{"id":9233,"date":"2017-05-02T19:45:05","date_gmt":"2017-05-02T19:45:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9233"},"modified":"2026-01-21T15:01:37","modified_gmt":"2026-01-21T15:01:37","slug":"dividing-whole-numbers-in-applications","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/dividing-whole-numbers-in-applications\/","title":{"raw":"Dividing Whole Numbers in Applications","rendered":"Dividing Whole Numbers in Applications"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate word phrases into mathematical expressions representing division<\/li>\r\n \t<li>Solve word problems by using division<\/li>\r\n \t<li>Convert math expressions and word problems between division and multiplication<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Translate Word Phrases to Math Notation<\/h2>\r\nEarlier in this section, we translated math notation for division into words. Now we\u2019ll translate word phrases into math notation. Some of the words that indicate division are given in the table below.\r\n<table style=\"width: 60%;\" summary=\"A table with 4 columns and 3 rows. The first column is labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Operation<\/th>\r\n<th>Word Phrase<\/th>\r\n<th>Example<\/th>\r\n<th>Expression<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>Division<\/td>\r\n<td>divided by\r\n\r\nquotient of\r\n\r\ndivided into<\/td>\r\n<td>[latex]12[\/latex] divided by [latex]4[\/latex]\r\n\r\nthe quotient of [latex]12[\/latex] and [latex]4[\/latex]\r\n\r\n[latex]4[\/latex] divided into [latex]12[\/latex]<\/td>\r\n<td>[latex]12\\div 4[\/latex]\r\n\r\n[latex]\\frac{12}{4}[\/latex]\r\n\r\n[latex]12\\text{\/}4[\/latex]\r\n\r\n[latex]4\\overline{)12}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and simplify: the quotient of [latex]51[\/latex] and [latex]17[\/latex].\r\n\r\nSolution:\r\n<p style=\"padding-left: 30px;\">the quotient of 51 and 17: \u00a0 The word <em>quotient<\/em> tells us to divide<\/p>\r\n<p style=\"padding-left: 30px;\">translate: \u00a0 [latex]51\\div 17[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">divide: \u00a0 [latex]3[\/latex]<\/p>\r\n<p style=\"padding-left: 30px;\">We could just as correctly have translated <em>the quotient of<\/em> [latex]51[\/latex] <em>and<\/em>\u00a0 [latex]17[\/latex] using the notation\r\n[latex]17\\overline{)51}[\/latex] \u00a0 or \u00a0[latex]\\frac{51}{17}[\/latex].<\/p>\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]188579[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Divide Whole Numbers in Applications<\/h2>\r\nWe will use the same strategy we used in previous sections to solve applications. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify it to get the answer. Finally, we write a sentence to answer the question.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nCecelia bought a [latex]\\text{160-ounce}[\/latex] box of oatmeal at the big box store. She wants to divide the [latex]160[\/latex] ounces of oatmeal into [latex]\\text{8-ounce}[\/latex] servings. She will put each serving into a plastic bag so she can take one bag to work each day. How many servings will she get from the big box?\r\n\r\nSolution\r\nWe are asked to find how many servings she will get from the big box.\r\n<table id=\"eip-id1168287366351\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\" \">\r\n<tbody>\r\n<tr>\r\n<td>Write a phrase.<\/td>\r\n<td>[latex]160[\/latex] ounces divided by [latex]8[\/latex] ounces<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to math notation.<\/td>\r\n<td>[latex]160\\div 8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify by dividing.<\/td>\r\n<td>[latex]20[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence to answer the question.<\/td>\r\n<td>Cecelia will get [latex]20[\/latex] servings from the big box.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144646&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\r\n\r\n<\/div>\r\n<span style=\"color: #000000;\">In the following video, we show another example of how to translate a situation into an algebraic expression.<\/span>\r\n\r\nhttps:\/\/youtu.be\/y2K-S3tscz0\r\n\r\nNow that we have practiced using both multiplication and division to solve application problems, let's combine both skills to answer the next question.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTo save money and reduce waste, Frances bought a giant box of crackers with the plan to divide them up into small bags to take to school with her every day. The box contains [latex]48[\/latex] oz. of crackers. Answer the following questions about Frances and her crackers:\r\n1) How many [latex]2[\/latex] oz. bags of crackers can Frances make from the big bag?\r\n2) If there are [latex]150[\/latex] calories in a [latex]1[\/latex] oz serving of crackers, how many calories are each 2 oz. bag?\r\n[reveal-answer q=\"241184\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"241184\"]\r\n\r\n1. We are asked to find how many [latex]2[\/latex] oz. bags can be made from [latex]48[\/latex] oz.\r\n<table id=\"eip-id1168287366351\" class=\"unnumbered unstyled\" summary=\" \">\r\n<tbody>\r\n<tr>\r\n<td>Write a phrase.<\/td>\r\n<td>[latex]48[\/latex]\u00a0ounces divided by[latex]2[\/latex] ounces<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to math notation.<\/td>\r\n<td>[latex]48\\div 2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify by dividing.<\/td>\r\n<td>[latex]24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence to answer the question.<\/td>\r\n<td>Frances\u00a0will get [latex]24[\/latex] servings from the big box.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. We are asked how many calories are in each [latex]2[\/latex]\u00a0oz. bag of crackers.\r\n<table id=\"eip-id1168287366351\" class=\"unnumbered unstyled\" summary=\" \">\r\n<tbody>\r\n<tr>\r\n<td>Write a phrase.<\/td>\r\n<td>[latex]150[\/latex] \u00a0times [latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate to math notation.<\/td>\r\n<td>[latex]150\\cdot 2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify by multiplying.<\/td>\r\n<td>[latex]300[\/latex] calories<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence to answer the question.<\/td>\r\n<td>There are [latex]300[\/latex]\u00a0calories in each [latex]2[\/latex] oz. bag\u00a0of crackers.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<span style=\"color: #000000;\">In the following video, we show another example of how to translate a situation that contains both multiplication and division into an algebraic expression.<\/span>\r\n\r\nhttps:\/\/youtu.be\/DneLJVZDL7k\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]104843[\/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 into mathematical expressions representing division<\/li>\n<li>Solve word problems by using division<\/li>\n<li>Convert math expressions and word problems between division and multiplication<\/li>\n<\/ul>\n<\/div>\n<h2>Translate Word Phrases to Math Notation<\/h2>\n<p>Earlier in this section, we translated math notation for division into words. Now we\u2019ll translate word phrases into math notation. Some of the words that indicate division are given in the table below.<\/p>\n<table style=\"width: 60%;\" summary=\"A table with 4 columns and 3 rows. The first column is labeled\">\n<thead>\n<tr valign=\"top\">\n<th>Operation<\/th>\n<th>Word Phrase<\/th>\n<th>Example<\/th>\n<th>Expression<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Division<\/td>\n<td>divided by<\/p>\n<p>quotient of<\/p>\n<p>divided into<\/td>\n<td>[latex]12[\/latex] divided by [latex]4[\/latex]<\/p>\n<p>the quotient of [latex]12[\/latex] and [latex]4[\/latex]<\/p>\n<p>[latex]4[\/latex] divided into [latex]12[\/latex]<\/td>\n<td>[latex]12\\div 4[\/latex]<\/p>\n<p>[latex]\\frac{12}{4}[\/latex]<\/p>\n<p>[latex]12\\text{\/}4[\/latex]<\/p>\n<p>[latex]4\\overline{)12}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and simplify: the quotient of [latex]51[\/latex] and [latex]17[\/latex].<\/p>\n<p>Solution:<\/p>\n<p style=\"padding-left: 30px;\">the quotient of 51 and 17: \u00a0 The word <em>quotient<\/em> tells us to divide<\/p>\n<p style=\"padding-left: 30px;\">translate: \u00a0 [latex]51\\div 17[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">divide: \u00a0 [latex]3[\/latex]<\/p>\n<p style=\"padding-left: 30px;\">We could just as correctly have translated <em>the quotient of<\/em> [latex]51[\/latex] <em>and<\/em>\u00a0 [latex]17[\/latex] using the notation<br \/>\n[latex]17\\overline{)51}[\/latex] \u00a0 or \u00a0[latex]\\frac{51}{17}[\/latex].<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm188579\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=188579&theme=oea&iframe_resize_id=ohm188579&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Divide Whole Numbers in Applications<\/h2>\n<p>We will use the same strategy we used in previous sections to solve applications. First, we determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify it to get the answer. Finally, we write a sentence to answer the question.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Cecelia bought a [latex]\\text{160-ounce}[\/latex] box of oatmeal at the big box store. She wants to divide the [latex]160[\/latex] ounces of oatmeal into [latex]\\text{8-ounce}[\/latex] servings. She will put each serving into a plastic bag so she can take one bag to work each day. How many servings will she get from the big box?<\/p>\n<p>Solution<br \/>\nWe are asked to find how many servings she will get from the big box.<\/p>\n<table id=\"eip-id1168287366351\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\"\">\n<tbody>\n<tr>\n<td>Write a phrase.<\/td>\n<td>[latex]160[\/latex] ounces divided by [latex]8[\/latex] ounces<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]160\\div 8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify by dividing.<\/td>\n<td>[latex]20[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>Cecelia will get [latex]20[\/latex] servings from the big box.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144646\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144646&#38;theme=oea&#38;iframe_resize_id=ohm144646&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p><span style=\"color: #000000;\">In the following video, we show another example of how to translate a situation into an algebraic expression.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Divide Whole Numbers to Solve Applications\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/y2K-S3tscz0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Now that we have practiced using both multiplication and division to solve application problems, let&#8217;s combine both skills to answer the next question.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>To save money and reduce waste, Frances bought a giant box of crackers with the plan to divide them up into small bags to take to school with her every day. The box contains [latex]48[\/latex] oz. of crackers. Answer the following questions about Frances and her crackers:<br \/>\n1) How many [latex]2[\/latex] oz. bags of crackers can Frances make from the big bag?<br \/>\n2) If there are [latex]150[\/latex] calories in a [latex]1[\/latex] oz serving of crackers, how many calories are each 2 oz. bag?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q241184\">Show Solution<\/span><\/p>\n<div id=\"q241184\" class=\"hidden-answer\" style=\"display: none\">\n<p>1. We are asked to find how many [latex]2[\/latex] oz. bags can be made from [latex]48[\/latex] oz.<\/p>\n<table id=\"eip-id1168287366351\" class=\"unnumbered unstyled\" summary=\"\">\n<tbody>\n<tr>\n<td>Write a phrase.<\/td>\n<td>[latex]48[\/latex]\u00a0ounces divided by[latex]2[\/latex] ounces<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]48\\div 2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify by dividing.<\/td>\n<td>[latex]24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>Frances\u00a0will get [latex]24[\/latex] servings from the big box.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>2. We are asked how many calories are in each [latex]2[\/latex]\u00a0oz. bag of crackers.<\/p>\n<table id=\"eip-id1168287366351\" class=\"unnumbered unstyled\" summary=\"\">\n<tbody>\n<tr>\n<td>Write a phrase.<\/td>\n<td>[latex]150[\/latex] \u00a0times [latex]2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]150\\cdot 2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify by multiplying.<\/td>\n<td>[latex]300[\/latex] calories<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>There are [latex]300[\/latex]\u00a0calories in each [latex]2[\/latex] oz. bag\u00a0of crackers.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p><span style=\"color: #000000;\">In the following video, we show another example of how to translate a situation that contains both multiplication and division into an algebraic expression.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Divide and Multiply Whole Numbers to Solve Applications\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/DneLJVZDL7k?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm104843\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=104843&theme=oea&iframe_resize_id=ohm104843&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-9233\">\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>Divide and Multiply Whole Numbers to Solve Applications. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/DneLJVZDL7k\">https:\/\/youtu.be\/DneLJVZDL7k<\/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>Divide Whole Numbers to Solve Applications. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/y2K-S3tscz0\">https:\/\/youtu.be\/y2K-S3tscz0<\/a>. <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: 144450, 144646. <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 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