{"id":3686,"date":"2020-01-29T03:14:50","date_gmt":"2020-01-29T03:14:50","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3686"},"modified":"2021-02-05T23:51:06","modified_gmt":"2021-02-05T23:51:06","slug":"using-the-multiplication-and-division-properties-of-zero","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/using-the-multiplication-and-division-properties-of-zero\/","title":{"raw":"Using the Multiplication and Division Properties of Zero","rendered":"Using the Multiplication and Division Properties of Zero"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify the multiplication and division\u00a0properties of zero<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Use the Properties of Zero<\/h2>\r\nWe have already learned that zero is the additive identity, since it can be added to any number without changing the number\u2019s identity. But zero also has some special properties when it comes to multiplication and division.\r\n<h2>Multiplication by Zero<\/h2>\r\nWhat happens when you multiply a number by [latex]0?[\/latex] Multiplying by [latex]0[\/latex] makes the product equal zero. The product of any real number and [latex]0[\/latex] is [latex]0[\/latex].\r\n<div class=\"textbox shaded\">\r\n<h3>Multiplication by Zero<\/h3>\r\nFor any real number [latex]a[\/latex],\r\n<p style=\"padding-left: 60px\">[latex]a\\cdot 0=0[\/latex]<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nSimplify:\r\n1. [latex]-8\\cdot 0[\/latex]\r\n2. [latex]\\Large\\frac{5}{12}\\normalsize\\cdot 0[\/latex]\r\n3. [latex]0\\left(2.94\\right)[\/latex]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468273316\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr style=\"height: 15.7969px\">\r\n<td style=\"height: 15.7969px\">1.<\/td>\r\n<td style=\"height: 15.7969px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\"><\/td>\r\n<td style=\"height: 15px\">[latex]-8\\cdot 0[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">The product of any real number and 0 is 0.<\/td>\r\n<td style=\"height: 15px\">[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466080054\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr style=\"height: 15.3906px\">\r\n<td style=\"height: 15.3906px\">2.<\/td>\r\n<td style=\"height: 15.3906px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\"><\/td>\r\n<td style=\"height: 15px\">[latex]\\Large\\frac{5}{12}\\normalsize\\cdot 0[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">The product of any real number and 0 is 0.<\/td>\r\n<td style=\"height: 15px\">[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468270195\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0\\left(2.94\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The product of any real number and 0 is 0.<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n[ohm_question]146484[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Dividing with Zero<\/h2>\r\nWhat about dividing with [latex]0?[\/latex] Think about a real example: if there are no cookies in the cookie jar and three people want to share them, how many cookies would each person get? There are [latex]0[\/latex] cookies to share, so each person gets [latex]0[\/latex] cookies.\r\n<p style=\"text-align: center\">[latex]0\\div 3=0[\/latex]<\/p>\r\nRemember that we can always check division with the related multiplication fact. So, we know that\r\n<p style=\"text-align: center\">[latex]0\\div 3=0\\text{ because }0\\cdot 3=0[\/latex]<\/p>\r\n<strong>Tip<\/strong>: If we think of 0\/4 in terms of pizza, where we have 4 slices and you get 0.\u00a0 This could happen, but you would get 0!\r\n<div class=\"textbox shaded\">\r\n<h3>Division of Zero<\/h3>\r\nFor any real number [latex]a[\/latex], except [latex]0,\\Large\\frac{0}{a}\\normalsize =0[\/latex] and [latex]0\\div a=0[\/latex].\r\n\r\nZero divided by any real number except zero is zero.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nSimplify:\r\n1. [latex]0\\div 5[\/latex]\r\n2. [latex]\\Large\\frac{0}{-2}[\/latex]\r\n3. [latex]0\\div\\Large\\frac{7}{8}[\/latex]\r\n[reveal-answer q=\"340688\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"340688\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469701576\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0\\div 5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Zero divided by any real number, except 0, is zero.<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468275715\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{0}{-2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Zero divided by any real number, except 0, is zero.<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168466092352\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]0\\div\\Large\\frac{7}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Zero divided by any real number, except 0, is zero.<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n[ohm_question]146485[\/ohm_question]\r\n\r\n<\/div>\r\nNow let\u2019s think about dividing a number <em>by<\/em> zero. What is the result of dividing [latex]4[\/latex] by [latex]0?[\/latex] Think about the related multiplication fact. Is there a number that multiplied by [latex]0[\/latex] gives [latex]4?[\/latex]\r\n<p style=\"text-align: center\">[latex]4\\div 0=[\/latex]means [latex]x\\cdot {0}=4[\/latex]<\/p>\r\nSince any real number multiplied by [latex]0[\/latex] equals [latex]0[\/latex], there is no real number that can be multiplied by [latex]0[\/latex] to obtain [latex]4[\/latex]. We can conclude that there is no answer to [latex]4\\div 0[\/latex], and so we say that division by zero is undefined.\r\n\r\n&nbsp;\r\n\r\n<strong>Tip<\/strong>: If we think of 3\/0 in terms of pizza, where we have 0 slices and you want 3.\u00a0 This is like arguing with a three year old!\u00a0 I know you want 3 slices, but we don't have any pizza.\u00a0 Therefore, this can NOT happen!\u00a0 So 3\/0 is undefined.\r\n<div class=\"textbox shaded\">\r\n<h3>Division by Zero<\/h3>\r\nFor any real number [latex]a,\\Large\\frac{a}{0}[\/latex], and [latex]a\\div 0[\/latex] are undefined.\r\n\r\nDivision <em>by<\/em> zero is undefined.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nSimplify:\r\n1. [latex]7.5\\div 0[\/latex]\r\n2. [latex]\\Large\\frac{-32}{0}[\/latex]\r\n3. [latex]\\Large\\frac{4}{9}\\normalsize\\div 0[\/latex]\r\n[reveal-answer q=\"998388\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"998388\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468227789\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]7.5\\div 0[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Division by zero is undefined.<\/td>\r\n<td>undefined<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467171522\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{-32}{0}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Division by zero is undefined.<\/td>\r\n<td>undefined<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469683649\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{4}{9}\\normalsize\\div 0[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Division by zero is undefined.<\/td>\r\n<td>undefined<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n[ohm_question]146487[\/ohm_question]\r\n\r\n<\/div>\r\nBelow we\u00a0summarize the properties of zero.\r\n<div class=\"textbox shaded\">\r\n<h3>Properties of Zero<\/h3>\r\n<strong>Multiplication by Zero:<\/strong> For any real number [latex]a[\/latex],\r\n<p style=\"padding-left: 30px\">[latex]\\begin{array}{c}a\\cdot 0=0\\text{ The product of any number and 0 is 0.}\\hfill \\end{array}[\/latex]<\/p>\r\n<strong>Division by Zero:<\/strong> For any real number [latex]a,a\\ne 0[\/latex]\r\n<p style=\"padding-left: 30px\">[latex]{\\Large\\frac{0}{a}}=0[\/latex] Zero divided by any real number, except itself, is zero.\r\n[latex]{\\Large\\frac{a}{0}}[\/latex] is undefined. Division by zero is undefined.<\/p>\r\n\r\n<\/div>\r\nWatch the following video for more examples of using the multiplication and division property of zero.\r\n\r\nhttps:\/\/youtu.be\/fcVnwjBgDmk","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Identify the multiplication and division\u00a0properties of zero<\/li>\n<\/ul>\n<\/div>\n<h2>Use the Properties of Zero<\/h2>\n<p>We have already learned that zero is the additive identity, since it can be added to any number without changing the number\u2019s identity. But zero also has some special properties when it comes to multiplication and division.<\/p>\n<h2>Multiplication by Zero<\/h2>\n<p>What happens when you multiply a number by [latex]0?[\/latex] Multiplying by [latex]0[\/latex] makes the product equal zero. The product of any real number and [latex]0[\/latex] is [latex]0[\/latex].<\/p>\n<div class=\"textbox shaded\">\n<h3>Multiplication by Zero<\/h3>\n<p>For any real number [latex]a[\/latex],<\/p>\n<p style=\"padding-left: 60px\">[latex]a\\cdot 0=0[\/latex]<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Simplify:<br \/>\n1. [latex]-8\\cdot 0[\/latex]<br \/>\n2. [latex]\\Large\\frac{5}{12}\\normalsize\\cdot 0[\/latex]<br \/>\n3. [latex]0\\left(2.94\\right)[\/latex]<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168468273316\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr style=\"height: 15.7969px\">\n<td style=\"height: 15.7969px\">1.<\/td>\n<td style=\"height: 15.7969px\"><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><\/td>\n<td style=\"height: 15px\">[latex]-8\\cdot 0[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">The product of any real number and 0 is 0.<\/td>\n<td style=\"height: 15px\">[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466080054\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr style=\"height: 15.3906px\">\n<td style=\"height: 15.3906px\">2.<\/td>\n<td style=\"height: 15.3906px\"><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><\/td>\n<td style=\"height: 15px\">[latex]\\Large\\frac{5}{12}\\normalsize\\cdot 0[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">The product of any real number and 0 is 0.<\/td>\n<td style=\"height: 15px\">[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468270195\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]0\\left(2.94\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The product of any real number and 0 is 0.<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146484\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146484&theme=oea&iframe_resize_id=ohm146484&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Dividing with Zero<\/h2>\n<p>What about dividing with [latex]0?[\/latex] Think about a real example: if there are no cookies in the cookie jar and three people want to share them, how many cookies would each person get? There are [latex]0[\/latex] cookies to share, so each person gets [latex]0[\/latex] cookies.<\/p>\n<p style=\"text-align: center\">[latex]0\\div 3=0[\/latex]<\/p>\n<p>Remember that we can always check division with the related multiplication fact. So, we know that<\/p>\n<p style=\"text-align: center\">[latex]0\\div 3=0\\text{ because }0\\cdot 3=0[\/latex]<\/p>\n<p><strong>Tip<\/strong>: If we think of 0\/4 in terms of pizza, where we have 4 slices and you get 0.\u00a0 This could happen, but you would get 0!<\/p>\n<div class=\"textbox shaded\">\n<h3>Division of Zero<\/h3>\n<p>For any real number [latex]a[\/latex], except [latex]0,\\Large\\frac{0}{a}\\normalsize =0[\/latex] and [latex]0\\div a=0[\/latex].<\/p>\n<p>Zero divided by any real number except zero is zero.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Simplify:<br \/>\n1. [latex]0\\div 5[\/latex]<br \/>\n2. [latex]\\Large\\frac{0}{-2}[\/latex]<br \/>\n3. [latex]0\\div\\Large\\frac{7}{8}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q340688\">Show Solution<\/span><\/p>\n<div id=\"q340688\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168469701576\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]0\\div 5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Zero divided by any real number, except 0, is zero.<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468275715\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{0}{-2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Zero divided by any real number, except 0, is zero.<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466092352\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]0\\div\\Large\\frac{7}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Zero divided by any real number, except 0, is zero.<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146485\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146485&theme=oea&iframe_resize_id=ohm146485&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Now let\u2019s think about dividing a number <em>by<\/em> zero. What is the result of dividing [latex]4[\/latex] by [latex]0?[\/latex] Think about the related multiplication fact. Is there a number that multiplied by [latex]0[\/latex] gives [latex]4?[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]4\\div 0=[\/latex]means [latex]x\\cdot {0}=4[\/latex]<\/p>\n<p>Since any real number multiplied by [latex]0[\/latex] equals [latex]0[\/latex], there is no real number that can be multiplied by [latex]0[\/latex] to obtain [latex]4[\/latex]. We can conclude that there is no answer to [latex]4\\div 0[\/latex], and so we say that division by zero is undefined.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Tip<\/strong>: If we think of 3\/0 in terms of pizza, where we have 0 slices and you want 3.\u00a0 This is like arguing with a three year old!\u00a0 I know you want 3 slices, but we don&#8217;t have any pizza.\u00a0 Therefore, this can NOT happen!\u00a0 So 3\/0 is undefined.<\/p>\n<div class=\"textbox shaded\">\n<h3>Division by Zero<\/h3>\n<p>For any real number [latex]a,\\Large\\frac{a}{0}[\/latex], and [latex]a\\div 0[\/latex] are undefined.<\/p>\n<p>Division <em>by<\/em> zero is undefined.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Simplify:<br \/>\n1. [latex]7.5\\div 0[\/latex]<br \/>\n2. [latex]\\Large\\frac{-32}{0}[\/latex]<br \/>\n3. [latex]\\Large\\frac{4}{9}\\normalsize\\div 0[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q998388\">Show Solution<\/span><\/p>\n<div id=\"q998388\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468227789\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]7.5\\div 0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Division by zero is undefined.<\/td>\n<td>undefined<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467171522\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{-32}{0}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Division by zero is undefined.<\/td>\n<td>undefined<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469683649\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{4}{9}\\normalsize\\div 0[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Division by zero is undefined.<\/td>\n<td>undefined<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146487\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146487&theme=oea&iframe_resize_id=ohm146487&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Below we\u00a0summarize the properties of zero.<\/p>\n<div class=\"textbox shaded\">\n<h3>Properties of Zero<\/h3>\n<p><strong>Multiplication by Zero:<\/strong> For any real number [latex]a[\/latex],<\/p>\n<p style=\"padding-left: 30px\">[latex]\\begin{array}{c}a\\cdot 0=0\\text{ The product of any number and 0 is 0.}\\hfill \\end{array}[\/latex]<\/p>\n<p><strong>Division by Zero:<\/strong> For any real number [latex]a,a\\ne 0[\/latex]<\/p>\n<p style=\"padding-left: 30px\">[latex]{\\Large\\frac{0}{a}}=0[\/latex] Zero divided by any real number, except itself, is zero.<br \/>\n[latex]{\\Large\\frac{a}{0}}[\/latex] is undefined. Division by zero is undefined.<\/p>\n<\/div>\n<p>Watch the following video for more examples of using the multiplication and division property of zero.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Multiplying and Dividing Involving Zero\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/fcVnwjBgDmk?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-3686\">\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>Question ID 146520, 146484, 14485. <strong>Authored 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>Multiplying and Dividing Involving Zero. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/fcVnwjBgDmk\">https:\/\/youtu.be\/fcVnwjBgDmk<\/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, 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":9,"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\":\"Multiplying and Dividing Involving Zero\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/fcVnwjBgDmk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146520, 146484, 14485\",\"author\":\"Lumen 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