{"id":3586,"date":"2019-12-31T18:00:02","date_gmt":"2019-12-31T18:00:02","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3586"},"modified":"2021-02-05T23:49:15","modified_gmt":"2021-02-05T23:49:15","slug":"translating-word-phrases-into-expressions-with-integers-using-multiplication-and-division","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/translating-word-phrases-into-expressions-with-integers-using-multiplication-and-division\/","title":{"raw":"Translating Word Phrases into Expressions With Integers Using Multiplication and Division","rendered":"Translating Word Phrases into Expressions With Integers Using Multiplication and Division"},"content":{"raw":"<div class=\"textbox learning-objectives\"><h3>Learning Outcomes<\/h3><ul><li>Translate expressions with integers and simplify<\/li><\/ul><\/div>Once again, all our prior work translating words to algebra transfers to phrases that include both multiplying and dividing integers. Remember that the key word for multiplication is <em>product<\/em> and for division is <em>quotient.<\/em>\n\n<div class=\"textbox exercises\"><h3>Exercises<\/h3>Translate to an algebraic expression and simplify if possible: the product of [latex]-2[\/latex] and [latex]14[\/latex].\n\nSolution:\nThe word <em>product<\/em> tells us to multiply.\n\n<table id=\"eip-id1168469702004\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td><\/td><td>the product of [latex]-2[\/latex] and [latex]14[\/latex]<\/td><\/tr><tr><td>Translate.<\/td><td>[latex]\\left(-2\\right)\\left(14\\right)[\/latex]<\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]-28[\/latex]<\/td><\/tr><\/tbody><\/table><\/div>&nbsp;\n\n<div class=\"textbox key-takeaways\"><h3>TRY&nbsp;IT<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145358&amp;theme=oea&amp;iframe_resize_id=mom1[\/embed]\n\n\n\n<\/div>&nbsp;\n\n<div class=\"textbox exercises\"><h3>Exercises<\/h3>Translate to an algebraic expression and simplify if possible: the quotient of [latex]-56[\/latex] and [latex]-7[\/latex].\n[reveal-answer q=\"30599\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"30599\"]\n\nSolution:\nThe word <em>quotient<\/em> tells us to divide.\n\n<table id=\"eip-id1168469522858\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td><\/td><td>the quotient of [latex]\u221256[\/latex] and [latex]\u22127[\/latex]<\/td><\/tr><tr><td>Translate.<\/td><td>[latex]-56\\div \\left(-7\\right)[\/latex]<\/td><\/tr><tr><td>Simplify.<\/td><td>[latex]8[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>&nbsp;\n\n<div class=\"textbox key-takeaways\"><h3>TRY&nbsp;IT<\/h3>[ohm_question]145360[\/ohm_question]\n\n<\/div>The following video shows more examples of how to translate expressions that contain integer multiplication and division.\n\nhttps:\/\/youtu.be\/FWI4pzT3GpY\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate expressions with integers and simplify<\/li>\n<\/ul>\n<\/div>\n<p>Once again, all our prior work translating words to algebra transfers to phrases that include both multiplying and dividing integers. Remember that the key word for multiplication is <em>product<\/em> and for division is <em>quotient.<\/em><\/p>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Translate to an algebraic expression and simplify if possible: the product of [latex]-2[\/latex] and [latex]14[\/latex].<\/p>\n<p>Solution:<br \/>\nThe word <em>product<\/em> tells us to multiply.<\/p>\n<table id=\"eip-id1168469702004\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>the product of [latex]-2[\/latex] and [latex]14[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]\\left(-2\\right)\\left(14\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-28[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY&nbsp;IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145358\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145358&#38;theme=oea&#38;iframe_resize_id=ohm145358&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Translate to an algebraic expression and simplify if possible: the quotient of [latex]-56[\/latex] and [latex]-7[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q30599\">Show Solution<\/span><\/p>\n<div id=\"q30599\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe word <em>quotient<\/em> tells us to divide.<\/p>\n<table id=\"eip-id1168469522858\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>the quotient of [latex]\u221256[\/latex] and [latex]\u22127[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]-56\\div \\left(-7\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]8[\/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&nbsp;IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145360\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145360&theme=oea&iframe_resize_id=ohm145360&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The following video shows more examples of how to translate expressions that contain integer multiplication and division.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Write and Determine Products and Quotients From Statements\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/FWI4pzT3GpY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\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-3586\">\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>Write and Determine Products and Quotients From Statements. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/FWI4pzT3GpY\">https:\/\/youtu.be\/FWI4pzT3GpY<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 145358, 145360. <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":16,"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\":\"Write and Determine Products and Quotients From Statements\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/FWI4pzT3GpY\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 145358, 145360\",\"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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