If you are solving problems that include measurements involving more than one type of measurement, you will need to convert from one unit of measure to another. 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.<\/p>\r\n
Consider the scenario: Alan is making chili. He is using a recipe that makes [latex]24[\/latex] cups of chili. He has a [latex]5[\/latex]-quart pot and a [latex]2[\/latex]-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? In order to determine which pot is better, you need to convert the measurements into one single, common unit of capacity.<\/p>\r\n We know the following conversion factors:<\/p>\r\n [latex] \\frac{2\\text{ pints}}{1\\text{ quart}}[\/latex]<\/p>\r\n [latex] \\frac{2\\text{ cups}} {1\\text{ pint}}[\/latex]<\/p>\r\n Use the factor label method to convert quarts to cups.<\/p>\r\n [latex] 5 \\cancel{\\text{ quarts}} \\times \\frac{2\\cancel{\\text{ pints}}}{1\\cancel{\\text{ quart}}} \\times \\frac{2\\text{ cups}} {1\\cancel{\\text{ pint}}} = 20 \\text{ cups}[\/latex]<\/p>\r\n Since the [latex]5[\/latex]-quart pot only holds [latex]20[\/latex] cups this is not enough to hold all of Alan\u2019s chili.<\/p>\r\n Let\u2019s see how many cups are in the second pot Alan could use.<\/p>\r\n We know the following conversion factors:<\/p>\r\n [latex] \\frac{4\\text{ quarts}}{1\\text{ gallon}}[\/latex]<\/p>\r\n [latex] \\frac{2\\text{ pints}}{1\\text{ quart}}[\/latex]<\/p>\r\n [latex] \\frac{2\\text{ cups}} {1\\text{ pint}}[\/latex]<\/p>\r\n Use the factor label method to convert gallons to cups.<\/p>\r\n [latex] 2 \\cancel{\\text{ gallons}} \\times \\frac{4\\cancel{\\text{ quarts}}}{1\\cancel{\\text{ gallon}}} \\times \\frac{2\\cancel{\\text{ pints}}}{1\\cancel{\\text{ quart}}} \\times \\frac{2\\text{ cups}} {1\\cancel{\\text{ pint}}} = 32 \\text{ cups}[\/latex]<\/p>\r\n Since the [latex]2[\/latex]-gallon pot holds [latex]32[\/latex] cups the pot will hold all of Alan\u2019s chili.<\/p>\r\n We now know Alan\u2019s chili will only fit in the [latex]2[\/latex]-gallon pot.<\/p>\r\n\r\n[\/hidden-answer]<\/section>\r\n There are times when you will need to perform computations on 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>\r\n Consider the scenario: 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 [latex]1 [\/latex] quart, Richard brought [latex]3[\/latex] pints, and LeVar brought [latex]9[\/latex] cups. How many cups of soup did they have altogether? In order to determine the number of cups of soup that was brought, you need to convert the measurements into one single, common unit of capacity.<\/p>\r\n [latex]1\\text{ quart}+3\\text{ pints}+9\\text{ cups}[\/latex]<\/p>\r\n This is given in the table of equivalents.<\/p>\r\n [latex]1\\text{ quart}=4\\text{ cups}[\/latex]<\/p>\r\n Use the factor label method to convert pints to cups.<\/p>\r\n [latex]\\frac{3\\text{ pints}}{1}\\cdot\\frac{2\\text{ cups}}{1\\text{ pint}}=\\text{___ cups}[\/latex]<\/p>\r\n [latex]\\frac{3\\cancel{\\text{ pints}}}{1}\\cdot\\frac{2\\text{ cups}}{1\\cancel{\\text{ pint}}}=\\text{6 cups}[\/latex]<\/p>\r\n Add the [latex]3[\/latex] quantities.<\/p>\r\n [latex]4\\text{ cups}+6\\text{ cups}+9\\text{ cups}=19\\text{ cups}[\/latex]<\/p>\r\n There are [latex]19[\/latex] cups of soup for the dinner. If you are solving problems that include measurements involving more than one type of measurement, you will need to convert from one unit of measure to another. 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.<\/p>\n Consider the scenario: Alan is making chili. He is using a recipe that makes [latex]24[\/latex] cups of chili. He has a [latex]5[\/latex]-quart pot and a [latex]2[\/latex]-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? In order to determine which pot is better, you need to convert the measurements into one single, common unit of capacity.<\/p>\n
\r\n[reveal-answer q=\"4330\"]Show Solution[\/reveal-answer]
\r\n[hidden-answer a=\"4330\"]Alan needs a pot that can hold [latex]24[\/latex] cups of chili. Let\u2019s take the first pot Alan could use : a [latex]5[\/latex]-quart pot. In order to know if the pot will hold [latex]24[\/latex] cups of chili we must find out how many cups are in [latex]5[\/latex]-quarts.\r\n\r\n
\r\n[reveal-answer q=\"4331\"]Show Solution[\/reveal-answer]
\r\n[hidden-answer a=\"4331\"]Since the problem asks for the total amount of soup, you must add the three quantities. Before adding, you must convert the quantities to the same unit. The problem does not require a particular unit, so you can choose. Cups might be the easiest computation.\r\n\r\n
\r\n[\/hidden-answer]<\/p>\r\n<\/section>\r\nApply Unit Conversions With Capacity<\/h2>\n