{"id":3566,"date":"2019-12-31T17:03:56","date_gmt":"2019-12-31T17:03:56","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3566"},"modified":"2021-02-05T23:48:56","modified_gmt":"2021-02-05T23:48:56","slug":"translating-word-phrases-into-expressions-with-integers","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/translating-word-phrases-into-expressions-with-integers\/","title":{"raw":"Translating Word Phrases into Expressions With Integers","rendered":"Translating Word Phrases into Expressions With Integers"},"content":{"raw":"<div class=\"textbox learning-objectives\"><h3>Learning Outcomes<\/h3><ul><li>Translate word phrases that contain negative numbers, or opposites<\/li><\/ul><\/div>Now we can translate word phrases into expressions with integers. Look for words that indicate a negative sign. For example, the word <em>negative<\/em> in \"negative twenty\" indicates [latex]-20[\/latex]. So does the word <em>opposite<\/em> in \"the opposite of [latex]20\\text{.\"}[\/latex]\n\n<div class=\"textbox exercises\"><h3>Example<\/h3>Translate each phrase into an expression with integers:\n\n<ol><li>The opposite of positive fourteen<\/li><li>The opposite of [latex]-11[\/latex]<\/li><li>Negative sixteen<\/li><li>Two minus negative seven<\/li><\/ol>Solution:\n\n<ol id=\"eip-id1168466348672\" class=\"circled\"><li>The opposite of positive fourteen:&nbsp; [latex]-14[\/latex]<\/li><li>The opposite of [latex]\u221211[\/latex]:&nbsp; [latex]-\\left(-11\\right)[\/latex]<\/li><li>Negative sixteen:&nbsp; [latex]-16[\/latex]<\/li><li>Two minus negative seven:&nbsp; [latex]2-\\left(-7\\right)[\/latex]<\/li><\/ol><\/div>&nbsp;\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144975&amp;theme=oea&amp;iframe_resize_id=mom1[\/embed]\n\n\n\n<\/div>As we saw at the start of this section, negative numbers are needed to describe many real-world situations. We\u2019ll look at some more applications of negative numbers in the next example.\n\n<div class=\"textbox exercises\"><h3>example<\/h3>Translate into an expression with integers:\n\n<ol><li>The temperature is [latex]12[\/latex] degrees Fahrenheit below zero.<\/li><li>The football team had a gain of [latex]3[\/latex] yards.<\/li><li>The elevation of the Dead Sea is [latex]1,302[\/latex] feet below sea level.<\/li><li>A checking account is overdrawn by [latex]$40[\/latex]<\/li><\/ol>[reveal-answer q=\"821025\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"821025\"]\n\nSolution\nLook for key phrases in each sentence. Then look for words that indicate negative signs. Don\u2019t forget to include units of measurement described in the sentence.\n\n<table id=\"eip-id1166567530079\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td>1.<\/td><td>The temperature is [latex]12[\/latex]&nbsp;degrees Fahrenheit below zero.<\/td><\/tr><tr><td><em>Below zero<\/em> tells us that [latex]12[\/latex] is a negative number.<\/td><td>[latex]-12[\/latex] F<\/td><\/tr><\/tbody><\/table><table id=\"eip-id1166568935976\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td>2.<\/td><td>The football team had a gain of [latex]3[\/latex] yards.<\/td><\/tr><tr><td>A <em>gain<\/em> tells us that [latex]3[\/latex] is a positive number.<\/td><td>[latex]3[\/latex] yards<\/td><\/tr><\/tbody><\/table><table id=\"eip-id1166568936114\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td>3.<\/td><td>The elevation of the Dead Sea is [latex]1,302[\/latex] feet below sea level.<\/td><\/tr><tr><td><em>Below sea level<\/em> tells us that [latex]1,302[\/latex] is a negative number.<\/td><td>[latex]-1,302[\/latex] feet<\/td><\/tr><\/tbody><\/table><table id=\"eip-id1166566291529\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td>4.<\/td><td>A checking account is overdrawn by [latex]$40[\/latex].<\/td><\/tr><tr><td><em>Overdrawn<\/em> tells us that [latex]40[\/latex] is a negative number.<\/td><td>[latex]-$40[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>&nbsp;\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144976&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\n\n\n\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate word phrases that contain negative numbers, or opposites<\/li>\n<\/ul>\n<\/div>\n<p>Now we can translate word phrases into expressions with integers. Look for words that indicate a negative sign. For example, the word <em>negative<\/em> in &#8220;negative twenty&#8221; indicates [latex]-20[\/latex]. So does the word <em>opposite<\/em> in &#8220;the opposite of [latex]20\\text{.\"}[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Translate each phrase into an expression with integers:<\/p>\n<ol>\n<li>The opposite of positive fourteen<\/li>\n<li>The opposite of [latex]-11[\/latex]<\/li>\n<li>Negative sixteen<\/li>\n<li>Two minus negative seven<\/li>\n<\/ol>\n<p>Solution:<\/p>\n<ol id=\"eip-id1168466348672\" class=\"circled\">\n<li>The opposite of positive fourteen:&nbsp; [latex]-14[\/latex]<\/li>\n<li>The opposite of [latex]\u221211[\/latex]:&nbsp; [latex]-\\left(-11\\right)[\/latex]<\/li>\n<li>Negative sixteen:&nbsp; [latex]-16[\/latex]<\/li>\n<li>Two minus negative seven:&nbsp; [latex]2-\\left(-7\\right)[\/latex]<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144975\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144975&#38;theme=oea&#38;iframe_resize_id=ohm144975&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>As we saw at the start of this section, negative numbers are needed to describe many real-world situations. We\u2019ll look at some more applications of negative numbers in the next example.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate into an expression with integers:<\/p>\n<ol>\n<li>The temperature is [latex]12[\/latex] degrees Fahrenheit below zero.<\/li>\n<li>The football team had a gain of [latex]3[\/latex] yards.<\/li>\n<li>The elevation of the Dead Sea is [latex]1,302[\/latex] feet below sea level.<\/li>\n<li>A checking account is overdrawn by [latex]$40[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q821025\">Show Solution<\/span><\/p>\n<div id=\"q821025\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nLook for key phrases in each sentence. Then look for words that indicate negative signs. Don\u2019t forget to include units of measurement described in the sentence.<\/p>\n<table id=\"eip-id1166567530079\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td>The temperature is [latex]12[\/latex]&nbsp;degrees Fahrenheit below zero.<\/td>\n<\/tr>\n<tr>\n<td><em>Below zero<\/em> tells us that [latex]12[\/latex] is a negative number.<\/td>\n<td>[latex]-12[\/latex] F<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1166568935976\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td>The football team had a gain of [latex]3[\/latex] yards.<\/td>\n<\/tr>\n<tr>\n<td>A <em>gain<\/em> tells us that [latex]3[\/latex] is a positive number.<\/td>\n<td>[latex]3[\/latex] yards<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1166568936114\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td>The elevation of the Dead Sea is [latex]1,302[\/latex] feet below sea level.<\/td>\n<\/tr>\n<tr>\n<td><em>Below sea level<\/em> tells us that [latex]1,302[\/latex] is a negative number.<\/td>\n<td>[latex]-1,302[\/latex] feet<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1166566291529\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>4.<\/td>\n<td>A checking account is overdrawn by [latex]$40[\/latex].<\/td>\n<\/tr>\n<tr>\n<td><em>Overdrawn<\/em> tells us that [latex]40[\/latex] is a negative number.<\/td>\n<td>[latex]-$40[\/latex]<\/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=\"ohm144976\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144976&#38;theme=oea&#38;iframe_resize_id=ohm144976&#38;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-3566\">\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>Revision and Adaptation. <strong>Provided 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>Question ID: 144975, 144976. <strong>Authored by<\/strong>: Alyson Day. <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>: IMathAS Community License CC-BY + GPL<\/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":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Question ID: 144975, 144976\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen 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