{"id":3584,"date":"2019-12-31T17:59:27","date_gmt":"2019-12-31T17:59:27","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3584"},"modified":"2021-02-05T23:49:14","modified_gmt":"2021-02-05T23:49:14","slug":"simplifying-and-evaluating-expressions-with-integers-that-use-all-four-operations","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/simplifying-and-evaluating-expressions-with-integers-that-use-all-four-operations\/","title":{"raw":"Simplifying and Evaluating Expressions With Integers That Use all Four Operations","rendered":"Simplifying and Evaluating Expressions With Integers That Use all Four Operations"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use the order of operations to simplify expressions that involve integer multiplication, division, addition, and subtraction<\/li>\r\n \t<li>Evaluate integer expressions using the order of operations<\/li>\r\n<\/ul>\r\n<\/div>\r\nNow we\u2019ll simplify expressions that use all four operations\u2013addition, subtraction, multiplication, and division\u2013with integers. Remember to follow the order of operations.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{Simplify: }7\\left(-2\\right)+4\\left(-7\\right)-6[\/latex]\r\n\r\nSolution:\r\nWe use the order of operations. Multiply first and then add and subtract from left to right.\r\n<table id=\"eip-id1168468659486\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]7\\left(-2\\right)+4\\left(-7\\right)-6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply first.<\/td>\r\n<td>[latex]-14+\\left(-28\\right)-6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]-42 - 6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]-48[\/latex]<\/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[ohm_question]145332[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see another example of how to use the order of operations to simplify an expression that contains integers.\r\n\r\nhttps:\/\/youtu.be\/RJ7uU9HbdqA\r\n\r\nIn our next example we will simplify expressions with integers that also contain exponents.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify:\r\n<ol>\r\n \t<li>\u00a0[latex]{\\left(-2\\right)}^{4}[\/latex]<\/li>\r\n \t<li>\u00a0[latex]{-2}^{4}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"699809\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"699809\"]\r\n\r\nSolution:\r\nThe exponent tells how many times to multiply the base.\r\n1. The exponent is [latex]4[\/latex] and the base is [latex]-2[\/latex]. We raise [latex]-2[\/latex] to the fourth power.\r\n<table id=\"eip-id1168468584362\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(-2\\right)}^{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write in expanded form.<\/td>\r\n<td>[latex]\\left(-2\\right)\\left(-2\\right)\\left(-2\\right)\\left(-2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]4\\left(-2\\right)\\left(-2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-8\\left(-2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]16[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. The exponent is [latex]4[\/latex] and the base is [latex]2[\/latex]. We raise [latex]2[\/latex] to the fourth power and then take the opposite.\r\n<table id=\"eip-id1168466711166\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-{2}^{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write in expanded form.<\/td>\r\n<td>[latex]-\\left(2\\cdot 2\\cdot 2\\cdot 2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-\\left(4\\cdot 2\\cdot 2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-\\left(8\\cdot 2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-16[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow you try it.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]145337[\/ohm_question]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/qB5PZzmjenI\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{Simplify: }12 - 3\\left(9 - 12\\right)[\/latex]\r\n[reveal-answer q=\"843317\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"843317\"]\r\n\r\nSolution:\r\nAccording to the order of operations, we simplify inside parentheses first. Then we will multiply and finally we will subtract.\r\n<table id=\"eip-id1168466156737\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]12 - 3\\left(9 - 12\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the parentheses first.<\/td>\r\n<td>[latex]12 - 3\\left(-3\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]12-\\left(-9\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]\\text{21}[\/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]145340[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]8\\left(-9\\right)\\div {\\left(-2\\right)}^{3}[\/latex]\r\n[reveal-answer q=\"388448\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"388448\"]\r\n\r\nSolution:\r\nWe simplify the exponent first, then multiply and divide.\r\n<table id=\"eip-id1168466276311\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]8\\left(-9\\right)\\div {\\left(-2\\right)}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the exponent.<\/td>\r\n<td>[latex]8\\left(-9\\right)\\div \\left(-8\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-72\\div \\left(-8\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]\\text{9}[\/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]145345[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{Simplify:}-30\\div 2+\\left(-3\\right)\\left(-7\\right)[\/latex]\r\n[reveal-answer q=\"523980\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"523980\"]\r\n\r\nSolution:\r\nFirst we will multiply and divide from left to right. Then we will add.\r\n<table id=\"eip-id1168469759923\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-30\\div 2+\\left(-3\\right)\\left(-7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]-15+\\left(-3\\right)\\left(-7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-15+21[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]\\text{6}[\/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]145348[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to evaluate expressions with integers using the order of operations.\r\n\r\nhttps:\/\/youtu.be\/UlfXxzuJIfs\r\n<h3>Evaluate Variable Expressions with Integers<\/h3>\r\nNow we can evaluate expressions that include multiplication and division with integers. Remember that to evaluate an expression, substitute the numbers in place of the variables, and then simplify.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{Evaluate }2{x}^{2}-3x+8\\text{ when }x=-4[\/latex]\r\n[reveal-answer q=\"674664\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"674664\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469859776\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"This figure has 6 rows. The first row has 2 times x squared, minus 3 times x, plus 8. The second row states substitute negative 4 for x and has 2 times negative 4 squared, minus 3 times negative 4, plus 8. The third row states simply exponents and has 2 times 16, minus 3 times negative 4, plus 8. The fourth row states multiply and has 32 minus negative 12 plus 8. The fifth row states subtract and has 44 plus 8. The sixth row states add and has 52.\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]2{x}^{2}-3x+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\text{Substitute}\\color{red}{--4}\\text{ for }x[\/latex]<\/td>\r\n<td>[latex]2(\\color{red}{--4})^{2}--3(\\color{red}{--4})+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify exponents.<\/td>\r\n<td>[latex]2(16)--3(--4)+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]32--(--12)+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]44+8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]52[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nKeep in mind that when we substitute [latex]-4[\/latex] for [latex]x[\/latex], we use parentheses to show the multiplication. Without parentheses, it would look like [latex]2\\cdot {-4}^{2}-3\\cdot -4+8[\/latex].\r\n\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]145352[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{Evaluate }3x+4y - 6\\text{ when }x=-1\\text{ and }y=2[\/latex].\r\n[reveal-answer q=\"144132\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"144132\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468285202\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"This figure has 4 rows. The first row has 3 times x plus 4 times y minus 6. The second row states substitute x equals negative 1 and y equals 2. It is followed by 3 times negative 1, plus 4 times negative 2, minus 6. The third row states multiply and is has negative 3 plus 8 minus 6. The fourth row states simplify and has negative 1.\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3x+4y--6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]x=-1[\/latex] and [latex]y=2[\/latex] .<\/td>\r\n<td>[latex]3(\\color{red}{--1})+4(\\color{blue}{2})--6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]--3+8--6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]--1[\/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]145353[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to substitute integers into variable expressions.\r\n\r\nhttps:\/\/youtu.be\/dkFIVfJTG9E","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use the order of operations to simplify expressions that involve integer multiplication, division, addition, and subtraction<\/li>\n<li>Evaluate integer expressions using the order of operations<\/li>\n<\/ul>\n<\/div>\n<p>Now we\u2019ll simplify expressions that use all four operations\u2013addition, subtraction, multiplication, and division\u2013with integers. Remember to follow the order of operations.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{Simplify: }7\\left(-2\\right)+4\\left(-7\\right)-6[\/latex]<\/p>\n<p>Solution:<br \/>\nWe use the order of operations. Multiply first and then add and subtract from left to right.<\/p>\n<table id=\"eip-id1168468659486\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]7\\left(-2\\right)+4\\left(-7\\right)-6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply first.<\/td>\n<td>[latex]-14+\\left(-28\\right)-6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]-42 - 6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]-48[\/latex]<\/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=\"ohm145332\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145332&theme=oea&iframe_resize_id=ohm145332&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see another example of how to use the order of operations to simplify an expression that contains integers.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Simplify an Expression With Integers Using the Order of Operations\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/RJ7uU9HbdqA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In our next example we will simplify expressions with integers that also contain exponents.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify:<\/p>\n<ol>\n<li>\u00a0[latex]{\\left(-2\\right)}^{4}[\/latex]<\/li>\n<li>\u00a0[latex]{-2}^{4}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q699809\">Show Solution<\/span><\/p>\n<div id=\"q699809\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe exponent tells how many times to multiply the base.<br \/>\n1. The exponent is [latex]4[\/latex] and the base is [latex]-2[\/latex]. We raise [latex]-2[\/latex] to the fourth power.<\/p>\n<table id=\"eip-id1168468584362\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(-2\\right)}^{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write in expanded form.<\/td>\n<td>[latex]\\left(-2\\right)\\left(-2\\right)\\left(-2\\right)\\left(-2\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]4\\left(-2\\right)\\left(-2\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-8\\left(-2\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]16[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>2. The exponent is [latex]4[\/latex] and the base is [latex]2[\/latex]. We raise [latex]2[\/latex] to the fourth power and then take the opposite.<\/p>\n<table id=\"eip-id1168466711166\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]-{2}^{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write in expanded form.<\/td>\n<td>[latex]-\\left(2\\cdot 2\\cdot 2\\cdot 2\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-\\left(4\\cdot 2\\cdot 2\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-\\left(8\\cdot 2\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-16[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now you try it.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145337\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145337&theme=oea&iframe_resize_id=ohm145337&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Evaluating Negative Numbers Raised to Powers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/qB5PZzmjenI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{Simplify: }12 - 3\\left(9 - 12\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q843317\">Show Solution<\/span><\/p>\n<div id=\"q843317\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nAccording to the order of operations, we simplify inside parentheses first. Then we will multiply and finally we will subtract.<\/p>\n<table id=\"eip-id1168466156737\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]12 - 3\\left(9 - 12\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract the parentheses first.<\/td>\n<td>[latex]12 - 3\\left(-3\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]12-\\left(-9\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]\\text{21}[\/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=\"ohm145340\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145340&theme=oea&iframe_resize_id=ohm145340&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]8\\left(-9\\right)\\div {\\left(-2\\right)}^{3}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q388448\">Show Solution<\/span><\/p>\n<div id=\"q388448\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe simplify the exponent first, then multiply and divide.<\/p>\n<table id=\"eip-id1168466276311\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]8\\left(-9\\right)\\div {\\left(-2\\right)}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the exponent.<\/td>\n<td>[latex]8\\left(-9\\right)\\div \\left(-8\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-72\\div \\left(-8\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]\\text{9}[\/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=\"ohm145345\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145345&theme=oea&iframe_resize_id=ohm145345&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{Simplify:}-30\\div 2+\\left(-3\\right)\\left(-7\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q523980\">Show Solution<\/span><\/p>\n<div id=\"q523980\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nFirst we will multiply and divide from left to right. Then we will add.<\/p>\n<table id=\"eip-id1168469759923\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]-30\\div 2+\\left(-3\\right)\\left(-7\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]-15+\\left(-3\\right)\\left(-7\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-15+21[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]\\text{6}[\/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=\"ohm145348\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145348&theme=oea&iframe_resize_id=ohm145348&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to evaluate expressions with integers using the order of operations.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex 1:  Order of Operations with Integers\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/UlfXxzuJIfs?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Evaluate Variable Expressions with Integers<\/h3>\n<p>Now we can evaluate expressions that include multiplication and division with integers. Remember that to evaluate an expression, substitute the numbers in place of the variables, and then simplify.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{Evaluate }2{x}^{2}-3x+8\\text{ when }x=-4[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q674664\">Show Solution<\/span><\/p>\n<div id=\"q674664\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168469859776\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"This figure has 6 rows. The first row has 2 times x squared, minus 3 times x, plus 8. The second row states substitute negative 4 for x and has 2 times negative 4 squared, minus 3 times negative 4, plus 8. The third row states simply exponents and has 2 times 16, minus 3 times negative 4, plus 8. The fourth row states multiply and has 32 minus negative 12 plus 8. The fifth row states subtract and has 44 plus 8. The sixth row states add and has 52.\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]2{x}^{2}-3x+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\text{Substitute}\\color{red}{--4}\\text{ for }x[\/latex]<\/td>\n<td>[latex]2(\\color{red}{--4})^{2}--3(\\color{red}{--4})+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents.<\/td>\n<td>[latex]2(16)--3(--4)+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]32--(--12)+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]44+8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]52[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Keep in mind that when we substitute [latex]-4[\/latex] for [latex]x[\/latex], we use parentheses to show the multiplication. Without parentheses, it would look like [latex]2\\cdot {-4}^{2}-3\\cdot -4+8[\/latex].<\/p>\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=\"ohm145352\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145352&theme=oea&iframe_resize_id=ohm145352&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{Evaluate }3x+4y - 6\\text{ when }x=-1\\text{ and }y=2[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q144132\">Show Solution<\/span><\/p>\n<div id=\"q144132\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468285202\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"This figure has 4 rows. The first row has 3 times x plus 4 times y minus 6. The second row states substitute x equals negative 1 and y equals 2. It is followed by 3 times negative 1, plus 4 times negative 2, minus 6. The third row states multiply and is has negative 3 plus 8 minus 6. The fourth row states simplify and has negative 1.\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3x+4y--6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]x=-1[\/latex] and [latex]y=2[\/latex] .<\/td>\n<td>[latex]3(\\color{red}{--1})+4(\\color{blue}{2})--6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]--3+8--6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]--1[\/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=\"ohm145353\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145353&theme=oea&iframe_resize_id=ohm145353&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to substitute integers into variable expressions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Ex: Substitute and Evaluate  Expressions x^2+3, (x+3)^2, x^2+2x+3\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/dkFIVfJTG9E?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-3584\">\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>Ex: Simplify an Expression With Integers Using the Order of Operations. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/RJ7uU9HbdqA\">https:\/\/youtu.be\/RJ7uU9HbdqA<\/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>Ex 1: Order of Operations with Integers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/UlfXxzuJIfs\">https:\/\/youtu.be\/UlfXxzuJIfs<\/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>Ex: Substitute and Evaluate Expressions x^2+3, (x+3)^2, x^2+2x+3. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/dkFIVfJTG9E\">https:\/\/youtu.be\/dkFIVfJTG9E<\/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>Ex: Evaluating Negative Numbers Raised to Powers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/qB5PZzmjenI\">https:\/\/youtu.be\/qB5PZzmjenI<\/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: 145332, 145337, 145340, 145345, 145348, 145352, 145353. <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":15,"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\":\"Ex: Simplify an Expression With Integers Using the Order of Operations\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/RJ7uU9HbdqA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 1: Order of Operations with Integers\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/UlfXxzuJIfs\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Substitute and Evaluate Expressions x^2+3, (x+3)^2, x^2+2x+3\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/dkFIVfJTG9E\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Evaluating Negative Numbers Raised to Powers\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/qB5PZzmjenI\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 145332, 145337, 145340, 145345, 145348, 145352, 145353\",\"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-3584","chapter","type-chapter","status-web-only","hentry"],"part":1193,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3584","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3584\/revisions"}],"predecessor-version":[{"id":3618,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3584\/revisions\/3618"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/1193"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3584\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3584"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3584"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3584"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}