplify.\r\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\cdot1\\text{ ton}}{1\\cdot2,000}=\\text{___ tons}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\text{ ton}}{2,000}=\\text{____ tons}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\text{ ton}}{2,000}=2\\frac{1}{10}\\text{ tons}[\/latex]<\/p>\r\nThe total amount of trash generated is [latex] \\displaystyle 2\\frac{1}{10}[\/latex] tons.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT NOW<\/h3>\r\n<iframe id=\"mom9\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=126629&amp;theme=oea&amp;iframe_resize_id=mom9\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nLet's revisit the coffee price problem that was posed earlier. We can use unit conversion to solve this problem.\r\n<div class=\"exercises textbox\">\r\n<h3>Example<\/h3>\r\nThe grocery store sells a 36 ounce canister of ground coffee for $14, and sells bulk coffee for $7 per pound. Which is the better deal?\r\n\r\n[reveal-answer q=\"58752\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"58752\"]\r\n\r\nSince canister pricing is for ounces, convert the weight of the canister to pounds.\r\n\r\nFirst use the factor label method to convert ounces to pounds.\r\n<p style=\"text-align: center;\">[latex]36\\text{ ounces}=\\text{___ pounds}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{36\\text{ ounces}}{1}\\cdot\\frac{1\\text{ pound}}{16\\text{ ounces}}=\\text{___ pound}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{36\\cancel{\\text{ ounces}}}{1}\\cdot\\frac{1\\text{ pound}}{16\\cancel{\\text{ ounces}}}=\\text{___ pound}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{36}{1}\\cdot\\frac{1\\text{ pound}}{16}=2\\frac{1}{4}\\text{ pounds}[\/latex]<\/p>\r\nNow calculate the price per pound by dividing.\r\n<p style=\"text-align: center;\">[latex]\\frac{14}{2\\frac{1}{4}\\text{ pounds}}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{14}{2\\frac{1}{4}\\text{ pounds}}\\approx[\/latex] $$6.22 per pound<\/p>\r\n&nbsp;\r\n\r\nThe canister is a better deal at $6.22 per pound.\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT NOW<\/h3>\r\nThe average weight of a northern bluefin tuna is 1,800 pounds. The average weight of a great white shark is [latex] \\displaystyle 2\\frac{1}{2}[\/latex] tons. On average, how much more does a great white shark weigh, in pounds, than a northern bluefin tuna?\r\n[reveal-answer q=\"221505\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"221505\"]3200 lbs.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3>Summary<\/h3>\r\nIn the U.S. customary system of measurement, weight is measured in three units: ounces, pounds, and tons. A pound is equivalent to 16 ounces, and a ton is equivalent to 2,000 pounds. While an object\u0092s weight can be described using any of these units, it is typical to describe very heavy objects using tons and very light objects using an ounce. Pounds are used to describe the weight of many objects and people.\r\n\r\nOften, in order to compare the weights of two objects or people or to solve problems involving weight, you must convert from one unit of measurement to another unit of measurement. Using conversion factors with the factor label method is an effective strategy for converting units and solving problems.\r\n<h2>Units of Capacity<\/h2>\r\n<b>Capacity<\/b> is the amount of liquid (or other pourable substance) that an object can hold when it\u0092s 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 <b>fluid ounce<\/b>. \u0093Ounce\u0094 is also used as a measure of weight, so it is important to use the word \u0093fluid\u0094 with ounce when you are talking about capacity. Sometimes the prefix \u0093fluid\u0094 is 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 <b>cup<\/b>, <b>pint<\/b>, <b>quart<\/b>, and <b>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<table width=\"523\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td><b>Fluid Ounce<\/b>\r\n\r\nA 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<td>\r\n<p align=\"center\"><b><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200959\/image090.gif\" width=\"104\" height=\"112\" \/><\/b><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><b>Cup<\/b>\r\n\r\nA unit equal to 8 fluid ounces. The capacity of a standard measuring cup is one cup.<\/td>\r\n<td>\r\n<p align=\"center\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201000\/image091.jpg\" width=\"161\" height=\"108\" \/><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><b>Pint<\/b>\r\n\r\nA 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<td>\r\n<p align=\"center\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201001\/image092.jpg\" width=\"128\" height=\"179\" \/><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><b>Quart<\/b>\r\n\r\nA unit equal to 32 fluid ounces, or 4 cups. You often see quarts of milk being sold in the supermarket.<\/td>\r\n<td>\r\n<p align=\"center\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201002\/image093.gif\" width=\"70\" height=\"114\" \/><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><b>Gallon<\/b>\r\n\r\nA 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<td>\r\n<p align=\"center\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201003\/image094.jpg\" width=\"155\" height=\"104\" \/><\/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<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom25\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=18868&amp;theme=oea&amp;iframe_resize_id=mom25\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n\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<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td>\r\n<p align=\"center\"><b>Unit Equivalents<\/b><\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\"><b>Conversion Factors (heavier to lighter units of measurement)<\/b><\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\"><b>Conversion Factors<\/b><\/p>\r\n<p align=\"center\"><b>(lighter to heavier units of measurement)<\/b><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\r\n<p align=\"center\">1 cup = 8 fluid ounces<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{\\text{1 cup}}{\\text{8 fluid ounces}}[\/latex]<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{\\text{8 fluid ounces}}{\\text{1 cup}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\r\n<p align=\"center\">1 pint = 2 cups<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{\\text{1 pint}}{2\\text{ cups}}[\/latex]<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{2\\text{ cups}}{1\\text{ pint}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\r\n<p align=\"center\">1 quart = 2 pints<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{\\text{1 quart}}{2\\text{ pints}}[\/latex]<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{2\\text{ pints}}{\\text{1 quart}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\r\n<p align=\"center\">1 quart = 4 cups<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{\\text{1 quart}}{4\\text{ cups}}[\/latex]<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{4\\text{ cups}}{\\text{1 quart}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\r\n<p align=\"center\">1 gallon = 4 quarts<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{\\text{1 gallon}}{4\\text{ quarts}}[\/latex]<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{4\\text{ quarts}}{\\text{1 gallon}}[\/latex]<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\r\n<p align=\"center\">1 gallon = 16 cups<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[latex] \\displaystyle \\frac{1\\text{ gallon}}{\\text{16 cups}}[\/latex]<\/p>\r\n<\/td>\r\n<td>\r\n<p align=\"center\">[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<h3>Converting Between Units of Capacity<\/h3>\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<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nHow many pints is [latex] \\displaystyle 2\\frac{3}{4}[\/latex] <b>gallons?<\/b>\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<p style=\"text-align: center;\">[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\u0097 gallons and quarts.\r\n<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">\u00a0[latex]\\frac{11}{4}\\cdot{4}{1}\\cdot\\frac{2\\text{ pints}}{1}=\\text{___ pints}[\/latex]<\/p>\r\nMultiply and simplify.\r\n<p style=\"text-align: center;\">[latex]\\frac{11\\cdot4\\cdot2\\text{ pints}}{4\\cdot1\\cdot1}=\\text{___ pints}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[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<div class=\"textbox exercises\">\r\n<h3>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<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">[latex]\\frac{32\\cdot1\\cdot1\\cdot1\\cdot1\\text{ gal}}{1\\cdot8\\cdot2\\cdot2\\cdot4}=\\text{___ gal}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[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<div class=\"textbox key-takeaways\">\r\n<h3>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<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=989&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe>\r\n<iframe id=\"mom20\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=23258&amp;theme=oea&amp;iframe_resize_id=mom20\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\n<h3>Applying Unit Conversions<\/h3>\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<div class=\"textbox exercises\">\r\n<h3>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<p style=\"text-align: center;\">[latex]1\\text{ quart}+3\\text{ pints}+9\\text{ cups}[\/latex]<\/p>\r\nThis is given in the table of equivalents.\r\n<p style=\"text-align: center;\">[latex]1\\text{ quart}=4\\text{ cups}[\/latex]<\/p>\r\nUse the factor label method to convert pints to cups.\r\n<p style=\"text-align: center;\">[latex]\\frac{3\\text{ pints}}{1}\\cdot\\frac{2\\text{ cups}}{1\\text{ pint}}=\\text{___ cups}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{3\\cancel{\\text{ pints}}}{1}\\cdot\\frac{2\\text{ cups}}{1\\cancel{\\text{ pint}}}=\\text{6 cups}[\/latex]<\/p>\r\n&nbsp;\r\n\r\nAdd the 3 quantities.\r\n<p style=\"text-align: center;\">[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<div class=\"textbox exercises\">\r\n<h3>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<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">[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<p style=\"text-align: center;\">[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\nIn the following video we provide another example of using unit conversions to solve a problem. \u00a0We show 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<div class=\"textbox key-takeaways\">\r\n<h3>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\nIn the following ~10 minute video, we provide a mini-lesson that covers US measurements for length, weight, and capacity, and how to convert between larger and smaller units for each type. This is a good summary of the concepts covered in the US Units of Measurement section of this module.\r\n\r\n&nbsp;\r\n\r\nhttps:\/\/youtu.be\/ozSnWr4do5o\r\n<h3>Summary<\/h3>\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":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<div>\n<ul>\n<li>Define units of length and convert from one to another.<\/li>\n<li>Perform arithmetic calculations on units of length.<\/li>\n<li>Solve application problems involving units of length.<\/li>\n<li>Define units of weight and convert from one to another.<\/li>\n<li>Perform arithmetic calculations on units of weight.<\/li>\n<li>Solve application problems involving units of weight.<\/li>\n<li>Describe the general relationship between the U.S. customary units and metric units of length, weight\/mass, and volume.<\/li>\n<li>Define the metric prefixes and use them to perform basic conversions among metric units.<\/li>\n<li>Solve application problems involving metric units of length, mass, and volume.<\/li>\n<li>State the freezing and boiling points of water on the Celsius and Fahrenheit temperature scales.<\/li>\n<li>Convert from one temperature scale to the other, using conversion formulas.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p><strong>Measurement<\/strong> is a number that describes the size or amount of something. You can measure many things like length, area, capacity, weight, temperature and time. In the United States, two main systems of measurement are used: the <strong>metric system<\/strong> and the <strong>U.S. customary measurement system<\/strong>.<\/p>\n<p>In this section we will explore units for length, weight, and capacity, as well as solve problems that involve converting between different units of length, weight or capacity.<\/p>\n<h2>Units of Length<\/h2>\n<p>This topic addresses the measurement of length using the U.S. customary measurement system.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21220507\/meter-512181_1280.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-942\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/21220507\/meter-512181_1280-1024x1024.jpg\" alt=\"coiled measuring tape spiraling against a red background\" width=\"600\" height=\"600\" \/><\/a><\/p>\n<p>Suppose you want to purchase tubing for a project, and you see two signs in a hardware store: <i>$1.88 for 2 feet<\/i> of tubing and <i>$5.49 for 3 yards<\/i> of tubing. If both types of tubing will work equally well for your project, which is the better price? You need to know about two <b>units of measurement<\/b>, yards and feet, in order to determine the answer.<\/p>\n<p><b>Length<\/b> is the distance from one end of an object to the other end, or from one object to another. For example, the length of a letter-sized piece of paper is 11 inches. The system for measuring length in the United States is based on the four customary units of length: <b>inch<\/b>, <b>foot<\/b>, <b>yard<\/b>, and <b>mile<\/b>. Below are examples to show measurement in each of these units.<\/p>\n<table cellpadding=\"0\" style=\"width: 613px; border-spacing: 0px;\">\n<tbody>\n<tr>\n<td><b>Unit<\/b><\/td>\n<td><b>Description<\/b><\/td>\n<td><b>Image<\/b><\/td>\n<\/tr>\n<tr>\n<td>Inch\/Inches<\/td>\n<td>Some people donate their hair to be made into wigs for cancer patients who have lost hair as a result of treatment. One company requires hair donations to be at least 8 inches long.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 1\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200906\/image049.jpg\" width=\"64\" height=\"132\" alt=\"image\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Frame size of a bike: the distance from the center of the crank to the top of the seat tube. Frame size is usually measured in inches. This frame is 16 inches.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 2\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200907\/image050.jpg\" width=\"264\" height=\"157\" alt=\"image\" \/><\/td>\n<\/tr>\n<tr>\n<td>Foot\/Feet<\/td>\n<td>Rugs are typically sold in standard lengths. One typical size is a rug that is 8 feet wide and 11 feet long. This is often described as an 8 by 11 rug.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 3\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200909\/image051.jpg\" width=\"116\" height=\"174\" alt=\"image\" \/><\/td>\n<\/tr>\n<tr>\n<td>Yard\/Yards<\/td>\n<td>Soccer fields vary some in their size. An official field can be any length between 100 and 130 yards.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 4\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200910\/image052.gif\" width=\"255\" height=\"153\" alt=\"image\" \/><\/td>\n<\/tr>\n<tr>\n<td>Mile\/Miles<\/td>\n<td>A marathon is 26.2 miles long. One marathon route is shown in the map to the right.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" id=\"Picture 5\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200911\/image053.jpg\" width=\"192\" height=\"323\" alt=\"image\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>You can use any of these four U.S. customary measurement units to describe the length of something, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the length of a rug in feet rather than miles, and to describe a marathon in miles rather than inches.<\/p>\n<p>You may need to convert between units of measurement. For example, you might want to express your height using feet and inches (5 feet 4 inches) or using only inches (64 inches). You need to know the unit equivalents in order to make these conversions between units.<\/p>\n<p>The table below shows equivalents and conversion factors for the four customary units of measurement of length.<\/p>\n<table cellpadding=\"0\" style=\"border-spacing: 0px;\">\n<tbody>\n<tr>\n<td><b>Unit Equivalents<\/b><\/td>\n<td><b>Conversion Factors <\/b><\/p>\n<p><b>(longer to shorter units of measurement)<\/b><\/td>\n<td><b>Conversion Factors<\/b><\/p>\n<p><b>(shorter to longer units of measurement)<\/b><\/td>\n<\/tr>\n<tr>\n<td>1 foot = 12 inches<\/td>\n<td>[latex]\\displaystyle \\frac{12\\ \\text{inches}}{1\\ \\text{foot}}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{1\\text{ foot}}{12\\text{ inches}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 yard = 3 feet<\/td>\n<td>[latex]\\displaystyle \\frac{3\\text{ feet}}{1\\text{ yard}}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{\\text{1 yard}}{\\text{3 feet}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>1 mile = 5,280 feet<\/td>\n<td>[latex]\\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex]<\/td>\n<td>[latex]\\displaystyle \\frac{\\text{1 mile}}{\\text{5,280 feet}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Note that each of these conversion factors is a ratio of equal values, so each conversion factor equals 1. Multiplying a measurement by a conversion factor does not change the size of the measurement at all since it is the same as multiplying by 1; it just changes the units that you are using to measure.<\/p>\n<h3>Convert Between Different Units of Length<\/h3>\n<p>You can use the conversion factors to convert a measurement, such as feet, to another type of measurement, such as inches.<\/p>\n<p>Note that there are many more inches for a measurement than there are feet for the same measurement, as feet is a longer unit of measurement. You could use the conversion factor [latex]\\displaystyle \\frac{\\text{12 inches}}{\\text{1 foot}}[\/latex].<\/p>\n<p>If a length is measured in feet, and you\u0092d like to convert the length to yards, you can think, \u0093I am converting from a shorter unit to a longer one, so the length in yards will be less than the length in feet.\u0094 You could use the conversion factor [latex]\\displaystyle \\frac{\\text{1 yard}}{\\text{3 feet}}[\/latex].<\/p>\n<p>If a distance is measured in miles, and you want to know how many feet it is, you can think, \u0093I am converting from a longer unit of measurement to a shorter one, so the number of feet would be greater than the number of miles.\u0094 You could use the conversion factor [latex]\\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex].<\/p>\n<p>You can use the <b>factor<\/b> <b>label<\/b> <b>method<\/b> (also known as <b>dimensional analysis<\/b>) to convert a length from one unit of measure to another using the conversion factors. In the factor label method, you multiply by unit fractions to convert a measurement from one unit to another. Study the example below to see how the factor label method can be used to convert [latex]\\displaystyle 3\\frac{1}{2}[\/latex] feet into an equivalent number of inches.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>How many inches are in [latex]\\displaystyle 3\\frac{1}{2}[\/latex] feet?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q284681\">Show Solution<\/span><\/p>\n<div id=\"q284681\" class=\"hidden-answer\" style=\"display: none\">\n<p>Begin by reasoning about your answer. Since a foot is longer than an inch, this means the answer would be greater than [latex]\\displaystyle 3\\frac{1}{2}[\/latex].<\/p>\n<p>Find the conversion factor that compares inches and feet, with \u0093inches\u0094 in the numerator, and multiply.<\/p>\n<p style=\"text-align: center;\">[latex]3\\frac{1}{2}\\text{feet}\\cdot\\frac{12\\text{ inches}}{1\\text{foot}}=\\text{? inches}[\/latex]<\/p>\n<p>Rewrite the mixed number as an improper fraction before multiplying.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\text{feet}\\cdot\\frac{12\\text{ inches}}{1\\text{foot}}=\\text{? inches}[\/latex]<\/p>\n<p>You can cancel similar units when they appear in the numerator <i>and<\/i> the denominator. So here, cancel the similar units \u0093feet\u0094 and \u0093foot.\u0094 This eliminates this unit from the problem.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\cancel{\\text{feet}}\\cdot\\frac{12\\text{ inches}}{\\cancel{1\\text{foot}}}=\\text{? inches}[\/latex]<\/p>\n<p>Rewrite as multiplication of numerators and denominators.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7\\cdot12\\text{ inches}}{2}=\\frac{84\\text{ inches}}{2}=42\\text{ inches}[\/latex]<\/p>\n<p>There are 42 inches in [latex]\\displaystyle 3\\frac{1}{2}[\/latex] feet.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Notice that by using the factor label method you can cancel the units out of the problem, just as if they were numbers. You can only cancel if the unit being cancelled is in both the numerator and denominator of the fractions you are multiplying.<\/p>\n<p>In the problem above, you cancelled <i>feet<\/i> and <i>foot<\/i> leaving you with <i>inches<\/i>, which is what you were trying to find.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\cancel{\\text{feet}}\\cdot\\frac{12\\text{ inches}}{\\cancel{1\\text{foot}}}=\\text{? inches}[\/latex]<\/p>\n<p>What if you had used the wrong conversion factor?<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{7}{2}\\text{feet}\\cdot\\frac{1\\text{foor}}{12\\text{ inches}}=\\text{? inches}[\/latex]?<\/p>\n<p>You could not cancel the feet because the unit is not the same in <i>both <\/i>the numerator and the denominator. So if you complete the computation, you would still have both feet and inches in the answer and no conversion would take place.<\/p>\n<p>Here is another example of a length conversion using the factor label method.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>How many yards is 7 feet?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q571283\">Show Solution<\/span><\/p>\n<div id=\"q571283\" class=\"hidden-answer\" style=\"display: none\">\n<p>Start by reasoning about the size of your answer. Since a yard is longer than a foot, there will be fewer yards. So your answer will be less than 7.<\/p>\n<p>Find the conversion factor that compares feet and yards, with yards in the numerator.<\/p>\n<p style=\"text-align: center;\">[latex]7\\text{ feet}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}=\\text{? yards}[\/latex]<\/p>\n<p>Cancel the similar units \u0093feet\u0094 and \u0093feet\u0094 leaving only yards.<\/p>\n<p style=\"text-align: center;\">[latex]7\\cancel{\\text{ feet}}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}=\\text{? yards}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]7\\cdot\\frac{1\\text{ yard}}{3}=\\text{? yards}[\/latex]<\/p>\n<p>7 feet equals [latex]\\displaystyle 2\\frac{1}{3}[\/latex] yards.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=117507&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=986&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"250\"><\/iframe><br \/>\n<iframe loading=\"lazy\" id=\"mom10\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=992&amp;theme=oea&amp;iframe_resize_id=mom10\" width=\"100%\" height=\"250\"><\/iframe><br \/>\n<iframe loading=\"lazy\" id=\"mom15\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=993&amp;theme=oea&amp;iframe_resize_id=mom15\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<h3>Apply Unit Conversions With Length<\/h3>\n<p>There are times when you will need to perform computations on measurements that are given in different units. For example, consider the tubing problem given earlier. You must decide which of the two options is a better price, and you have to compare prices given in different unit measurements.<\/p>\n<p>In order to compare, you need to convert the measurements into one single, common unit of measurement. To be sure you have made the computation accurately, think about whether the unit you are converting to is smaller or larger than the number you have. Its relative size will tell you whether the number you are trying to find is greater or lesser than the given number.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>An interior decorator needs border trim for a home she is wallpapering. She needs 15 feet of border trim for the living room, 30 feet of border trim for the bedroom, and 26 feet of border trim for the dining room. How many yards of border trim does she need?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q483916\">Show Solution<\/span><\/p>\n<div id=\"q483916\" class=\"hidden-answer\" style=\"display: none\">\n<p>You need to find the total length of border trim that is needed for all three rooms in the house. Since the measurements for each room are given in feet, you can add the numbers.<\/p>\n<p style=\"text-align: center;\">[latex]15\\text{ feet}+30\\text{ feet}+26\\text{ feet}=71\\text{ feet}[\/latex]<\/p>\n<p>How many yards is 71 feet?<\/p>\n<p>Reason about the size of your answer. Since a yard is longer than a foot, there will be fewer yards. Expect your answer to be less than 71. Use the conversion factor [latex]\\frac{1\\text{ yard}}{3\\text{ feet}}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{71\\text{ feet}}{1}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}=\\text{? yards}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{71\\cancel{\\text{ feet}}}{1}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}={23}\\frac{2}{3}\\text{ yards}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom3\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=126605&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<\/div>\n<p>The next example uses the factor label method to solve a problem that requires converting from miles to feet.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Two runners were comparing how much they had trained earlier that day. Jo said, \u0093According to my pedometer, I ran 8.3 miles.\u0094 Alex said, \u0093That\u0092s a little more than what I ran. I ran 8.1 miles.\u0094 How many more feet did Jo run than Alex?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q508168\">Show Solution<\/span><\/p>\n<div id=\"q508168\" class=\"hidden-answer\" style=\"display: none\">\n<p>You need to find the difference between the distance Jo ran and the distance Alex ran. Since both distances are given in the same unit, you can subtract and keep the unit the same.<\/p>\n<p style=\"text-align: center;\">[latex]8.3\\text{ miles}-8.1\\text{ miles}=0.2\\text{ mile}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]0.2\\text{ mile}=\\frac{2}{10}\\text{ mile}[\/latex]<\/p>\n<p>Since the problem asks for the difference in <i>feet<\/i>, you must convert from miles to feet. How many feet is 0.2 mile? Reason about the size of your answer. Since a mile is longer than a foot, the distance when expressed as feet will be a number greater than 0.2.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2}{10}\\text{ mile}=[\/latex] ___ feet<\/p>\n<p>Use the conversion factor [latex]\\displaystyle \\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2\\text{mile}}{10}\\cdot\\frac{5,280\\text{ feet}}{1\\text{ mile}}[\/latex] = ___ feet<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2\\cancel{\\text{mile}}}{10}\\cdot\\frac{5,280\\text{ feet}}{1\\cancel{\\text{ mile}}}[\/latex] = ___ feet<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2}{10}\\cdot\\frac{5,280\\text{ feet}}{1}[\/latex] = ___ feet<\/p>\n<p>Multiply. Divide.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{2\\bullet \\text{5,280 feet}}{10\\bullet 1}[\/latex]= ___ feet<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{10,560\\text{ feet}}{10}[\/latex]= ___ feet<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{10,560 feet}}{\\text{10}}[\/latex]= 1,056 feet<\/p>\n<p>Jo ran 1,056 feet further than Alex.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the next example we show how to compare the price of two different kinds of tubing for a project you are making. One\u00a0type of tubing is given in cost per yards, and the other is given in cost per feet. It is easier to make a comparison when the units are the same, so we convert one price into the same units as the other. For problems like this, it doesn&#8217;t matter which cost you convert, either one will work.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>You are walking through a hardware store and notice two sales on tubing.<\/p>\n<p>3 yards of Tubing A costs $5.49.<\/p>\n<p>Tubing B sells for $1.88 for 2 feet.<\/p>\n<p>Either tubing is acceptable for your project. Which tubing is less expensive?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q468145\">Show Solution<\/span><\/p>\n<div id=\"q468145\" class=\"hidden-answer\" style=\"display: none\">\nFind the unit price for each tubing. This will make it easier to compare.<\/p>\n<h4>Tubing A<\/h4>\n<p>Find the cost per yard of Tubing A by dividing the cost of 3 yards of the tubing by 3.<\/p>\n<p style=\"text-align: center;\">3 yards = $5.49<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{5.49\\div3}{3\\text{ yards}\\div3}=\\frac{\\$1.83}{1\\text{ yard}}[\/latex]<\/p>\n<p>Tubing B is sold by the foot. Find the cost per foot by dividing $1.88 by 2 feet.<\/p>\n<h4>Tubing B<\/h4>\n<p style=\"text-align: center;\">2 feet = $1.88<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1.88\\div2}{2\\text{ feet}\\div2}=\\frac{\\$0.94}{1\\text{ foot}}[\/latex]<\/p>\n<p>To compare the prices, you need to have the same unit of measure.<\/p>\n<p>Use the conversion factor [latex]\\displaystyle \\frac{3\\text{ feet}}{1\\text{ yard}}[\/latex], cancel and multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{\\$0.94}{1\\text{ foot}}\\cdot\\frac{3\\text{ feet}}{1\\text{ yard}}=\\frac{\\$\\text{____}}{\\text{____ yard}}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{\\$0.94}{1\\cancel{\\text{ foot}}}\\cdot\\frac{3\\cancel{\\text{ feet}}}{1\\text{ yard}}=\\frac{\\$2.82}{1\\text{ yard}}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\$2.82\\text{ per yard}[\/latex]<\/p>\n<p>Compare prices for 1 yard of each tubing.<\/p>\n<p>Tubing A: $1.83 per yard<\/p>\n<p>Tubing B: $2.82 per yard<\/p>\n<p>Tubing A is less expensive than Tubing B.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the problem above, you could also have found the price per foot for each kind of tubing and compared the unit prices of each per foot.<\/p>\n<p>You need to convert from one unit of measure to another if you are solving problems that include measurements involving more than one type of measurement. Each of the units can be converted to one of the other units using the table of equivalents, the conversion factors, and\/or the factor label method shown in this topic.The four basic units of measurement that are used in the U.S. customary measurement system are: inch, foot, yard, and mile. Typically, people use yards, miles, and sometimes feet to describe long distances. Measurement in inches is common for shorter objects or lengths.<\/p>\n<h2>Units of Weight<\/h2>\n<p>When you mention how heavy or light an object is, you are referring to its weight. In the U.S. customary system of measurement, weight is measured in ounces, pounds, and tons. These measurements actually refer to how much the gravitational force of the Earth pulls on the object. Like other units of measurement, you can convert between these units and you sometimes need to do this to solve problems.<\/p>\n<p>The grocery store sells a 36 ounce canister of ground coffee for $14, and sells bulk coffee for $9 per pound. Which is the better deal? To answer this question, you need to understand the relationship between ounces and pounds.<\/p>\n<p>You often use the word <b>weight<\/b> to describe how heavy or light an object or person is. Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An <b>ounce<\/b> is the smallest unit for measuring weight, a <b>pound<\/b> is a larger unit, and a <b>ton<\/b> is the largest unit.<\/p>\n<table cellpadding=\"0\" style=\"width: 560px; border-spacing: 0px;\">\n<tbody>\n<tr>\n<td>Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons&#8211;that\u0092s equal to 400,000 pounds.<\/td>\n<td><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/14211333\/Mother_and_baby_sperm_whale.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1534\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/14211333\/Mother_and_baby_sperm_whale-300x169.jpg\" alt=\"Sperm whale mother and baby off the coast of Mauritius. The calf has remoras attached to it.\" width=\"300\" height=\"169\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td>Meat is a product that is typically sold by the pound. One pound of ground beef makes about four hamburger patties.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200932\/image072.gif\" width=\"186\" height=\"136\" alt=\"image\" \/><\/td>\n<\/tr>\n<tr>\n<td>Ounces are used to measure lighter objects. A stack of 11 pennies is equal to about one ounce.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200933\/image073.jpg\" width=\"76\" height=\"116\" alt=\"image\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>You can use any of the customary measurement units to describe the weight of something, but it makes more sense to use certain units for certain purposes. For example, it makes more sense to describe the weight of a human being in pounds rather than tons. It makes more sense to describe the weight of a car in tons rather than ounces.<\/p>\n<p style=\"text-align: center;\">1 pound = 16 ounces<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{16\\text{ ounces}}{1\\text{ pound}}[\/latex]<\/p>\n<h3>Converting Between Units of Weight<\/h3>\n<p>Four ounces is a typical serving size of meat. Since meat is sold by the pound, you might want to convert the weight of a package of meat from pounds to ounces in order to determine how many servings are contained in a package of meat.<\/p>\n<p>The weight capacity of a truck is often provided in tons. You might need to convert pounds into tons if you are trying to determine whether a truck can safely transport a big shipment of heavy materials.<\/p>\n<p>The table below shows the unit conversions and conversion factors that are used to make conversions between customary units of weight.<\/p>\n<table cellpadding=\"0\" style=\"border-spacing: 0px;\">\n<thead>\n<tr>\n<th>Unit Equivalents<\/th>\n<th>Conversion Factors (heavier to lighter units of measurement)<\/th>\n<th>Conversion Factors(lighter to heavier units of measurement)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\n<p style=\"text-align: center;\">1 pound = 16 ounces<\/p>\n<\/td>\n<td>[latex]\\frac{16\\text{ ounces}}{1\\text{ pound}}[\/latex]<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{1 pound}}{\\text{16 ounces}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"text-align: center;\">1 ton = 2000 pounds<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\frac{2000\\text{ pounds}}{1\\text{ ton}}[\/latex]<\/p>\n<p style=\"text-align: center;\">\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{1 ton}}{\\text{2000 pounds}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>You can use the <i>factor label method<\/i> to convert one customary unit of weight to another customary unit of weight. This method uses conversion factors, which allow you to \u0093cancel\u0094 units to end up with your desired unit of measurement.<\/p>\n<p>Each of these conversion factors is a ratio of equal values, so each conversion factor equals 1. Multiplying a measurement by a conversion factor does not change the size of the measurement at all, since it is the same as multiplying by 1. It just changes the units that you are using to measure it in.<\/p>\n<p>Two examples illustrating the factor label method are shown below.<\/p>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>How many ounces are in [latex]\\displaystyle 2\\frac{1}{4}[\/latex]<b> pounds?<\/b><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q56269\">Show Solution<\/span><\/p>\n<div id=\"q56269\" class=\"hidden-answer\" style=\"display: none\">\n<p>Begin by reasoning about your answer. Since a pound is heavier than an ounce, expect your answer to be a number greater than [latex]\\displaystyle 2\\tfrac{1}{4}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]2\\frac{1}{4}\\text{ pounds}=\\text{___ ounces}[\/latex]<\/p>\n<p>Multiply by the conversion factor that relates ounces and pounds: [latex]\\displaystyle \\frac{16\\text{ ounces}}{1\\text{ pound}}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]2\\frac{1}{4}\\text{ pounds}\\cdot\\frac{16\\text{ ounces}}{1\\text{ pound}}=\\text{____ ounces}[\/latex]<\/p>\n<p>Write the mixed number as an improper fraction.<\/p>\n<p>The common unit \u0093pound\u0094 can be cancelled because it appears in both the numerator and denominator.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{9\\text{ pounds}}{4}\\cdot\\frac{16\\text{ ounces}}{1\\text{ pound}}=\\text{____ ounces}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{9\\cancel{\\text{ pounds}}}{4}\\cdot\\frac{16\\text{ ounces}}{1\\cancel{\\text{ pound}}}=\\text{____ ounces}[\/latex]<\/p>\n<p>Multiply and simplify.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{9}{4}\\cdot\\frac{16\\text{ ounces}}{1}=\\text{____ ounces}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{9\\cdot16\\text{ ounces}}{4\\cdot1}=\\text{___ ounces}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{144\\text{ ounces}}{4}=\\text{____ ounces}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{144\\text{ ounces}}{4}=\\text{36 ounces}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>There are 36 ounces in [latex]\\displaystyle 2\\frac{1}{4}[\/latex] pounds.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT NOW<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=988&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"180\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom20\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=108209&amp;theme=oea&amp;iframe_resize_id=mom20\" width=\"100%\" height=\"230\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>How many tons is 6,500 pounds?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q565442\">Show Solution<\/span><\/p>\n<div id=\"q565442\" class=\"hidden-answer\" style=\"display: none\">\n<p>Begin by reasoning about your answer. Since a ton is heavier than a pound, expect your answer to be a number less than 6,500.<\/p>\n<p style=\"text-align: center;\">[latex]6,500\\text{ pounds}=\\text{___ tons}[\/latex]<\/p>\n<p>Multiply by the conversion factor that relates tons to pounds: [latex]\\displaystyle \\frac{\\text{1 ton}}{\\text{2,000 pounds}}[\/latex].<\/p>\n<p>Apply the Factor Label method.<\/p>\n<p>Multiply and simplify.<\/p>\n<p style=\"text-align: center;\">[latex]6,500\\text{ pounds}\\cdot\\frac{1\\text{ ton}}{2,000\\text{ pounds}}=\\text{____ tons}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{6,500\\text{ pounds}}{1}\\cdot\\frac{1\\text{ ton}}{2,000\\text{ pounds}}=\\text{____ tons}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{6,500\\cancel{\\text{ pounds}}}{1}\\cdot\\frac{1\\text{ ton}}{2,000\\cancel{\\text{ pounds}}}=\\text{____ tons}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{6,500}{1}\\cdot\\frac{1\\text{ ton}}{2,000}=\\text{____ tons}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{6,500\\text{ pounds}}{\\text{2,000}}\\text{= 3}\\frac{1}{4}\\text{ tons}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>6,500 pounds is equal to [latex]\\displaystyle 3\\frac{1}{4}[\/latex] tons.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT NOW<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom5\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=23259&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"200\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Applications of Unit Conversions With Weight<\/h3>\n<p>There are times when you need to perform calculations on measurements that are given in different units. To solve these problems, you need to convert one of the measurements to the same unit of measurement as the other measurement.<\/p>\n<p>Think about whether the unit you are converting to is smaller or larger than the unit you are converting from. This will help you be sure that you are making the right computation. You can use the factor label method to make the conversion from one unit to another.<\/p>\n<p>Here is an example of a problem that requires converting between units.<\/p>\n<div class=\"exercises textbox\">\n<h3>Example<\/h3>\n<p>A municipal trash facility allows a person to throw away a maximum of 30 pounds of trash per week. Last week, 140 people threw away the maximum allowable trash. How many tons of trash did this equal?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q198853\">Show Solution<\/span><\/p>\n<div id=\"q198853\" class=\"hidden-answer\" style=\"display: none\">\n<p>&nbsp;<\/p>\n<p>Determine the total trash for the week expressed in pounds.<\/p>\n<p>If 140 people each throw away 30 pounds, you can find the total by multiplying.<\/p>\n<p style=\"text-align: center;\">[latex]140\\cdot30\\text{ pounds}=4,200\\text{ pounds}[\/latex]<\/p>\n<p>Then convert 4,200 pounds to tons. Reason about your answer. Since a ton is heavier than a pound, expect your answer to be a number less than 4,200.<\/p>\n<p style=\"text-align: center;\">[latex]4,200\\text{ pounds}=\\text{___ tons}[\/latex]<\/p>\n<p>Find the conversion factor appropriate for the situation:<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{1\\text{ ton}}{2,000\\text{ pounds}}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\text{ pounds}}{1}\\cdot\\frac{1\\text{ ton}}{2,000\\text{ pounds}}=\\text{___ tons}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\cancel{\\text{ pounds}}}{1}\\cdot\\frac{1\\text{ ton}}{2,000\\cancel{\\text{ pounds}}}=\\text{___ tons}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{4,200}{1}\\cdot\\frac{1\\text{ ton}}{2,000}=\\text{___ tons}[\/latex]<\/p>\n<p>Multiply and simplify.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\cdot1\\text{ ton}}{1\\cdot2,000}=\\text{___ tons}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\text{ ton}}{2,000}=\\text{____ tons}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{4,200\\text{ ton}}{2,000}=2\\frac{1}{10}\\text{ tons}[\/latex]<\/p>\n<p>The total amount of trash generated is [latex]\\displaystyle 2\\frac{1}{10}[\/latex] tons.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT NOW<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom9\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=126629&amp;theme=oea&amp;iframe_resize_id=mom9\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Let&#8217;s revisit the coffee price problem that was posed earlier. We can use unit conversion to solve this problem.<\/p>\n<div class=\"exercises textbox\">\n<h3>Example<\/h3>\n<p>The grocery store sells a 36 ounce canister of ground coffee for $14, and sells bulk coffee for $7 per pound. Which is the better deal?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q58752\">Show Solution<\/span><\/p>\n<div id=\"q58752\" class=\"hidden-answer\" style=\"display: none\">\n<p>Since canister pricing is for ounces, convert the weight of the canister to pounds.<\/p>\n<p>First use the factor label method to convert ounces to pounds.<\/p>\n<p style=\"text-align: center;\">[latex]36\\text{ ounces}=\\text{___ pounds}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{36\\text{ ounces}}{1}\\cdot\\frac{1\\text{ pound}}{16\\text{ ounces}}=\\text{___ pound}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{36\\cancel{\\text{ ounces}}}{1}\\cdot\\frac{1\\text{ pound}}{16\\cancel{\\text{ ounces}}}=\\text{___ pound}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{36}{1}\\cdot\\frac{1\\text{ pound}}{16}=2\\frac{1}{4}\\text{ pounds}[\/latex]<\/p>\n<p>Now calculate the price per pound by dividing.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{14}{2\\frac{1}{4}\\text{ pounds}}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{14}{2\\frac{1}{4}\\text{ pounds}}\\approx[\/latex] $$6.22 per pound<\/p>\n<p>&nbsp;<\/p>\n<p>The canister is a better deal at $6.22 per pound.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT NOW<\/h3>\n<p>The average weight of a northern bluefin tuna is 1,800 pounds. The average weight of a great white shark is [latex]\\displaystyle 2\\frac{1}{2}[\/latex] tons. On average, how much more does a great white shark weigh, in pounds, than a northern bluefin tuna?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q221505\">Show Solution<\/span><\/p>\n<div id=\"q221505\" class=\"hidden-answer\" style=\"display: none\">3200 lbs.<\/div>\n<\/div>\n<\/div>\n<h3>Summary<\/h3>\n<p>In the U.S. customary system of measurement, weight is measured in three units: ounces, pounds, and tons. A pound is equivalent to 16 ounces, and a ton is equivalent to 2,000 pounds. While an object\u0092s weight can be described using any of these units, it is typical to describe very heavy objects using tons and very light objects using an ounce. Pounds are used to describe the weight of many objects and people.<\/p>\n<p>Often, in order to compare the weights of two objects or people or to solve problems involving weight, you must convert from one unit of measurement to another unit of measurement. Using conversion factors with the factor label method is an effective strategy for converting units and solving problems.<\/p>\n<h2>Units of Capacity<\/h2>\n<p><b>Capacity<\/b> is the amount of liquid (or other pourable substance) that an object can hold when it\u0092s full. When a liquid, such as milk, is being described in gallons or quarts, this is a measure of capacity.<\/p>\n<p>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<p>There are five main units for measuring capacity in the U.S. customary measurement system. The smallest unit of measurement is a <b>fluid ounce<\/b>. \u0093Ounce\u0094 is also used as a measure of weight, so it is important to use the word \u0093fluid\u0094 with ounce when you are talking about capacity. Sometimes the prefix \u0093fluid\u0094 is not used when it is clear from the context that the measurement is capacity, not weight.<\/p>\n<p>The other units of capacity in the customary system are the <b>cup<\/b>, <b>pint<\/b>, <b>quart<\/b>, and <b>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<table cellpadding=\"0\" style=\"width: 523px; border-spacing: 0px;\">\n<tbody>\n<tr>\n<td><b>Fluid Ounce<\/b><\/p>\n<p>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<td>\n<p style=\"text-align: center;\"><b><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30200959\/image090.gif\" width=\"104\" height=\"112\" alt=\"image\" \/><\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Cup<\/b><\/p>\n<p>A unit equal to 8 fluid ounces. The capacity of a standard measuring cup is one cup.<\/td>\n<td>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201000\/image091.jpg\" width=\"161\" height=\"108\" alt=\"image\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Pint<\/b><\/p>\n<p>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<td>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201001\/image092.jpg\" width=\"128\" height=\"179\" alt=\"image\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Quart<\/b><\/p>\n<p>A unit equal to 32 fluid ounces, or 4 cups. You often see quarts of milk being sold in the supermarket.<\/td>\n<td>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201002\/image093.gif\" width=\"70\" height=\"114\" alt=\"image\" \/><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td><b>Gallon<\/b><\/p>\n<p>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<td>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/30201003\/image094.jpg\" width=\"155\" height=\"104\" alt=\"image\" \/><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>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<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom25\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=18868&amp;theme=oea&amp;iframe_resize_id=mom25\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Sometimes 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.<\/p>\n<p>The table below shows some of the most common equivalents and conversion factors for the five customary units of measurement of capacity.<\/p>\n<table cellpadding=\"0\" style=\"border-spacing: 0px;\">\n<tbody>\n<tr>\n<td>\n<p style=\"text-align: center;\"><b>Unit Equivalents<\/b><\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\"><b>Conversion Factors (heavier to lighter units of measurement)<\/b><\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\"><b>Conversion Factors<\/b><\/p>\n<p style=\"text-align: center;\"><b>(lighter to heavier units of measurement)<\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"text-align: center;\">1 cup = 8 fluid ounces<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{1 cup}}{\\text{8 fluid ounces}}[\/latex]<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{8 fluid ounces}}{\\text{1 cup}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"text-align: center;\">1 pint = 2 cups<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{1 pint}}{2\\text{ cups}}[\/latex]<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{2\\text{ cups}}{1\\text{ pint}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"text-align: center;\">1 quart = 2 pints<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{1 quart}}{2\\text{ pints}}[\/latex]<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{2\\text{ pints}}{\\text{1 quart}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"text-align: center;\">1 quart = 4 cups<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{1 quart}}{4\\text{ cups}}[\/latex]<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{4\\text{ cups}}{\\text{1 quart}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"text-align: center;\">1 gallon = 4 quarts<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{1 gallon}}{4\\text{ quarts}}[\/latex]<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{4\\text{ quarts}}{\\text{1 gallon}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"text-align: center;\">1 gallon = 16 cups<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{1\\text{ gallon}}{\\text{16 cups}}[\/latex]<\/p>\n<\/td>\n<td>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{16 cups}}{1\\text{ gallon}}[\/latex]<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>Converting Between Units of Capacity<\/h3>\n<p>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.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>How many pints is [latex]\\displaystyle 2\\frac{3}{4}[\/latex] <b>gallons?<\/b><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q442206\">Show Solution<\/span><\/p>\n<div id=\"q442206\" class=\"hidden-answer\" style=\"display: none\">\n<p>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].<\/p>\n<p style=\"text-align: center;\">[latex]2\\frac{3}{4}\\text{ gallons}=\\text{___ pints}[\/latex]<\/p>\n<p>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.<\/p>\n<p>Set up the equation so that two sets of labels cancel\u0097 gallons and quarts.<\/p>\n<p style=\"text-align: center;\">[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>\n<p style=\"text-align: center;\">[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>\n<p style=\"text-align: center;\">\u00a0[latex]\\frac{11}{4}\\cdot{4}{1}\\cdot\\frac{2\\text{ pints}}{1}=\\text{___ pints}[\/latex]<\/p>\n<p>Multiply and simplify.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{11\\cdot4\\cdot2\\text{ pints}}{4\\cdot1\\cdot1}=\\text{___ pints}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{88\\text{ pints}}{4}=22\\text{ pints}[\/latex]<\/p>\n<p>[latex]\\displaystyle 2\\frac{3}{4}[\/latex] gallons is 22 pints.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>How many gallons is 32 fluid ounces?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q49180\">Show Solution<\/span><\/p>\n<div id=\"q49180\" class=\"hidden-answer\" style=\"display: none\">\n<p>Begin by reasoning about your answer. Since gallons is a larger unit than fluid ounces, expect the answer to be less than 32.<\/p>\n<p style=\"text-align: center;\">[latex]32\\text{ fluid ounces}=\\text{___ gallons}[\/latex]<\/p>\n<p>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.<\/p>\n<p style=\"text-align: center;\">[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>\n<p>Cancel units that appear in both the numerator and denominator.<\/p>\n<p style=\"text-align: center;\">[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>\n<p style=\"text-align: center;\">[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>\n<p>Multiply and simplify.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{32\\cdot1\\cdot1\\cdot1\\cdot1\\text{ gal}}{1\\cdot8\\cdot2\\cdot2\\cdot4}=\\text{___ gal}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle \\frac{32\\text{ gal}}{\\text{128}}=\\frac{1}{4}\\text{ gal}[\/latex]<\/p>\n<p>32 fluid ounces is the same as [latex]\\frac{1}{4}[\/latex] gallon.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Find the sum of 4 gallons and 2 pints. Express your answer in cups.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q69640\">Show Solution<\/span><\/p>\n<div id=\"q69640\" class=\"hidden-answer\" style=\"display: none\">4 gallons + 2 pints = 64 cups + 4 cups = 68 cups<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=989&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe><br \/>\n<iframe loading=\"lazy\" id=\"mom20\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=23258&amp;theme=oea&amp;iframe_resize_id=mom20\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<h3>Applying Unit Conversions<\/h3>\n<p>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.<\/p>\n<p>Consider the situation posed earlier in this topic.<\/p>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>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?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q749363\">Show Solution<\/span><\/p>\n<div id=\"q749363\" class=\"hidden-answer\" style=\"display: none\">\n<p>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.<\/p>\n<p>The problem does not require a particular unit, so you can choose. Cups might be the easiest computation.<\/p>\n<p style=\"text-align: center;\">[latex]1\\text{ quart}+3\\text{ pints}+9\\text{ cups}[\/latex]<\/p>\n<p>This is given in the table of equivalents.<\/p>\n<p style=\"text-align: center;\">[latex]1\\text{ quart}=4\\text{ cups}[\/latex]<\/p>\n<p>Use the factor label method to convert pints to cups.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{3\\text{ pints}}{1}\\cdot\\frac{2\\text{ cups}}{1\\text{ pint}}=\\text{___ cups}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{3\\cancel{\\text{ pints}}}{1}\\cdot\\frac{2\\text{ cups}}{1\\cancel{\\text{ pint}}}=\\text{6 cups}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>Add the 3 quantities.<\/p>\n<p style=\"text-align: center;\">[latex]4\\text{ cups}+6\\text{ cups}+9\\text{ cups}=19\\text{ cups}[\/latex]<\/p>\n<p>There are 19 cups of soup for the dinner.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>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?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q50819\">Show Solution<\/span><\/p>\n<div id=\"q50819\" class=\"hidden-answer\" style=\"display: none\">\n<p>This problem requires you to find the sum of the capacity of each container and then convert that sum to cups.<\/p>\n<p style=\"text-align: center;\">[latex]1\\text{ gallon}+2\\text{ quarts}=\\text{___ cups}[\/latex]<\/p>\n<p>First, find the sum in quarts. 1 gallon is equal to 4 quarts.<\/p>\n<p style=\"text-align: center;\">[latex]4\\text{ quarts}+2\\text{ quarts}=6\\text{ quarts}[\/latex]<\/p>\n<p>Since the problem asks for the capacity in cups, convert 6 quarts to cups.<\/p>\n<p>Cancel units that appear in both the numerator and denominator.<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center;\">[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>\n<p style=\"text-align: center;\">[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>\n<p style=\"text-align: center;\">[latex]6\\times2\\times2=24\\text{ cups}[\/latex]<\/p>\n<p>Natasha will have 24 cups of lemonade.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Another 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.<\/p>\n<p>In the following video we provide another example of using unit conversions to solve a problem. \u00a0We show how to find the number of lemons needed to make a pie, given that each lemon yields about 4 tablespoons of juice.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Unit Conversion Application - Number of Lemons for a Lemon Pie\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/4NJ6oqXflbE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>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?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q193631\">Show Solution<\/span><\/p>\n<div id=\"q193631\" class=\"hidden-answer\" style=\"display: none\">\n<p>The chili will only fit in the 2 gallon pot<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following ~10 minute video, we provide a mini-lesson that covers US measurements for length, weight, and capacity, and how to convert between larger and smaller units for each type. This is a good summary of the concepts covered in the US Units of Measurement section of this module.<\/p>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"American Unit Conversion\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ozSnWr4do5o?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Summary<\/h3>\n<p>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.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1058\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID 126635, 126782. <strong>Authored by<\/strong>: Day, Alyson. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Units 1 - 8 Developmental Math 2014 An Open Program: Arithmetic, Geometry and Statistics. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Units of Length. <strong>Authored by<\/strong>: Developmental Math 2014An Open Program. <strong>Provided by<\/strong>: Monterey Institute for Technology and Education (MITE). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/dl.dropboxusercontent.com\/u\/28928849\/MAT142\/MeasurementNROC.pdf\">https:\/\/dl.dropboxusercontent.com\/u\/28928849\/MAT142\/MeasurementNROC.pdf<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>meter-tape-measure-measure-gage. <strong>Authored by<\/strong>: EME. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/en\/meter-tape-measure-measure-gage-512181\/\">https:\/\/pixabay.com\/en\/meter-tape-measure-measure-gage-512181\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><li>Question ID 117507. <strong>Authored by<\/strong>: Volpe, Amy. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li>Question ID 126605. <strong>Authored by<\/strong>: Day, Alyson. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li>Sperm Whale Mother and Baby. <strong>Authored by<\/strong>: By Gabriel Barathieu . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/commons.wikimedia.org\/w\/index.php?curid=24212362\">https:\/\/commons.wikimedia.org\/w\/index.php?curid=24212362<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Question ID 988, 108209. <strong>Authored by<\/strong>: David Lippman. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li>Question ID 23259. <strong>Authored by<\/strong>: Sze, David. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li>Question ID 989, 18868. <strong>Authored by<\/strong>: Lippman, David. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: iMathAS Community License CC-BY + GPL<\/li><li>Unit Conversion Application - Number of Lemons for a Lemon Pie. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/4NJ6oqXflbE\">https:\/\/youtu.be\/4NJ6oqXflbE<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>American Unit Conversion . <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/ozSnWr4do5o\">https:\/\/youtu.be\/ozSnWr4do5o<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Units 1 - 8 Developmental Math 2014 An Open Program: Arithmetic, Geometry and Statistics\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\"http:\/\/nrocnetwork.org\/dm-opentext\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Units of Length\",\"author\":\"Developmental Math 2014An Open Program\",\"organization\":\"Monterey Institute for Technology and Education (MITE)\",\"url\":\"https:\/\/dl.dropboxusercontent.com\/u\/28928849\/MAT142\/MeasurementNROC.pdf\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"meter-tape-measure-measure-gage\",\"author\":\"EME\",\"organization\":\"\",\"url\":\"https:\/\/pixabay.com\/en\/meter-tape-measure-measure-gage-512181\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID 117507\",\"author\":\"Volpe, Amy\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"cc\",\"description\":\"Question ID 126605\",\"author\":\"Day, Alyson\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"cc\",\"description\":\"Sperm Whale Mother and Baby\",\"author\":\"By Gabriel Barathieu \",\"organization\":\"\",\"url\":\"https:\/\/commons.wikimedia.org\/w\/index.php?curid=24212362\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID 988, 108209\",\"author\":\"David Lippman\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"cc\",\"description\":\"Question ID 23259\",\"author\":\"Sze, David\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"original\",\"description\":\"Question ID 126635, 126782\",\"author\":\"Day, Alyson\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"cc\",\"description\":\"Question ID 989, 18868\",\"author\":\"Lippman, David\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"iMathAS Community License CC-BY + GPL\"},{\"type\":\"cc\",\"description\":\"Unit Conversion Application - 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