{"id":4466,"date":"2020-04-13T13:50:28","date_gmt":"2020-04-13T13:50:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4466"},"modified":"2021-02-06T00:04:46","modified_gmt":"2021-02-06T00:04:46","slug":"making-unit-conversions-in-the-u-s-system-of-measurement-2","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/making-unit-conversions-in-the-u-s-system-of-measurement-2\/","title":{"raw":"Making Unit Conversions in the U.S. System of Measurement","rendered":"Making Unit Conversions in the U.S. System of Measurement"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Make conversions between U. S. units of length, volume, time, and weight<\/li>\r\n \t<li>Use mixed units of measurement in the U.S. system<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>There are two systems of measurement commonly used around the world. Most countries use the metric system. The United States uses a different system of measurement, usually called the U.S. system. We will look at the U.S. system first.<\/p>\r\n<p>The U.S. system of measurement uses units of inch, foot, yard, and mile to measure length and pound and ton to measure weight. For capacity, the units used are cup, pint, quart and gallons. Both the U.S. system and the metric system measure time in seconds, minutes, or hours.<\/p>\r\n<p>The equivalencies among the basic units of the U.S. system of measurement are listed in the table below. The table also shows, in parentheses, the common abbreviations for each measurement.<\/p>\r\n\r\n<table id=\"fs-id1627796\" summary=\"The table is labeled in the first row as \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th colspan=\"2\">U.S. System Units<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td><strong>Length<\/strong><\/td>\r\n<td><strong>Volume<\/strong><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]1[\/latex] foot (ft) = [latex]12[\/latex] inches (in)\r\n\r\n[latex]1[\/latex] yard (yd) = [latex]3[\/latex] feet (ft)\r\n\r\n[latex]1[\/latex] mile (mi) = [latex]5280[\/latex] feet (ft)<\/td>\r\n<td>[latex]3[\/latex] teaspoons (t) = [latex]1[\/latex] tablespoon (T)\r\n\r\n[latex]16[\/latex] Tablespoons (T) = [latex]1[\/latex] cup (C)\r\n\r\n[latex]1[\/latex] cup (C) = [latex]8[\/latex] fluid ounces (fl oz)\r\n\r\n[latex]1[\/latex] pint (pt) = [latex]2[\/latex] cups (C)\r\n\r\n[latex]1[\/latex] quart (qt) = [latex]2[\/latex] pints (pt)\r\n\r\n[latex]1[\/latex] gallon (gal) = [latex]4[\/latex] quarts (qt)<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Weight<\/strong><\/td>\r\n<td><strong>Time<\/strong><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]1[\/latex] pound (lb) = [latex]16[\/latex] ounces (oz)\r\n\r\n[latex]1[\/latex] ton = [latex]2000[\/latex] pounds (lb)<\/td>\r\n<td>[latex]1[\/latex] minute (min) = [latex]60[\/latex] seconds (s)\r\n\r\n[latex]1[\/latex] hour (h) = [latex]60[\/latex] minutes (min)\r\n\r\n[latex]1[\/latex] day = [latex]24[\/latex] hours (h)\r\n\r\n[latex]1[\/latex] week (wk) = [latex]7[\/latex] days\r\n\r\n[latex]1[\/latex] year (yr) = [latex]365[\/latex] days<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn many real-life applications, we need to convert between units of measurement. We will use the identity property of multiplication to do these conversions. We\u2019ll restate the Identity Property of Multiplication here for easy reference.\r\n\r\n[latex]\\text{For any real number }a,a\\cdot 1=a[\/latex] \u00a0 \u00a0[latex]1\\cdot a=a[\/latex]\r\n\r\nTo use the identity property of multiplication, we write [latex]1[\/latex] in a form that will help us convert the units. For example, suppose we want to convert inches to feet. We know that [latex]1[\/latex] foot is equal to [latex]12[\/latex] inches, so we can write [latex]1[\/latex] as the fraction [latex]\\Large\\frac{\\text{1 ft}}{\\text{12 in}}[\/latex]. When we multiply by this fraction, we do not change the value but just change the units.\r\n\r\nBut [latex]\\Large\\frac{\\text{12 in}}{\\text{1 ft}}[\/latex] also equals [latex]1[\/latex]. How do we decide whether to multiply by [latex]\\Large\\frac{\\text{1 ft}}{\\text{12 in}}[\/latex] or [latex]\\Large\\frac{\\text{12 in}}{\\text{1 ft}}?[\/latex] We choose the fraction that will make the units we want to convert <em>from<\/em> divide out. For example, suppose we wanted to convert [latex]60[\/latex] inches to feet. If we choose the fraction that has inches in the denominator, we can eliminate the inches.\r\n\r\n[latex]60\\overline{)\\text{in}}\\cdot\\Large\\frac{\\text{1 ft}}{12\\overline{)\\text{in}}}\\normalsize=\\text{5 ft}[\/latex]\r\n\r\nOn the other hand, if we wanted to convert [latex]5[\/latex] feet to inches, we would choose the fraction that has feet in the denominator.\r\n\r\n[latex]\\text{5 ft}\\cdot\\Large\\frac{\\text{12 in}}{1\\overline{)\\text{ft}}}\\normalsize=\\text{60 in}[\/latex]\r\n\r\nWe treat the unit words like factors and \u2018divide out\u2019 common units like we do common factors.\r\n<div class=\"textbox shaded\">\r\n<h3>Make unit conversions.<\/h3>\r\n<ol id=\"eip-id1168467154948\" class=\"stepwise\">\r\n \t<li>Multiply the measurement to be converted by [latex]1[\/latex]; write [latex]1[\/latex] as a fraction relating the units given and the units needed.<\/li>\r\n \t<li>Multiply.<\/li>\r\n \t<li>Simplify the fraction, performing the indicated operations and removing the common units.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMary Anne is [latex]66[\/latex] inches tall. What is her height in feet?\r\n\r\nSolution\r\n<table id=\"eip-id1168466282719\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Convert [latex]66[\/latex] inches into feet.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the measurement to be converted by [latex]1[\/latex].<\/td>\r\n<td>[latex]66[\/latex] inches [latex]\\cdot 1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write [latex]1[\/latex] as a fraction relating the units given and the units needed.<\/td>\r\n<td>[latex]\\text{66 inches}\\cdot \\Large\\frac{\\text{1 foot}}{\\text{12 inches}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{\\text{66 inches}\\cdot \\text{1 foot}}{\\text{12 inches}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td>[latex]\\Large\\frac{66\\overline{)\\text{inches}}\\cdot \\text{1 foot}}{12\\overline{)\\text{inches}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{\\text{66 feet}}{12}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\text{5.5 feet}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that the when we simplified the fraction, we first divided out the inches.\r\nMary Anne is [latex]5.5[\/latex] feet tall.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146826[\/ohm_question]\r\n\r\n[ohm_question]146830[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of converting between units of length in the U.S. system of measurement.\r\n\r\nhttps:\/\/youtu.be\/atN7JU1BaIY\r\n\r\nWhen we use the Identity Property of Multiplication to convert units, we need to make sure the units we want to change from will divide out. Usually this means we want the conversion fraction to have those units in the denominator.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nNdula, an elephant at the San Diego Safari Park, weighs almost [latex]3.2[\/latex] tons. Convert her weight to pounds.\r\n\r\n(credit: Guldo Da Rozze, Flickr)\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222445\/CNX_BMath_Figure_07_05_001.png\" alt=\"A photograph of an adult elephant.\" \/>\r\n[reveal-answer q=\"657668\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"657668\"]\r\n\r\nSolution\r\nWe will convert [latex]3.2[\/latex] tons into pounds, using the equivalencies in the table from earlier. We will use the Identity Property of Multiplication, writing [latex]1[\/latex] as the fraction [latex]\\Large\\frac{\\text{2000 pounds}}{\\text{1 ton}}[\/latex].\r\n<table id=\"eip-id1168467461254\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\text{3.2 tons}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the measurement to be converted by [latex]1[\/latex].<\/td>\r\n<td>[latex]\\text{3.2 tons}\\cdot 1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write [latex]1[\/latex] as a fraction relating tons and pounds.<\/td>\r\n<td>[latex]\\text{3.2 tons}\\cdot\\Large\\frac{\\text{2000 lbs}}{\\text{1 ton}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{3.2\\overline{)\\text{tons}}\\cdot \\text{2000 lbs}}{1\\overline{)\\text{ton}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\text{6400 lbs}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>Ndula weighs almost [latex]6,400[\/latex] pounds.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146831[\/ohm_question]\r\n\r\n[ohm_question]146833[\/ohm_questio\r\n\r\n<\/div>\r\nIn \u00a0the next video we show more examples of how to convert between units of weight using the U. S. system of measurement.\r\n\r\nhttps:\/\/youtu.be\/_wxrSBEhLpI\r\n\r\nSometimes to convert from one unit to another, we may need to use several other units in between, so we will need to multiply several fractions.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nJuliet is going with her family to their summer home. She will be away for [latex]9[\/latex] weeks. Convert the time to minutes.\r\n[reveal-answer q=\"756612\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"756612\"]\r\n\r\nSolution\r\nTo convert weeks into minutes, we will convert weeks to days, days to hours, and then hours to minutes. To do this, we will multiply by conversion factors of [latex]1[\/latex].\r\n<table id=\"eip-id1168468646927\" class=\"unnumbered unstyled\" summary=\"Write 9 weeks as the fraction 9 weeks over 1. Multiply by 1 using the fractions 7 days over 1 week, 24 hours over 1 day, and 60 minutes over 1 hour. The expression becomes 9 weeks over 1 times 7 days over 1 week times 24 hours over 1 day times 60 minutes over 1 hour. Cancel the common units of weeks, days, and hours. Multiply to get 9 times 7 times 24 times 60 minutes all over 1 times 1 times 1 times 1. Perform the multiplication to get 90,720 minutes over 1 which simplifies to 90,720 minutes.\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\text{9 weeks}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write 1 as [latex]\\Large\\frac{7\\text{days}}{1\\text{week}}\\normalsize ,\\Large\\frac{24\\text{hours}}{1\\text{day}}\\normalsize ,\\Large\\frac{60\\text{minutes}}{1\\text{hour}}[\/latex] .<\/td>\r\n<td>[latex]\\Large\\frac{9 wk}{1}\\normalsize\\cdot\\Large\\frac{7 days}{1 wk}\\normalsize\\cdot\\Large\\frac{24 hr}{1 day}\\normalsize\\cdot\\Large\\frac{60 min}{1 hr}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Cancel common units.<\/td>\r\n<td>[latex]\\Large\\frac{9 wk}{1}\\normalsize\\cdot\\Large\\frac{7\\color{blue}{days}}{1 wk}\\normalsize\\cdot\\Large\\frac{24\\color{red}{hr}}{1\\color{blue}{day}}\\normalsize\\cdot\\Large\\frac{60 min}{1\\color{red}{hr}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{9\\cdot 7\\cdot 24\\cdot 60\\text{min}}{1\\cdot 1\\cdot 1\\cdot 1}\\normalsize =90,720\\text{min}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>Juliet will be away for [latex]90,720[\/latex] minutes.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nThe distance between Earth and the moon is about [latex]250,000[\/latex] miles. Convert this length to yards.\r\n\r\n[latex]440,000,000[\/latex] yards\r\n\r\n#146835\r\n\r\nA team of astronauts spends [latex]15[\/latex] weeks in space. Convert the time to minutes.\r\n\r\n[latex]151,200[\/latex] minutes\r\n\r\n#146836\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nHow many fluid ounces are in [latex]1[\/latex] gallon of milk?\r\n\r\n(credit: www.bluewaikiki.com, Flickr)\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222450\/CNX_BMath_Figure_07_05_003.png\" alt=\"A photograph of a milk display in a grocery store.\" \/>\r\n[reveal-answer q=\"84293\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"84293\"]\r\n\r\nSolution\r\nUse conversion factors to get the right units: convert gallons to quarts, quarts to pints, pints to cups, and cups to fluid ounces.\r\n<table id=\"eip-id1168467247162\" class=\"unnumbered unstyled\" summary=\"Write 9 weeks as the fraction 9 weeks over 1. Multiply by 1 using the fractions 7 days over 1 week, 24 hours over 1 day, and 60 minutes over 1 hour. The expression becomes 9 weeks over 1 times 7 days over 1 week times 24 hours over 1 day times 60 minutes over 1 hour. Cancel the common units of weeks, days, and hours. Multiply to get 9 times 7 times 24 times 60 minutes all over 1 times 1 times 1 times 1. Perform the multiplication to get 90,720 minutes over 1 which simplifies to 90,720 minutes.\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]1[\/latex] gallon<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the measurement to be converted by 1.<\/td>\r\n<td>[latex]\\Large\\frac{\\text{1 gal}}{1}\\normalsize\\cdot\\Large\\frac{\\text{4 qt}}{\\text{1 gal}}\\normalsize\\cdot\\Large\\frac{\\text{2 pt}}{\\text{1 qt}}\\normalsize\\cdot\\Large\\frac{\\text{2 C}}{\\text{1 pt}}\\normalsize\\cdot\\Large\\frac{\\text{8 fl oz}}{\\text{1 C}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{1\\overline{)\\text{gal}}}{1}\\normalsize\\cdot\\Large\\frac{4\\overline{)\\text{qt}}}{1\\overline{)\\text{gal}}}\\normalsize\\cdot\\Large\\frac{2\\overline{)\\text{pt}}}{1\\overline{)\\text{qt}}}\\normalsize\\cdot\\Large\\frac{2\\overline{)\\text{C}}}{1\\overline{)\\text{pt}}}\\normalsize\\cdot\\Large\\frac{\\text{8 fl oz}}{1\\overline{)\\text{C}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{1\\cdot 4\\cdot 2\\cdot 2\\cdot \\text{8 fl oz}}{1\\cdot 1\\cdot 1\\cdot 1\\cdot 1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]128[\/latex] fluid ounces<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>There are [latex]128[\/latex] fluid ounces in a gallon.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146837[\/ohm_question]\r\n\r\nHow many teaspoons are in [latex]1[\/latex] cup?\r\n\r\n[ohm_question]146838[\/ohm_question]\r\n\r\n<\/div>\r\n<h3>Use Mixed Units of Measurement in the U.S. System<\/h3>\r\nPerforming arithmetic operations on measurements with mixed units of measures requires care. Be sure to add or subtract like units.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nCharlie bought three steaks for a barbecue. Their weights were [latex]14[\/latex] ounces, [latex]1[\/latex] pound [latex]2[\/latex] ounces, and [latex]1[\/latex] pound [latex]6[\/latex] ounces. How many total pounds of steak did he buy?\r\n\r\n(credit: Helen Penjam, Flickr)\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222453\/CNX_BMath_Figure_07_05_004.png\" alt=\"A photograph of meat being cooked on a charcoal grill.\" \/>\r\n[reveal-answer q=\"627324\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"627324\"]\r\n\r\nSolution\r\nWe will add the weights of the steaks to find the total weight of the steaks.\r\n<table id=\"eip-id1168468433365\" class=\"unnumbered unstyled\" summary=\"The figure shows the addition problem 14 ounces plus 1 pound 2 ounces plus 1 pound 6 ounces written vertically with pounds lining up on the left and ounces lining up on the right. Add the ounces first. 14 plus 2 plus 6 is 22 ounces. Then add the pounds. 1 plus 1 is 2 pounds. Since 22 ounces is more than one pound, convert 22 ounces to pounds and ounces by dividing 22 by 16 to get 1 pound with a remainder of 6 ounces. Add the pounds, 2 plus one for a total of 3 pounds 6 ounces.\">\r\n<tbody>\r\n<tr>\r\n<td>Add the ounces. Then add the pounds.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222455\/CNX_BMath_Figure_07_05_022_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert [latex]22[\/latex] ounces to pounds and ounces.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the pounds.<\/td>\r\n<td>[latex]2[\/latex] pounds [latex]+1[\/latex] pound, [latex]6[\/latex] ounces\r\n\r\n[latex]3[\/latex] pounds, [latex]6[\/latex] ounces<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>Charlie bought [latex]3[\/latex] pounds [latex]6[\/latex] ounces of steak.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146961[\/ohm_question]\r\n\r\n[ohm_question]146962[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAnthony bought four planks of wood that were each [latex]6[\/latex] feet [latex]4[\/latex] inches long. If the four planks are placed end-to-end, what is the total length of the wood?\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222456\/CNX_BMath_Figure_07_05_007_img.png\" alt=\"The image shows 4 planks of wood placed end-to-end horizontally. Each plank is labeled 6 feet 4 inches. A line starts at the left of the first plank and runs horizontally to the right of the fourth plank. The line is labeled with the letter l to represent length.\" \/>\r\n[reveal-answer q=\"98937\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"98937\"]\r\n\r\nSolution\r\nWe will multiply the length of one plank by [latex]4[\/latex] to find the total length.\r\n<table id=\"eip-id1168466705985\" class=\"unnumbered unstyled\" summary=\"The figure shows the multiplication problem 6 feet 4 inches times 4. Multiply inches first. 4 times 4 is 16 inches. Then multiply feet. 6 times 4 is 24 feet. Since 16 inches is more than one foot convert 16 inches to feet and inches by dividing 16 by 12 to get 1 foot with a remainder of 4 inches. Add the feet, 24 plus 1, to get 25 feet 4 inches.\">\r\n<tbody>\r\n<tr>\r\n<td>Multiply the inches and then the feet.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222458\/CNX_BMath_Figure_07_05_023_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert [latex]16[\/latex] inches to feet.<\/td>\r\n<td>[latex]24[\/latex] feet [latex]+1[\/latex] foot [latex]4[\/latex] inches<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the feet.<\/td>\r\n<td>[latex]25[\/latex] feet [latex]4[\/latex] inches<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>Anthony bought [latex]25[\/latex] feet [latex]4[\/latex] inches of wood.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146965[\/ohm_question]\r\n\r\n[ohm_question]146970[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Make conversions between U. S. units of length, volume, time, and weight<\/li>\n<li>Use mixed units of measurement in the U.S. system<\/li>\n<\/ul>\n<\/div>\n<p>There are two systems of measurement commonly used around the world. Most countries use the metric system. The United States uses a different system of measurement, usually called the U.S. system. We will look at the U.S. system first.<\/p>\n<p>The U.S. system of measurement uses units of inch, foot, yard, and mile to measure length and pound and ton to measure weight. For capacity, the units used are cup, pint, quart and gallons. Both the U.S. system and the metric system measure time in seconds, minutes, or hours.<\/p>\n<p>The equivalencies among the basic units of the U.S. system of measurement are listed in the table below. The table also shows, in parentheses, the common abbreviations for each measurement.<\/p>\n<table id=\"fs-id1627796\" summary=\"The table is labeled in the first row as\">\n<thead>\n<tr valign=\"top\">\n<th colspan=\"2\">U.S. System Units<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td><strong>Length<\/strong><\/td>\n<td><strong>Volume<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]1[\/latex] foot (ft) = [latex]12[\/latex] inches (in)<\/p>\n<p>[latex]1[\/latex] yard (yd) = [latex]3[\/latex] feet (ft)<\/p>\n<p>[latex]1[\/latex] mile (mi) = [latex]5280[\/latex] feet (ft)<\/td>\n<td>[latex]3[\/latex] teaspoons (t) = [latex]1[\/latex] tablespoon (T)<\/p>\n<p>[latex]16[\/latex] Tablespoons (T) = [latex]1[\/latex] cup (C)<\/p>\n<p>[latex]1[\/latex] cup (C) = [latex]8[\/latex] fluid ounces (fl oz)<\/p>\n<p>[latex]1[\/latex] pint (pt) = [latex]2[\/latex] cups (C)<\/p>\n<p>[latex]1[\/latex] quart (qt) = [latex]2[\/latex] pints (pt)<\/p>\n<p>[latex]1[\/latex] gallon (gal) = [latex]4[\/latex] quarts (qt)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Weight<\/strong><\/td>\n<td><strong>Time<\/strong><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]1[\/latex] pound (lb) = [latex]16[\/latex] ounces (oz)<\/p>\n<p>[latex]1[\/latex] ton = [latex]2000[\/latex] pounds (lb)<\/td>\n<td>[latex]1[\/latex] minute (min) = [latex]60[\/latex] seconds (s)<\/p>\n<p>[latex]1[\/latex] hour (h) = [latex]60[\/latex] minutes (min)<\/p>\n<p>[latex]1[\/latex] day = [latex]24[\/latex] hours (h)<\/p>\n<p>[latex]1[\/latex] week (wk) = [latex]7[\/latex] days<\/p>\n<p>[latex]1[\/latex] year (yr) = [latex]365[\/latex] days<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In many real-life applications, we need to convert between units of measurement. We will use the identity property of multiplication to do these conversions. We\u2019ll restate the Identity Property of Multiplication here for easy reference.<\/p>\n<p>[latex]\\text{For any real number }a,a\\cdot 1=a[\/latex] \u00a0 \u00a0[latex]1\\cdot a=a[\/latex]<\/p>\n<p>To use the identity property of multiplication, we write [latex]1[\/latex] in a form that will help us convert the units. For example, suppose we want to convert inches to feet. We know that [latex]1[\/latex] foot is equal to [latex]12[\/latex] inches, so we can write [latex]1[\/latex] as the fraction [latex]\\Large\\frac{\\text{1 ft}}{\\text{12 in}}[\/latex]. When we multiply by this fraction, we do not change the value but just change the units.<\/p>\n<p>But [latex]\\Large\\frac{\\text{12 in}}{\\text{1 ft}}[\/latex] also equals [latex]1[\/latex]. How do we decide whether to multiply by [latex]\\Large\\frac{\\text{1 ft}}{\\text{12 in}}[\/latex] or [latex]\\Large\\frac{\\text{12 in}}{\\text{1 ft}}?[\/latex] We choose the fraction that will make the units we want to convert <em>from<\/em> divide out. For example, suppose we wanted to convert [latex]60[\/latex] inches to feet. If we choose the fraction that has inches in the denominator, we can eliminate the inches.<\/p>\n<p>[latex]60\\overline{)\\text{in}}\\cdot\\Large\\frac{\\text{1 ft}}{12\\overline{)\\text{in}}}\\normalsize=\\text{5 ft}[\/latex]<\/p>\n<p>On the other hand, if we wanted to convert [latex]5[\/latex] feet to inches, we would choose the fraction that has feet in the denominator.<\/p>\n<p>[latex]\\text{5 ft}\\cdot\\Large\\frac{\\text{12 in}}{1\\overline{)\\text{ft}}}\\normalsize=\\text{60 in}[\/latex]<\/p>\n<p>We treat the unit words like factors and \u2018divide out\u2019 common units like we do common factors.<\/p>\n<div class=\"textbox shaded\">\n<h3>Make unit conversions.<\/h3>\n<ol id=\"eip-id1168467154948\" class=\"stepwise\">\n<li>Multiply the measurement to be converted by [latex]1[\/latex]; write [latex]1[\/latex] as a fraction relating the units given and the units needed.<\/li>\n<li>Multiply.<\/li>\n<li>Simplify the fraction, performing the indicated operations and removing the common units.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Mary Anne is [latex]66[\/latex] inches tall. What is her height in feet?<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168466282719\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Convert [latex]66[\/latex] inches into feet.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Multiply the measurement to be converted by [latex]1[\/latex].<\/td>\n<td>[latex]66[\/latex] inches [latex]\\cdot 1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write [latex]1[\/latex] as a fraction relating the units given and the units needed.<\/td>\n<td>[latex]\\text{66 inches}\\cdot \\Large\\frac{\\text{1 foot}}{\\text{12 inches}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\Large\\frac{\\text{66 inches}\\cdot \\text{1 foot}}{\\text{12 inches}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td>[latex]\\Large\\frac{66\\overline{)\\text{inches}}\\cdot \\text{1 foot}}{12\\overline{)\\text{inches}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{\\text{66 feet}}{12}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]\\text{5.5 feet}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that the when we simplified the fraction, we first divided out the inches.<br \/>\nMary Anne is [latex]5.5[\/latex] feet tall.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146826\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146826&theme=oea&iframe_resize_id=ohm146826&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146830\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146830&theme=oea&iframe_resize_id=ohm146830&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of converting between units of length in the U.S. system of measurement.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Examples:  Converting Between Different Units of  Lengths Using Standard or American System\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/atN7JU1BaIY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>When we use the Identity Property of Multiplication to convert units, we need to make sure the units we want to change from will divide out. Usually this means we want the conversion fraction to have those units in the denominator.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Ndula, an elephant at the San Diego Safari Park, weighs almost [latex]3.2[\/latex] tons. Convert her weight to pounds.<\/p>\n<p>(credit: Guldo Da Rozze, Flickr)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222445\/CNX_BMath_Figure_07_05_001.png\" alt=\"A photograph of an adult elephant.\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q657668\">Show Solution<\/span><\/p>\n<div id=\"q657668\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe will convert [latex]3.2[\/latex] tons into pounds, using the equivalencies in the table from earlier. We will use the Identity Property of Multiplication, writing [latex]1[\/latex] as the fraction [latex]\\Large\\frac{\\text{2000 pounds}}{\\text{1 ton}}[\/latex].<\/p>\n<table id=\"eip-id1168467461254\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\text{3.2 tons}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the measurement to be converted by [latex]1[\/latex].<\/td>\n<td>[latex]\\text{3.2 tons}\\cdot 1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write [latex]1[\/latex] as a fraction relating tons and pounds.<\/td>\n<td>[latex]\\text{3.2 tons}\\cdot\\Large\\frac{\\text{2000 lbs}}{\\text{1 ton}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{3.2\\overline{)\\text{tons}}\\cdot \\text{2000 lbs}}{1\\overline{)\\text{ton}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\text{6400 lbs}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Ndula weighs almost [latex]6,400[\/latex] pounds.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146831\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146831&theme=oea&iframe_resize_id=ohm146831&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146833\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146833-2-0-0-0-0-0-0-0-0-2-0-0-0-0-0-0-0-0&theme=oea&iframe_resize_id=ohm146833&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>How many teaspoons are in [latex]1[\/latex] cup?<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146838\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146838&theme=oea&iframe_resize_id=ohm146838&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3>Use Mixed Units of Measurement in the U.S. System<\/h3>\n<p>Performing arithmetic operations on measurements with mixed units of measures requires care. Be sure to add or subtract like units.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Charlie bought three steaks for a barbecue. Their weights were [latex]14[\/latex] ounces, [latex]1[\/latex] pound [latex]2[\/latex] ounces, and [latex]1[\/latex] pound [latex]6[\/latex] ounces. How many total pounds of steak did he buy?<\/p>\n<p>(credit: Helen Penjam, Flickr)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222453\/CNX_BMath_Figure_07_05_004.png\" alt=\"A photograph of meat being cooked on a charcoal grill.\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q627324\">Show Solution<\/span><\/p>\n<div id=\"q627324\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe will add the weights of the steaks to find the total weight of the steaks.<\/p>\n<table id=\"eip-id1168468433365\" class=\"unnumbered unstyled\" summary=\"The figure shows the addition problem 14 ounces plus 1 pound 2 ounces plus 1 pound 6 ounces written vertically with pounds lining up on the left and ounces lining up on the right. Add the ounces first. 14 plus 2 plus 6 is 22 ounces. Then add the pounds. 1 plus 1 is 2 pounds. Since 22 ounces is more than one pound, convert 22 ounces to pounds and ounces by dividing 22 by 16 to get 1 pound with a remainder of 6 ounces. Add the pounds, 2 plus one for a total of 3 pounds 6 ounces.\">\n<tbody>\n<tr>\n<td>Add the ounces. Then add the pounds.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222455\/CNX_BMath_Figure_07_05_022_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Convert [latex]22[\/latex] ounces to pounds and ounces.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Add the pounds.<\/td>\n<td>[latex]2[\/latex] pounds [latex]+1[\/latex] pound, [latex]6[\/latex] ounces<\/p>\n<p>[latex]3[\/latex] pounds, [latex]6[\/latex] ounces<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Charlie bought [latex]3[\/latex] pounds [latex]6[\/latex] ounces of steak.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146961\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146961&theme=oea&iframe_resize_id=ohm146961&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146962\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146962&theme=oea&iframe_resize_id=ohm146962&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Anthony bought four planks of wood that were each [latex]6[\/latex] feet [latex]4[\/latex] inches long. If the four planks are placed end-to-end, what is the total length of the wood?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222456\/CNX_BMath_Figure_07_05_007_img.png\" alt=\"The image shows 4 planks of wood placed end-to-end horizontally. Each plank is labeled 6 feet 4 inches. A line starts at the left of the first plank and runs horizontally to the right of the fourth plank. The line is labeled with the letter l to represent length.\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q98937\">Show Solution<\/span><\/p>\n<div id=\"q98937\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe will multiply the length of one plank by [latex]4[\/latex] to find the total length.<\/p>\n<table id=\"eip-id1168466705985\" class=\"unnumbered unstyled\" summary=\"The figure shows the multiplication problem 6 feet 4 inches times 4. Multiply inches first. 4 times 4 is 16 inches. Then multiply feet. 6 times 4 is 24 feet. Since 16 inches is more than one foot convert 16 inches to feet and inches by dividing 16 by 12 to get 1 foot with a remainder of 4 inches. Add the feet, 24 plus 1, to get 25 feet 4 inches.\">\n<tbody>\n<tr>\n<td>Multiply the inches and then the feet.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222458\/CNX_BMath_Figure_07_05_023_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Convert [latex]16[\/latex] inches to feet.<\/td>\n<td>[latex]24[\/latex] feet [latex]+1[\/latex] foot [latex]4[\/latex] inches<\/td>\n<\/tr>\n<tr>\n<td>Add the feet.<\/td>\n<td>[latex]25[\/latex] feet [latex]4[\/latex] inches<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Anthony bought [latex]25[\/latex] feet [latex]4[\/latex] inches of wood.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146965\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146965&theme=oea&iframe_resize_id=ohm146965&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146970\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146970&theme=oea&iframe_resize_id=ohm146970&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-4466\">\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>Question ID 146970, 146965. <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><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Examples: Converting Between Different Units of Lengths Using Standard or American System. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/atN7JU1BaIY\">https:\/\/youtu.be\/atN7JU1BaIY<\/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>Examples: Converting Between Different Units of Weight in Standard or American System. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/_wxrSBEhLpI\">https:\/\/youtu.be\/_wxrSBEhLpI<\/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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <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>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":25777,"menu_order":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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