{"id":65,"date":"2023-01-25T16:33:59","date_gmt":"2023-01-25T16:33:59","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/us-units-of-measurement-learn-it-page-2\/"},"modified":"2024-10-18T20:52:02","modified_gmt":"2024-10-18T20:52:02","slug":"us-units-of-measurement-learn-it-2","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/us-units-of-measurement-learn-it-2\/","title":{"raw":"US Units of Measurement: Learn It 2","rendered":"US Units of Measurement: Learn It 2"},"content":{"raw":"<h2>Apply Unit Conversions With Length<\/h2>\r\n<p>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<p>Suppose you want to purchase tubing for a project, and you see two signs in a hardware store: <i>[latex]$1.88[\/latex] for [latex]2[\/latex] feet<\/i> of tubing and <i>[latex]$5.49[\/latex] for [latex]3[\/latex] yards<\/i> of tubing. If both types of tubing will work equally well for your project, which is the better price? In order to compare, you need to convert the measurements into one single, common unit of measurement.<\/p>\r\n<section class=\"textbox example\">Let\u2019s solve the tubing problem mentioned above. You are walking through a hardware store and notice two sales on tubing:\r\n\r\n<ul>\r\n\t<li>[latex]3[\/latex] yards of Tubing A costs [latex]$5.49[\/latex].<\/li>\r\n\t<li>Tubing B sells for [latex]$1.88[\/latex] for [latex]2[\/latex] feet.<\/li>\r\n<\/ul>\r\n<p>Either tubing is acceptable for your project. Which tubing is less expensive?<br \/>\r\n[reveal-answer q=\"4330\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"4330\"]<\/p>\r\n<p>Find the unit price for each tubing. This will make it easier to compare.<\/p>\r\n<p><strong>Tubing A<\/strong>: Find the cost per yard of Tubing A by dividing the cost of [latex]3[\/latex] yards of the tubing by [latex]3[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]3[\/latex] yards = [latex]$5.49[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{5.49}{3\\text{ yards}}=\\frac{\\$1.83}{1\\text{ yard}}[\/latex]<\/p>\r\n<p><strong>Tubing B<\/strong>: Tubing B is sold by the foot. Find the cost per foot by dividing [latex]$1.88[\/latex] by [latex]2[\/latex] feet.<\/p>\r\n<p style=\"text-align: center;\">[latex]2[\/latex] feet = [latex]$1.88[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{1.88}{2\\text{ feet}}=\\frac{\\$0.94}{1\\text{ foot}}[\/latex]<\/p>\r\n<p>To compare the prices, you need to have the same unit of measure.<\/p>\r\n<p>Use the conversion factor [latex] \\displaystyle \\frac{3\\text{ feet}}{1\\text{ yard}}[\/latex], cancel and multiply.<\/p>\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\n<p>Compare prices for [latex]1[\/latex] yard of each tubing.<\/p>\r\n<p>Tubing A: [latex]$1.83[\/latex] per yard<\/p>\r\n<p>Tubing B: [latex]$2.82[\/latex] per yard<\/p>\r\n<p>Tubing A is less expensive than Tubing B.<br \/>\r\n[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1853[\/ohm2_question]<\/section>\r\n<p>There are times when you will need to perform computations on measurements that are given in different units. In order to do so, you must convert the measurements into one single, common unit of measurement before performing your calculations.<\/p>\r\n<section class=\"textbox example\">An interior decorator needs border trim for a home she is wallpapering. She needs [latex]15[\/latex] feet of border trim for the living room, [latex]10[\/latex] yards of border trim for the bedroom, and [latex]27[\/latex] feet of border trim for the dining room. How many yards of border trim does she need?<br \/>\r\n[reveal-answer q=\"4331\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"4331\"]<br \/>\r\nYou need to find the total length of border trim that is required for all three rooms in the house. Since the measurements are given in different units we must first convert all measurements to the same unit of measurement. The question asks us to calculate the number of yards of border trim needed so it is best if we use yards as our common unit of measurement.First, we must convert the border trim for the living room. To convert [latex]15[\/latex] feet to yards we can use the conversion factor [latex]\\frac{1\\text{ yard}}{3\\text{ feet}}[\/latex]:\r\n\r\n<p style=\"text-align: center;\">[latex]\\frac{15\\text{ feet}}{1}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}= \\text{? yards}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{15\\cancel{\\text{ feet}}}{1}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}=5\\text{ yards}[\/latex]<\/p>\r\n<p>Since the border trim for the bedroom is given in yards, we can leave it as is.<\/p>\r\n<p>We now must convert the border trim for the dining room. Just like we did with the border trim for the living room, we can use the conversion factor [latex]\\frac{1\\text{ yard}}{3\\text{ feet}}[\/latex]:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{27\\text{ feet}}{1}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}= \\text{? yards}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{27\\cancel{\\text{ feet}}}{1}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}=9\\text{ yards}[\/latex]<\/p>\r\n<p>Now that we have all three numbers with the same unit, you can add the numbers together.<\/p>\r\n<p style=\"text-align: center;\">[latex]5\\text{ yards}+ 10\\text{ yards}+ 9\\text{ yards}=24\\text{ yards}[\/latex]<\/p>\r\n<p>Now consider if the question had asked for you to give the total calculation in feet. Do you expect that number to be larger or smaller than the total of the border trim in yards?<br \/>\r\n[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1854[\/ohm2_question]<\/section>","rendered":"<h2>Apply Unit Conversions With Length<\/h2>\n<p>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<p>Suppose you want to purchase tubing for a project, and you see two signs in a hardware store: <i>[latex]$1.88[\/latex] for [latex]2[\/latex] feet<\/i> of tubing and <i>[latex]$5.49[\/latex] for [latex]3[\/latex] yards<\/i> of tubing. If both types of tubing will work equally well for your project, which is the better price? In order to compare, you need to convert the measurements into one single, common unit of measurement.<\/p>\n<section class=\"textbox example\">Let\u2019s solve the tubing problem mentioned above. You are walking through a hardware store and notice two sales on tubing:<\/p>\n<ul>\n<li>[latex]3[\/latex] yards of Tubing A costs [latex]$5.49[\/latex].<\/li>\n<li>Tubing B sells for [latex]$1.88[\/latex] for [latex]2[\/latex] feet.<\/li>\n<\/ul>\n<p>Either tubing is acceptable for your project. Which tubing is less expensive?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q4330\">Show Solution<\/button><\/p>\n<div id=\"q4330\" class=\"hidden-answer\" style=\"display: none\">\n<p>Find the unit price for each tubing. This will make it easier to compare.<\/p>\n<p><strong>Tubing A<\/strong>: Find the cost per yard of Tubing A by dividing the cost of [latex]3[\/latex] yards of the tubing by [latex]3[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]3[\/latex] yards = [latex]$5.49[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{5.49}{3\\text{ yards}}=\\frac{\\$1.83}{1\\text{ yard}}[\/latex]<\/p>\n<p><strong>Tubing B<\/strong>: Tubing B is sold by the foot. Find the cost per foot by dividing [latex]$1.88[\/latex] by [latex]2[\/latex] feet.<\/p>\n<p style=\"text-align: center;\">[latex]2[\/latex] feet = [latex]$1.88[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1.88}{2\\text{ feet}}=\\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 [latex]1[\/latex] yard of each tubing.<\/p>\n<p>Tubing A: [latex]$1.83[\/latex] per yard<\/p>\n<p>Tubing B: [latex]$2.82[\/latex] per yard<\/p>\n<p>Tubing A is less expensive than Tubing B.\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1853\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1853&theme=lumen&iframe_resize_id=ohm1853&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>There are times when you will need to perform computations on measurements that are given in different units. In order to do so, you must convert the measurements into one single, common unit of measurement before performing your calculations.<\/p>\n<section class=\"textbox example\">An interior decorator needs border trim for a home she is wallpapering. She needs [latex]15[\/latex] feet of border trim for the living room, [latex]10[\/latex] yards of border trim for the bedroom, and [latex]27[\/latex] 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\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q4331\">Show Solution<\/button><\/p>\n<div id=\"q4331\" class=\"hidden-answer\" style=\"display: none\">\nYou need to find the total length of border trim that is required for all three rooms in the house. Since the measurements are given in different units we must first convert all measurements to the same unit of measurement. The question asks us to calculate the number of yards of border trim needed so it is best if we use yards as our common unit of measurement.First, we must convert the border trim for the living room. To convert [latex]15[\/latex] feet to yards we can use the conversion factor [latex]\\frac{1\\text{ yard}}{3\\text{ feet}}[\/latex]:<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{15\\text{ feet}}{1}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}= \\text{? yards}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{15\\cancel{\\text{ feet}}}{1}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}=5\\text{ yards}[\/latex]<\/p>\n<p>Since the border trim for the bedroom is given in yards, we can leave it as is.<\/p>\n<p>We now must convert the border trim for the dining room. Just like we did with the border trim for the living room, we can use the conversion factor [latex]\\frac{1\\text{ yard}}{3\\text{ feet}}[\/latex]:<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{27\\text{ feet}}{1}\\cdot\\frac{1\\text{ yard}}{3\\text{ feet}}= \\text{? yards}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{27\\cancel{\\text{ feet}}}{1}\\cdot\\frac{1\\text{ yard}}{3\\cancel{\\text{ feet}}}=9\\text{ yards}[\/latex]<\/p>\n<p>Now that we have all three numbers with the same unit, you can add the numbers together.<\/p>\n<p style=\"text-align: center;\">[latex]5\\text{ yards}+ 10\\text{ yards}+ 9\\text{ yards}=24\\text{ yards}[\/latex]<\/p>\n<p>Now consider if the question had asked for you to give the total calculation in feet. Do you expect that number to be larger or smaller than the total of the border trim in yards?\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1854\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1854&theme=lumen&iframe_resize_id=ohm1854&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":5,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":62,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/65"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":23,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/65\/revisions"}],"predecessor-version":[{"id":13479,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/65\/revisions\/13479"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/62"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/65\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=65"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=65"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=65"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=65"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}