{"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":"2025-09-02T18:28:54","modified_gmt":"2025-09-02T18:28:54","slug":"translating-word-phrases-into-expressions-with-integers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/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\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate word phrases that contain negative numbers, or opposites<\/li>\r\n<\/ul>\r\n<\/div>\r\nNow 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]\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTranslate each phrase into an expression with integers:\r\n<ol>\r\n \t<li>The opposite of positive fourteen<\/li>\r\n \t<li>The opposite of [latex]-11[\/latex]<\/li>\r\n \t<li>Negative sixteen<\/li>\r\n \t<li>Two minus negative seven<\/li>\r\n<\/ol>\r\nSolution:\r\n<ol id=\"eip-id1168466348672\" class=\"circled\">\r\n \t<li>The opposite of positive fourteen:\u00a0 [latex]-14[\/latex]<\/li>\r\n \t<li>The opposite of [latex]\u221211[\/latex]:\u00a0 [latex]-\\left(-11\\right)[\/latex]<\/li>\r\n \t<li>Negative sixteen:\u00a0 [latex]-16[\/latex]<\/li>\r\n \t<li>Two minus negative seven:\u00a0 [latex]2-\\left(-7\\right)[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question hide_question_numbers=1]144975[\/ohm_question]\r\n\r\n<\/div>\r\nAs 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.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate into an expression with integers:\r\n<ol>\r\n \t<li>The temperature is [latex]12[\/latex] degrees Fahrenheit below zero.<\/li>\r\n \t<li>The football team had a gain of [latex]3[\/latex] yards.<\/li>\r\n \t<li>The elevation of the Dead Sea is [latex]1,302[\/latex] feet below sea level.<\/li>\r\n \t<li>A checking account is overdrawn by [latex]$40[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"821025\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"821025\"]\r\n\r\nSolution\r\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.\r\n<table id=\"eip-id1166567530079\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td>The temperature is [latex]12[\/latex]\u00a0degrees Fahrenheit below zero.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><em>Below zero<\/em> tells us that [latex]12[\/latex] is a negative number.<\/td>\r\n<td>[latex]-12[\/latex] F<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1166568935976\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td>The football team had a gain of [latex]3[\/latex] yards.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>A <em>gain<\/em> tells us that [latex]3[\/latex] is a positive number.<\/td>\r\n<td>[latex]3[\/latex] yards<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1166568936114\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td>The elevation of the Dead Sea is [latex]1,302[\/latex] feet below sea level.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><em>Below sea level<\/em> tells us that [latex]1,302[\/latex] is a negative number.<\/td>\r\n<td>[latex]-1,302[\/latex] feet<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1166566291529\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>4.<\/td>\r\n<td>A checking account is overdrawn by [latex]$40[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><em>Overdrawn<\/em> tells us that [latex]40[\/latex] is a negative number.<\/td>\r\n<td>[latex]-$40[\/latex]<\/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 hide_question_numbers=1]144976[\/ohm_question]\r\n\r\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:\u00a0 [latex]-14[\/latex]<\/li>\n<li>The opposite of [latex]\u221211[\/latex]:\u00a0 [latex]-\\left(-11\\right)[\/latex]<\/li>\n<li>Negative sixteen:\u00a0 [latex]-16[\/latex]<\/li>\n<li>Two minus negative seven:\u00a0 [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&theme=oea&iframe_resize_id=ohm144975\" 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]\u00a0degrees 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&theme=oea&iframe_resize_id=ohm144976\" 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 Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3566","chapter","type-chapter","status-publish","hentry"],"part":1193,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3566","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3566\/revisions"}],"predecessor-version":[{"id":5678,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3566\/revisions\/5678"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/1193"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3566\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3566"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3566"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3566"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}