{"id":649,"date":"2023-03-09T16:21:45","date_gmt":"2023-03-09T16:21:45","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=649"},"modified":"2024-10-18T20:50:43","modified_gmt":"2024-10-18T20:50:43","slug":"integers-fresh-take","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/integers-fresh-take\/","title":{"raw":"Integers: Fresh Take","rendered":"Integers: Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Identify integers<\/li>\r\n\t<li>Compare positive and negative integers using a number line<\/li>\r\n\t<li>Understand absolute value<\/li>\r\n\t<li>Add, subtract, multiply, and divide integers<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Opposite and Integers<\/h2>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\r\n<p>The <strong>opposite <\/strong>of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.<\/p>\r\n<p><strong>Integers<\/strong> are counting numbers, their opposites, and zero.<\/p>\r\n<\/div>\r\n<p>The video below shows more examples of how to find the opposite of an integer.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/suk9KMzOKkU\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Determine+the+Opposites+of+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Determine the Opposites of Integers\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Integers on a Number Line<\/h2>\r\n<p>In the video below we show more examples of how to plot integers on a number line.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/jlc-m5sXNug\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Plot+Integers+on+the+Number+Line.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cPlot Integers on the Number Line\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Order Positive and Negative Numbers<\/h2>\r\n<section class=\"textbox seeExample\">Order each of the following pairs of numbers using [latex]&amp;lt[\/latex] or [latex]\\text{&gt;}[\/latex] .\r\n\r\n\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>[latex]14[\/latex] and [latex]6[\/latex]<\/li>\r\n\t<li>[latex]-1[\/latex] and [latex]9[\/latex]<\/li>\r\n\t<li>[latex]-1[\/latex] and [latex]- 4[\/latex]<\/li>\r\n\t<li>[latex]2[\/latex] and [latex]- 20[\/latex]<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"157184\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"157184\"]<\/p>\r\n<p>Begin by plotting the numbers on a number line as shown in the number line below.<\/p>\r\n<center><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220124\/CNX_BMath_Figure_03_01_015.png\" alt=\"A number line with points negative 20, negative 4, negative 1, 2, 6, 9, and 14 labeled with dots.\" width=\"745\" height=\"65\" \/><\/center>\r\n<p>&nbsp;<\/p>\r\n<table id=\"eip-id1168469859124\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1. Compare [latex]14[\/latex] and [latex]6[\/latex].<\/td>\r\n<td>[latex]14[\/latex] and [latex]6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]14[\/latex] is to the right of [latex]6[\/latex] on the number line.<\/td>\r\n<td>[latex]14&gt;6[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468303840\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2. Compare [latex]\u22121[\/latex] and [latex]9[\/latex].<\/td>\r\n<td>[latex]-1[\/latex] and [latex]9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\u22121[\/latex] is to the left of [latex]9[\/latex] on the number line.<\/td>\r\n<td>[latex]-1&lt;9[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467263438\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3. Compare [latex]\u22121[\/latex] and [latex]\u22124[\/latex].<\/td>\r\n<td>[latex]-1[\/latex] and [latex]- 4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\u22121[\/latex] is to the right of [latex]\u22124[\/latex] on the number line.<\/td>\r\n<td>[latex]-1&gt;-4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468416637\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>4. Compare [latex]2[\/latex] and [latex]\u221220[\/latex].<\/td>\r\n<td>[latex]2[\/latex] and [latex]- 20[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex] is to the right of [latex]\u221220[\/latex] on the number line.<\/td>\r\n<td>[latex]2&gt;-20[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<p>In the video below we show more examples of how to use inequality symbols to compare integers.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/YzTGfD6kw-s\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Compare+Integers+Using+An+Inequality+Symbol.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Compare Integers Using An Inequality Symbol\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Absolute Value<\/h2>\r\n<div class=\"textbox shaded\">\r\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\r\n<p>The <strong>absolute value<\/strong> of a number is its distance from zero on the number line, disregarding its direction or sign. It is always a non-negative value.<\/p>\r\n<\/div>\r\n<section class=\"textbox seeExample\">Simplify:\r\n\r\n\r\n<ol>\r\n\t<li>\u00a0[latex]|3|[\/latex]<\/li>\r\n\t<li>\u00a0[latex]|-44|[\/latex]<\/li>\r\n\t<li>\u00a0[latex]|0|[\/latex]<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"157188\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"157188\"]<\/p>\r\n<table id=\"eip-id1165118025864\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td>[latex]|3|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]3[\/latex] is [latex]3[\/latex] units from zero.<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1171842979184\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td>[latex]|-44|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\u221244[\/latex] is [latex]44[\/latex] units from zero.<\/td>\r\n<td>[latex]44[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1171842583307\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<td>&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td>[latex]|0|[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0[\/latex] is already at zero.<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<p>In the video below we show another example of how to find the absolute value of an integer.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/I8bTqGmkqGI\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex+1_+Determine+the+Absolute+Value+of+an+Integer.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx 1: Determine the Absolute Value of an Integer\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h3>Simplify Absolute Values<\/h3>\r\n<p>Watch the following video to see more examples of how to simplify expressions that contain absolute value.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/cd24nT7mAi0\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the \u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Simplify+Absolute+Value+Expressions.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSimplify Absolute Value Expressions\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Adding Integers<\/h2>\r\n<p>In the following video we present more examples of using color counters to model addition of integers.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/beI5bQB9a7Y\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Adding+Integers+with+the+Same+Sign+Using+Color+Counters.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cAdding Integers with the Same Sign Using Color Counters\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox seeExample\">Model each addition.\r\n\r\n\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>[latex]3 + 4[\/latex]<\/li>\r\n\t<li>[latex]\u22121 + 4[\/latex]<\/li>\r\n\t<li>[latex]4 + (\u22126)[\/latex]<\/li>\r\n\t<li>[latex]\u22122 + (\u22122)[\/latex]<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"767954\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"767954\"]<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>[latex]7[\/latex]<img class=\"alignnone wp-image-15477\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/11225146\/AddingIntegers_37.png\" alt=\"three blue positive markers separated from four additional blue positive markers\" width=\"356\" height=\"130\" \/>\r\n<p>&nbsp;<\/p>\r\n<\/li>\r\n\t<li>[latex]3[\/latex]<img class=\"alignnone wp-image-15478\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/11225202\/AddingIntegers_38.png\" alt=\"one red negative marker separated from four blue positive markers\" width=\"357\" height=\"62\" \/>\r\n<p>&nbsp;<\/p>\r\n<\/li>\r\n\t<li>[latex]-2[\/latex]<img class=\"alignnone wp-image-15490\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/11233032\/Artboard_31.png\" alt=\"four blue positive markers separated from six red negative markers\" width=\"355\" height=\"123\" \/>\r\n<p>&nbsp;<\/p>\r\n<\/li>\r\n\t<li>[latex]-4[\/latex]<img class=\"alignnone wp-image-15480\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/11225226\/AddingIntegers_40.png\" alt=\"two red negative markers separated from two additional red negative markers\" width=\"369\" height=\"64\" \/><\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10411454&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=CfkaifC7tGY&amp;video_target=tpm-plugin-pnrr8skj-CfkaifC7tGY\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Adding+Integers+%7C+How+to+Add+Positive+and+Negative+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cAdding Integers | How to Add Positive and Negative Integers\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Subtracting Integers<\/h2>\r\n<p>Watch the video below to see more examples of modeling integer subtraction with color counters.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/ZjiL7GfxgiI\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Subtracting+Integers+with+Color+Counters+(No+Extra+Zeros+Needed).txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSubtracting Integers with Color Counters (No Extra Zeros Needed)\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox seeExample\">Model each subtraction.\r\n\r\n\r\n<ol>\r\n\t<li>[latex]7 - (-8)[\/latex]<\/li>\r\n\t<li>[latex]-7 - (-2)[\/latex]<\/li>\r\n\t<li>[latex]4 - 1[\/latex]<\/li>\r\n\t<li>[latex]-6 - 8[\/latex]<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"324876\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"324876\"]<\/p>\r\n<ol>\r\n\t<li>[latex]15[\/latex]<img class=\"alignnone wp-image-15544\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/13220559\/SubtractingIntegers_37.png\" alt=\"15 blue circles with a space between the first 7 and last 8. Below the last 8 circles there are 8 red circles that are circled together.\" width=\"641\" height=\"132\" \/>\r\n<p>&nbsp;<\/p>\r\n<\/li>\r\n\t<li>[latex]-5[\/latex]<img class=\"alignnone wp-image-15545\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/13220610\/SubtractingIntegers_38.png\" alt=\"7 red circles with a space between the first 5 and last 2. The last 2 circles are circled together.\" width=\"359\" height=\"69\" \/>\r\n<p>&nbsp;<\/p>\r\n<\/li>\r\n\t<li>[latex]3[\/latex]<img class=\"alignnone wp-image-15546\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/13220621\/SubtractingIntegers_39.png\" alt=\"4 blue circles with a space between the first 3 and the last 1. The last circle is circled.\" width=\"358\" height=\"69\" \/>\r\n<p>&nbsp;<\/p>\r\n<\/li>\r\n\t<li>[latex]-14[\/latex]<img class=\"alignnone wp-image-15547\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/13220634\/SubtractingIntegers_40.png\" alt=\"14 red circles with a space between the first 6 and last 8. Below the last 8 circles there are 8 blue circles that are circled together.\" width=\"620\" height=\"137\" \/><\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10411455&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=1DKWG5CBeek&amp;video_target=tpm-plugin-bd468cnf-1DKWG5CBeek\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Subtracting+Integers+%7C+How+to+Subtract+Positive+and+Negative+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSubtracting Integers | How to Subtract Positive and Negative Integers\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Multiplying Integers<\/h2>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10411456&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=xI1cGTQohlQ&amp;video_target=tpm-plugin-gum81e72-xI1cGTQohlQ\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Multiplying+Integers+%7C+How+to+Multiply+Positive+and+Negative+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cMultiplying Integers | How to Multiply Positive and Negative Integers\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<p>Watch the following video for more examples of how to multiply integers with different signs, and the same sign.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/QY-Za42DItw\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Multiplying+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Multiplying Integers\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Dividing Integers<\/h2>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10411457&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=DR8LBKSdI20&amp;video_target=tpm-plugin-zn0mwwru-DR8LBKSdI20\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Dividing+Integers+%7C+How+to+Divide+Positive+and+Negative+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cDividing Integers | How to Divide Positive and Negative Integers\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<p>Watch the following video for more examples of how to divide integers with the same and different signs.<\/p>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/z5ZFiyLi5Y0\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Dividing+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Dividing Integers\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<h2>Simplifying and Evaluating Expressions With Integers That Use all Four Operations<\/h2>\r\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>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/RJ7uU9HbdqA\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Simplify+an+Expression+With+Integers+Using+the+Order+of+Operations.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Simplify an Expression With Integers Using the Order of Operations\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Identify integers<\/li>\n<li>Compare positive and negative integers using a number line<\/li>\n<li>Understand absolute value<\/li>\n<li>Add, subtract, multiply, and divide integers<\/li>\n<\/ul>\n<\/section>\n<h2>Opposite and Integers<\/h2>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\n<p>The <strong>opposite <\/strong>of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.<\/p>\n<p><strong>Integers<\/strong> are counting numbers, their opposites, and zero.<\/p>\n<\/div>\n<p>The video below shows more examples of how to find the opposite of an integer.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/suk9KMzOKkU\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Determine+the+Opposites+of+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Determine the Opposites of Integers\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Integers on a Number Line<\/h2>\n<p>In the video below we show more examples of how to plot integers on a number line.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/jlc-m5sXNug\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Plot+Integers+on+the+Number+Line.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cPlot Integers on the Number Line\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Order Positive and Negative Numbers<\/h2>\n<section class=\"textbox seeExample\">Order each of the following pairs of numbers using [latex]&lt[\/latex] or [latex]\\text{>}[\/latex] .<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>[latex]14[\/latex] and [latex]6[\/latex]<\/li>\n<li>[latex]-1[\/latex] and [latex]9[\/latex]<\/li>\n<li>[latex]-1[\/latex] and [latex]- 4[\/latex]<\/li>\n<li>[latex]2[\/latex] and [latex]- 20[\/latex]<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q157184\">Show Solution<\/button><\/p>\n<div id=\"q157184\" class=\"hidden-answer\" style=\"display: none\">\n<p>Begin by plotting the numbers on a number line as shown in the number line below.<\/p>\n<div style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220124\/CNX_BMath_Figure_03_01_015.png\" alt=\"A number line with points negative 20, negative 4, negative 1, 2, 6, 9, and 14 labeled with dots.\" width=\"745\" height=\"65\" \/><\/div>\n<p>&nbsp;<\/p>\n<table id=\"eip-id1168469859124\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1. Compare [latex]14[\/latex] and [latex]6[\/latex].<\/td>\n<td>[latex]14[\/latex] and [latex]6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]14[\/latex] is to the right of [latex]6[\/latex] on the number line.<\/td>\n<td>[latex]14>6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468303840\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2. Compare [latex]\u22121[\/latex] and [latex]9[\/latex].<\/td>\n<td>[latex]-1[\/latex] and [latex]9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\u22121[\/latex] is to the left of [latex]9[\/latex] on the number line.<\/td>\n<td>[latex]-1<9[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467263438\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>3. Compare [latex]\u22121[\/latex] and [latex]\u22124[\/latex].<\/td>\n<td>[latex]-1[\/latex] and [latex]- 4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\u22121[\/latex] is to the right of [latex]\u22124[\/latex] on the number line.<\/td>\n<td>[latex]-1>-4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468416637\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>4. Compare [latex]2[\/latex] and [latex]\u221220[\/latex].<\/td>\n<td>[latex]2[\/latex] and [latex]- 20[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2[\/latex] is to the right of [latex]\u221220[\/latex] on the number line.<\/td>\n<td>[latex]2>-20[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/section>\n<p>In the video below we show more examples of how to use inequality symbols to compare integers.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/YzTGfD6kw-s\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Compare+Integers+Using+An+Inequality+Symbol.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Compare Integers Using An Inequality Symbol\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Absolute Value<\/h2>\n<div class=\"textbox shaded\">\n<p><strong>The Main Idea\u00a0<\/strong><\/p>\n<p>The <strong>absolute value<\/strong> of a number is its distance from zero on the number line, disregarding its direction or sign. It is always a non-negative value.<\/p>\n<\/div>\n<section class=\"textbox seeExample\">Simplify:<\/p>\n<ol>\n<li>\u00a0[latex]|3|[\/latex]<\/li>\n<li>\u00a0[latex]|-44|[\/latex]<\/li>\n<li>\u00a0[latex]|0|[\/latex]<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q157188\">Show Solution<\/button><\/p>\n<div id=\"q157188\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"eip-id1165118025864\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<\/td>\n<td>[latex]|3|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]3[\/latex] is [latex]3[\/latex] units from zero.<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1171842979184\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<\/td>\n<td>[latex]|-44|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\u221244[\/latex] is [latex]44[\/latex] units from zero.<\/td>\n<td>[latex]44[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1171842583307\" class=\"unnumbered unstyled\" style=\"width: 75%;\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<\/td>\n<td>[latex]|0|[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]0[\/latex] is already at zero.<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/section>\n<p>In the video below we show another example of how to find the absolute value of an integer.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/I8bTqGmkqGI\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex+1_+Determine+the+Absolute+Value+of+an+Integer.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx 1: Determine the Absolute Value of an Integer\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h3>Simplify Absolute Values<\/h3>\n<p>Watch the following video to see more examples of how to simplify expressions that contain absolute value.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/cd24nT7mAi0\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the \u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Simplify+Absolute+Value+Expressions.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSimplify Absolute Value Expressions\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Adding Integers<\/h2>\n<p>In the following video we present more examples of using color counters to model addition of integers.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/beI5bQB9a7Y\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Adding+Integers+with+the+Same+Sign+Using+Color+Counters.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cAdding Integers with the Same Sign Using Color Counters\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox seeExample\">Model each addition.<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>[latex]3 + 4[\/latex]<\/li>\n<li>[latex]\u22121 + 4[\/latex]<\/li>\n<li>[latex]4 + (\u22126)[\/latex]<\/li>\n<li>[latex]\u22122 + (\u22122)[\/latex]<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q767954\">Show Solution<\/button><\/p>\n<div id=\"q767954\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: decimal;\">\n<li>[latex]7[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15477\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/11225146\/AddingIntegers_37.png\" alt=\"three blue positive markers separated from four additional blue positive markers\" width=\"356\" height=\"130\" \/>\n<p>&nbsp;<\/p>\n<\/li>\n<li>[latex]3[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15478\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/11225202\/AddingIntegers_38.png\" alt=\"one red negative marker separated from four blue positive markers\" width=\"357\" height=\"62\" \/>\n<p>&nbsp;<\/p>\n<\/li>\n<li>[latex]-2[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15490\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/11233032\/Artboard_31.png\" alt=\"four blue positive markers separated from six red negative markers\" width=\"355\" height=\"123\" \/>\n<p>&nbsp;<\/p>\n<\/li>\n<li>[latex]-4[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15480\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/11225226\/AddingIntegers_40.png\" alt=\"two red negative markers separated from two additional red negative markers\" width=\"369\" height=\"64\" \/><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10411454&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=CfkaifC7tGY&amp;video_target=tpm-plugin-pnrr8skj-CfkaifC7tGY\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Adding+Integers+%7C+How+to+Add+Positive+and+Negative+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cAdding Integers | How to Add Positive and Negative Integers\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Subtracting Integers<\/h2>\n<p>Watch the video below to see more examples of modeling integer subtraction with color counters.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/ZjiL7GfxgiI\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Subtracting+Integers+with+Color+Counters+(No+Extra+Zeros+Needed).txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSubtracting Integers with Color Counters (No Extra Zeros Needed)\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox seeExample\">Model each subtraction.<\/p>\n<ol>\n<li>[latex]7 - (-8)[\/latex]<\/li>\n<li>[latex]-7 - (-2)[\/latex]<\/li>\n<li>[latex]4 - 1[\/latex]<\/li>\n<li>[latex]-6 - 8[\/latex]<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q324876\">Show Solution<\/button><\/p>\n<div id=\"q324876\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]15[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15544\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/13220559\/SubtractingIntegers_37.png\" alt=\"15 blue circles with a space between the first 7 and last 8. Below the last 8 circles there are 8 red circles that are circled together.\" width=\"641\" height=\"132\" \/>\n<p>&nbsp;<\/p>\n<\/li>\n<li>[latex]-5[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15545\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/13220610\/SubtractingIntegers_38.png\" alt=\"7 red circles with a space between the first 5 and last 2. The last 2 circles are circled together.\" width=\"359\" height=\"69\" \/>\n<p>&nbsp;<\/p>\n<\/li>\n<li>[latex]3[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15546\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/13220621\/SubtractingIntegers_39.png\" alt=\"4 blue circles with a space between the first 3 and the last 1. The last circle is circled.\" width=\"358\" height=\"69\" \/>\n<p>&nbsp;<\/p>\n<\/li>\n<li>[latex]-14[\/latex]<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15547\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/13220634\/SubtractingIntegers_40.png\" alt=\"14 red circles with a space between the first 6 and last 8. Below the last 8 circles there are 8 blue circles that are circled together.\" width=\"620\" height=\"137\" \/><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10411455&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=1DKWG5CBeek&amp;video_target=tpm-plugin-bd468cnf-1DKWG5CBeek\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Subtracting+Integers+%7C+How+to+Subtract+Positive+and+Negative+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cSubtracting Integers | How to Subtract Positive and Negative Integers\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Multiplying Integers<\/h2>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10411456&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=xI1cGTQohlQ&amp;video_target=tpm-plugin-gum81e72-xI1cGTQohlQ\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Multiplying+Integers+%7C+How+to+Multiply+Positive+and+Negative+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cMultiplying Integers | How to Multiply Positive and Negative Integers\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<p>Watch the following video for more examples of how to multiply integers with different signs, and the same sign.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/QY-Za42DItw\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Multiplying+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Multiplying Integers\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Dividing Integers<\/h2>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10411457&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=DR8LBKSdI20&amp;video_target=tpm-plugin-zn0mwwru-DR8LBKSdI20\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Dividing+Integers+%7C+How+to+Divide+Positive+and+Negative+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cDividing Integers | How to Divide Positive and Negative Integers\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<p>Watch the following video for more examples of how to divide integers with the same and different signs.<\/p>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/z5ZFiyLi5Y0\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Dividing+Integers.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Dividing Integers\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<h2>Simplifying and Evaluating Expressions With Integers That Use all Four Operations<\/h2>\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<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/RJ7uU9HbdqA\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Intro+to+Business\/transcripts\/Ex_+Simplify+an+Expression+With+Integers+Using+the+Order+of+Operations.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cEx: Simplify an Expression With Integers Using the Order of Operations\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":24,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":290,"module-header":"fresh_take","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/649"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":32,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/649\/revisions"}],"predecessor-version":[{"id":15181,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/649\/revisions\/15181"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/290"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/649\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=649"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=649"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=649"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=649"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}