{"id":66,"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-3\/"},"modified":"2024-10-18T20:52:02","modified_gmt":"2024-10-18T20:52:02","slug":"us-units-of-measurement-learn-it-3","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/us-units-of-measurement-learn-it-3\/","title":{"raw":"US Units of Measurement: Learn It 3","rendered":"US Units of Measurement: Learn It 3"},"content":{"raw":"<h2>Weight<\/h2>\r\n<p><iframe src=\"https:\/\/lumenlearning.h5p.com\/content\/1291931925586624388\/embed\" width=\"1088\" height=\"637\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" aria-label=\"Weight Interactive\"><\/iframe><script src=\"https:\/\/lumenlearning.h5p.com\/js\/h5p-resizer.js\" charset=\"UTF-8\"><\/script><\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>units of weight<\/h3>\r\n<p>When you mention how heavy or light an object is, you are referring to its <b>weight<\/b>. Weight is measured in the U.S. customary system using three units: <strong>ounces<\/strong>, <strong>pounds<\/strong>, and <strong>tons<\/strong>.<\/p>\r\n<p>&nbsp;<\/p>\r\n<center>\r\n<table style=\"border-spacing: 0px;\" cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th style=\"text-align: center; width: 30%;\"\">Unit Equivalents<\/th>\r\n<th style=\"text-align: center;\">Conversion Factors <\/br>(heavier to lighter units of measurement)<\/th>\r\n<th style=\"text-align: center;\">Conversion Factors <\/br>(lighter to heavier units of measurement)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]1[\/latex] pound = [latex]16[\/latex] ounces<\/td>\r\n<td style=\"text-align: center;\">[latex]\\frac{16\\text{ ounces}}{1\\text{ pound}}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex] \\displaystyle \\frac{\\text{1 pound}}{\\text{16 ounces}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"text-align: center;\">[latex]1[\/latex] ton = [latex]2000[\/latex] pounds<\/td>\r\n<td style=\"text-align: center;\">[latex]\\frac{2000\\text{ pounds}}{1\\text{ ton}}[\/latex]<\/td>\r\n<td style=\"text-align: center;\">[latex] \\displaystyle \\frac{\\text{1 ton}}{\\text{2000 pounds}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/center>\r\n<\/div>\r\n<\/section>\r\n<p>Just like when converting between units of length, you can use the <b>factor <\/b><b>label <\/b><b>method<\/b> to convert weight from one unit of measure to another using the conversion factors. Remember, that by using the factor label method you can cancel the units out of the problem, just as if they were numbers.<\/p>\r\n<p>Study the example below to see how the factor label method can be used to convert [latex] \\displaystyle 2\\frac{1}{4}[\/latex] pounds to ounces.<\/p>\r\n<section class=\"textbox example\">How many ounces are in [latex] \\displaystyle 2\\frac{1}{4}[\/latex] pounds?<br \/>\r\n[reveal-answer q=\"4330\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"4330\"]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].Multiply by the conversion factor that relates ounces and pounds: [latex] \\displaystyle \\frac{16\\text{ ounces}}{1\\text{ pound}}[\/latex].\r\n\r\n\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\n<p>Write the mixed number as an improper fraction.<\/p>\r\n<p>The common unit, pound, can be cancelled because it appears in both the numerator and denominator.<\/p>\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\n<p>Multiply and simplify.<\/p>\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<p>There are [latex]36[\/latex] ounces in [latex] \\displaystyle 2\\frac{1}{4}[\/latex] pounds.<br \/>\r\n[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1858[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1857[\/ohm2_question]<\/section>","rendered":"<h2>Weight<\/h2>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumenlearning.h5p.com\/content\/1291931925586624388\/embed\" width=\"1088\" height=\"637\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" aria-label=\"Weight Interactive\"><\/iframe><script src=\"https:\/\/lumenlearning.h5p.com\/js\/h5p-resizer.js\" charset=\"UTF-8\"><\/script><\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>units of weight<\/h3>\n<p>When you mention how heavy or light an object is, you are referring to its <b>weight<\/b>. Weight is measured in the U.S. customary system using three units: <strong>ounces<\/strong>, <strong>pounds<\/strong>, and <strong>tons<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;\">\n<table style=\"border-spacing: 0px;\" cellpadding=\"0\">\n<thead>\n<tr>\n<th style=\"text-align: center; width: 30%;\">Unit Equivalents<\/th>\n<th style=\"text-align: center;\">Conversion Factors (heavier to lighter units of measurement)<\/th>\n<th style=\"text-align: center;\">Conversion Factors (lighter to heavier units of measurement)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">[latex]1[\/latex] pound = [latex]16[\/latex] ounces<\/td>\n<td style=\"text-align: center;\">[latex]\\frac{16\\text{ ounces}}{1\\text{ pound}}[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{1 pound}}{\\text{16 ounces}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">[latex]1[\/latex] ton = [latex]2000[\/latex] pounds<\/td>\n<td style=\"text-align: center;\">[latex]\\frac{2000\\text{ pounds}}{1\\text{ ton}}[\/latex]<\/td>\n<td style=\"text-align: center;\">[latex]\\displaystyle \\frac{\\text{1 ton}}{\\text{2000 pounds}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/section>\n<p>Just like when converting between units of length, you can use the <b>factor <\/b><b>label <\/b><b>method<\/b> to convert weight from one unit of measure to another using the conversion factors. Remember, that by using the factor label method you can cancel the units out of the problem, just as if they were numbers.<\/p>\n<p>Study the example below to see how the factor label method can be used to convert [latex]\\displaystyle 2\\frac{1}{4}[\/latex] pounds to ounces.<\/p>\n<section class=\"textbox example\">How many ounces are in [latex]\\displaystyle 2\\frac{1}{4}[\/latex] pounds?<\/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\">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].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, pound, 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>There are [latex]36[\/latex] ounces in [latex]\\displaystyle 2\\frac{1}{4}[\/latex] pounds.\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1858\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1858&theme=lumen&iframe_resize_id=ohm1858&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1857\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1857&theme=lumen&iframe_resize_id=ohm1857&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":6,"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\/66"}],"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":22,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/66\/revisions"}],"predecessor-version":[{"id":13827,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/66\/revisions\/13827"}],"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\/66\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=66"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=66"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=66"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=66"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}