{"id":67,"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-4\/"},"modified":"2024-10-18T20:52:03","modified_gmt":"2024-10-18T20:52:03","slug":"us-units-of-measurement-learn-it-4","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/us-units-of-measurement-learn-it-4\/","title":{"raw":"US Units of Measurement: Learn It 4","rendered":"US Units of Measurement: Learn It 4"},"content":{"raw":"<h2>Apply Unit Conversions With Weight<\/h2>\r\n<p>Just like when we wanted to solve problems with different units of length \u2013 If you are solving problems that include weights involving more than one unit of weight, you will need to convert from one unit 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 are wanting to find the best deal on coffee. The grocery store sells a [latex]36[\/latex] ounce canister of ground coffee for [latex]$14[\/latex], and sells bulk coffee for [latex]$9[\/latex] per pound. Which is the better deal? 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 coffee problem mentioned above. The grocery store sells a [latex]36[\/latex] ounce canister of ground coffee for [latex]$14[\/latex], and sells bulk coffee for [latex]$7[\/latex] per pound. Which is the better deal?<br \/>\r\n[reveal-answer q=\"4330\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"4330\"]Since canister pricing is for ounces, convert the weight of the canister to pounds.First use the factor label method to convert ounces to pounds.\r\n\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\n<p>Now calculate the price per pound by dividing.<\/p>\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 $6.22[\/latex] per pound<\/p>\r\n<p>The canister is a better deal at [latex]$6.22[\/latex] per pound.<br \/>\r\n[\/hidden-answer]<\/p>\r\n<\/section>\r\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>\r\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>\r\n<p>Here is an example of a problem that requires converting between units of weights.<\/p>\r\n<section class=\"textbox example\">A municipal trash facility allows a person to throw away a maximum of [latex]30[\/latex] pounds of trash per week. Last week, [latex]140[\/latex] people threw away the maximum allowable trash. How many tons of trash did this equal?<br \/>\r\n[reveal-answer q=\"4331\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"4331\"]Determine the total trash for the week expressed in pounds.If [latex]140[\/latex] people each throw away [latex]30[\/latex] pounds, you can find the total by multiplying.\r\n\r\n<p style=\"text-align: center;\">[latex]140\\cdot30\\text{ pounds}=4,200\\text{ pounds}[\/latex]<\/p>\r\n<p>Then convert [latex]4,200[\/latex] pounds to tons. Reason about your answer. Since a ton is heavier than a pound, expect your answer to be a number less than [latex]4,200[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]4,200\\text{ pounds}=\\text{___ tons}[\/latex]<\/p>\r\n<p>Find the conversion factor appropriate for the situation:<\/p>\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\n<p>Multiply and simplify.<\/p>\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\n<p>The total amount of trash generated is [latex] \\displaystyle 2\\frac{1}{10}[\/latex] tons.<br \/>\r\n[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1860[\/ohm2_question]<\/section>","rendered":"<h2>Apply Unit Conversions With Weight<\/h2>\n<p>Just like when we wanted to solve problems with different units of length \u2013 If you are solving problems that include weights involving more than one unit of weight, you will need to convert from one unit 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 are wanting to find the best deal on coffee. The grocery store sells a [latex]36[\/latex] ounce canister of ground coffee for [latex]$14[\/latex], and sells bulk coffee for [latex]$9[\/latex] per pound. Which is the better deal? 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 coffee problem mentioned above. The grocery store sells a [latex]36[\/latex] ounce canister of ground coffee for [latex]$14[\/latex], and sells bulk coffee for [latex]$7[\/latex] per pound. Which is the better deal?<\/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\">Since canister pricing is for ounces, convert the weight of the canister to pounds.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 $6.22[\/latex] per pound<\/p>\n<p>The canister is a better deal at [latex]$6.22[\/latex] per pound.\n<\/div>\n<\/div>\n<\/section>\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 of weights.<\/p>\n<section class=\"textbox example\">A municipal trash facility allows a person to throw away a maximum of [latex]30[\/latex] pounds of trash per week. Last week, [latex]140[\/latex] people threw away the maximum allowable trash. How many tons of trash did this equal?<\/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\">Determine the total trash for the week expressed in pounds.If [latex]140[\/latex] people each throw away [latex]30[\/latex] 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 [latex]4,200[\/latex] pounds to tons. Reason about your answer. Since a ton is heavier than a pound, expect your answer to be a number less than [latex]4,200[\/latex].<\/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.\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1860\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1860&theme=lumen&iframe_resize_id=ohm1860&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":7,"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\/67"}],"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":12,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/67\/revisions"}],"predecessor-version":[{"id":13481,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/67\/revisions\/13481"}],"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\/67\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=67"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=67"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=67"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}