{"id":6388,"date":"2017-05-02T00:10:07","date_gmt":"2017-05-02T00:10:07","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=6388"},"modified":"2019-12-31T18:18:52","modified_gmt":"2019-12-31T18:18:52","slug":"introduction-to-integers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/introduction-to-integers\/","title":{"raw":"Locating and Ordering Integers on the Number Line","rendered":"Locating and Ordering Integers on the Number Line"},"content":{"raw":"<div class=\"textbox learning-objectives\"><h3>Learning Outcomes<\/h3><ul><li>Locate&nbsp;positive and negative numbers on a number line<\/li><li>Compare and order positive and negative numbers using a number line<\/li><\/ul><\/div>&nbsp;\n\nDo you live in a place that has very cold winters? Have you ever experienced a temperature below zero? If so, you are already familiar with negative numbers. A negative number is a number that is less than [latex]0[\/latex]. Very cold temperatures are measured in degrees below zero and can be described by negative numbers. For example, [latex]-1^\\circ F[\/latex] (read as \"negative one degree Fahrenheit\") is [latex]1[\/latex] degree below [latex]0[\/latex]. A minus sign is shown before a number to indicate that it is negative. The figure of a thermometer below&nbsp;shows [latex]-20^\\circ F[\/latex], which is [latex]20[\/latex] degrees below [latex]0[\/latex].\n\nTemperatures below zero are described by negative numbers.\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220056\/CNX_BMath_Figure_03_01_002.png\" alt=\"This figure is a thermometer scaled in degrees Fahrenheit. The thermometer has a reading of 20 degrees.\">\nTemperatures are not the only negative numbers. A bank overdraft is another example of a negative number. If a person writes a check for more than he has in his account, his balance will be negative.\n\nElevations can also be represented by negative numbers. The elevation at sea level is [latex]0[\/latex] feet. Elevations above sea level are positive and elevations below sea level are negative. The elevation of the Dead Sea, which borders Israel and Jordan, is about [latex]1,302[\/latex] feet below sea level, so the elevation of the Dead Sea can be represented as [latex]-1,302[\/latex] feet. Refer to the image below for a depiction.\n\nThe surface of the Mediterranean Sea has an elevation of [latex]0[\/latex] ft. The diagram shows that nearby mountains have higher (positive) elevations whereas the Dead Sea has a lower (negative) elevation.\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220057\/CNX_BMath_Figure_03_01_003.png\" alt=\"This figure is a drawing of a side view of the coast of Israel, showing different elevations. The Mediterranean Sea is labeled 0 feet elevation and the Dead Sea is labeled negative 1302 feet elevation. The country of Jordan is also labeled in the figure.\">\nDepths below the ocean surface are also described by negative numbers. A submarine, for example, might descend to a depth of [latex]500[\/latex] feet. Its position would then be [latex]-500[\/latex] feet as labeled in the image below.\n\nDepths below sea level are described by negative numbers. A submarine [latex]500[\/latex] ft below sea level is at [latex]-500[\/latex] ft.\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220058\/CNX_BMath_Figure_03_01_004.png\" alt=\"This figure is a drawing of a submarine underwater. In the water is also a vertical number line, scaled in feet. The number line has 0 feet at the surface and negative 500 feet below the water where the submarine is located.\">\nBoth positive and negative numbers can be represented on a number line. Recall that the number line created in Add Whole Numbers started at [latex]0[\/latex] and showed the counting numbers increasing to the right as shown in the number line below. The counting numbers [latex](1, 2, 3, \\ldots )[\/latex] on the number line are all positive. We could write a plus sign, [latex]+[\/latex], before a positive number such as [latex]+2[\/latex] or [latex]+3[\/latex], but it is customary to omit the plus sign and write only the number. If there is no sign, the number is assumed to be positive.\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220100\/CNX_BMath_Figure_03_01_005.png\" alt=\"This figure is a number line scaled from 0 to 6.\">\nNow we need to extend the number line to include negative numbers. We mark several units to the left of zero, keeping the intervals the same width as those on the positive side. We label the marks with negative numbers, starting with [latex]-1[\/latex] at the first mark to the left of [latex]0,-2[\/latex] at the next mark, and so on. Refer to the number line below for reference.\n\nOn a number line, positive numbers are to the right of zero. Negative numbers are to the left of zero. What about zero? Zero is neither positive nor negative.\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220102\/CNX_BMath_Figure_03_01_006.png\" alt=\"This figure is a number line with 0 in the middle. Then, the scaling has positive numbers 1 to 4 to the right of 0 and negative numbers, negative 1 to negative 4 to the left of 0.\">\nThe arrows at either end of the line indicate that the number line extends forever in each direction. There is no greatest positive number and there is no smallest negative number.\n\n<div class=\"textbox exercises\"><h3>example<\/h3>Plot the numbers on a number line:\n\n<ol><li>[latex]3[\/latex]<\/li><li>[latex]-3[\/latex]<\/li><li>[latex]-2[\/latex]<\/li><\/ol>Solution\nDraw a number line. Mark [latex]0[\/latex] in the center and label several units to the left and right.\n\n1. To plot [latex]3[\/latex], start at [latex]0[\/latex] and count three units to the right. Place a point as shown in the number line below.\n\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220104\/CNX_BMath_Figure_03_01_007.png\" alt=\"This figure is a number line scaled from negative 4 to 4, with the point 3 labeled with a dot.\">\n\n2. To plot [latex]-3[\/latex], start at [latex]0[\/latex] and count three units to the left. Place a point as shown in&nbsp;the number line below.\n\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220107\/CNX_BMath_Figure_03_01_008.png\" alt=\"This figure is a number line scaled from negative 4 to 4, with the point negative 3 labeled with a dot.\">\n\n3. To plot [latex]-2[\/latex], start at [latex]0[\/latex] and count two units to the left. Place a point as shown in the number line below.\n\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220109\/CNX_BMath_Figure_03_01_009.png\" alt=\"This figure is a number line scaled from negative 4 to 4, with the point negative 2 labeled with a dot.\">\n\n<\/div>&nbsp;\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144924&amp;theme=oea&amp;iframe_resize_id=mom1[\/embed]\n\n\n\n<\/div>In the video below we show more examples of how to plot integers on a number line.\n\nhttps:\/\/youtu.be\/jlc-m5sXNug\n\n<h2>Order Positive and Negative Numbers<\/h2>We can use the number line to compare and order positive and negative numbers. Going from left to right, numbers increase in value. Going from right to left, numbers decrease in value. See the number line below.\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220114\/CNX_BMath_Figure_03_01_012.png\" alt=\"This figure is a number line. Above the number line there is an arrow pointing to the right labeled increasing. Below the number line there is an arrow pointing to the left labeled decreasing.\">\nJust as we did with positive numbers, we can use inequality symbols to show the ordering of positive and negative numbers. Remember that we use the notation [latex]a&lt;b[\/latex] (read [latex]a[\/latex] <em>is less than<\/em> [latex]b[\/latex] ) when [latex]a[\/latex] is to the left of [latex]b[\/latex] on the number line. We write [latex]a&gt;b[\/latex] (read [latex]a[\/latex] <em>is greater than<\/em> [latex]b[\/latex] ) when [latex]a[\/latex] is to the right of [latex]b[\/latex] on the number line. This is shown for the numbers [latex]3[\/latex] and [latex]5[\/latex] in the image below.\n\nThe number [latex]3[\/latex] is to the left of [latex]5[\/latex] on the number line. So [latex]3[\/latex] is less than [latex]5[\/latex], and [latex]5[\/latex] is greater than [latex]3[\/latex].\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220116\/CNX_BMath_Figure_03_01_013.png\" alt=\"This figure is a number line with points 3 and 5 labeled with dots. Below the number line is the statements 3 is less than 5 and 5 is greater than 3.\">\nThe numbers lines to follow show a few more examples.\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220118\/CNX_BMath_Figure_03_01_014a_img.png\" alt=\"This figure is a number line with points 1 and 4 labeled with dots.\">\n[latex]4[\/latex] is to the right of [latex]1[\/latex] on the number line, so [latex]4&gt;1[\/latex].\n[latex]1[\/latex] is to the left of [latex]4[\/latex] on the number line, so [latex]1&lt;4[\/latex].\n\n&nbsp;\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220120\/CNX_BMath_Figure_03_01_014b_img.png\" alt=\"This figure is a number line with points negative 2 and 1 labeled with dots.\">\n[latex]-2[\/latex] is to the left of [latex]1[\/latex] on the number line, so [latex]-2&lt;1[\/latex].\n[latex]1[\/latex] is to the right of [latex]-2[\/latex] on the number line, so [latex]1&gt;-2[\/latex].\n\n&nbsp;\n\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220122\/CNX_BMath_Figure_03_01_014c_img.png\" alt=\"This figure is a number line with points negative 3 and negative 1 labeled with dots.\">\n[latex]-1[\/latex] is to the right of [latex]-3[\/latex] on the number line, so [latex]-1&gt;-3[\/latex].\n[latex]-3[\/latex] is to the left of [latex]-1[\/latex] on the number line, so [latex]-3&lt;-1[\/latex].\n\n<div class=\"textbox exercises\"><h3>example<\/h3>Order each of the following pairs of numbers using [latex]&amp;lt[\/latex]; or [latex]\\text{&gt;:}[\/latex]\n\n[latex]14[\/latex]___[latex]6[\/latex]\n[latex]-1[\/latex]___[latex]9[\/latex]\n[latex]-1[\/latex]___ [latex]- 4[\/latex]\n[latex]2[\/latex]___ [latex]- 20[\/latex]\n[reveal-answer q=\"157184\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"157184\"]\n\nSolution:\nBegin by plotting the numbers on a number line as shown in the number line below.\n\n<img 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=\"This figure is a number line with points negative 20, negative 4, negative 1, 2, 6, 9, and 14 labeled with dots.\">\n\n<table id=\"eip-id1168469859124\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td>1. Compare [latex]14[\/latex] and [latex]6[\/latex].<\/td><td>[latex]14___6[\/latex]<\/td><\/tr><tr><td>[latex]14[\/latex] is to the right of [latex]6[\/latex] on the number line.<\/td><td>[latex]14&gt;6[\/latex]<\/td><\/tr><\/tbody><\/table><table id=\"eip-id1168468303840\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td>2. Compare [latex]\u22121[\/latex] and [latex]9[\/latex].<\/td><td>[latex]-1___9[\/latex]<\/td><\/tr><tr><td>[latex]\u22121[\/latex] is to the left of [latex]9[\/latex] on the number line.<\/td><td>[latex]-1&lt;9[\/latex]<\/td><\/tr><\/tbody><\/table><table id=\"eip-id1168467263438\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td>3. Compare [latex]\u22121[\/latex] and [latex]\u22124[\/latex].<\/td><td>[latex]-1___ - 4[\/latex]<\/td><\/tr><tr><td>[latex]\u22121[\/latex] is to the right of [latex]\u22124[\/latex] on the number line.<\/td><td>[latex]-1&gt;-4[\/latex]<\/td><\/tr><\/tbody><\/table><table id=\"eip-id1168468416637\" class=\"unnumbered unstyled\" summary=\".\"><tbody><tr><td>4. Compare [latex]2[\/latex] and [latex]\u221220[\/latex].<\/td><td>[latex]2___ - 20[\/latex]<\/td><\/tr><tr><td>[latex]2[\/latex] is to the right of [latex]\u221220[\/latex] on the number line.<\/td><td>[latex]2&gt;-20[\/latex]<\/td><\/tr><\/tbody><\/table>[\/hidden-answer]\n\n<\/div>&nbsp;\n\n<div class=\"textbox key-takeaways\"><h3>try it<\/h3>[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144925&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\n\n\n\n<\/div>In the video below we show more examples of how to use inequality symbols to compare integers.\n\nhttps:\/\/youtu.be\/YzTGfD6kw-s\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Locate&nbsp;positive and negative numbers on a number line<\/li>\n<li>Compare and order positive and negative numbers using a number line<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Do you live in a place that has very cold winters? Have you ever experienced a temperature below zero? If so, you are already familiar with negative numbers. A negative number is a number that is less than [latex]0[\/latex]. Very cold temperatures are measured in degrees below zero and can be described by negative numbers. For example, [latex]-1^\\circ F[\/latex] (read as &#8220;negative one degree Fahrenheit&#8221;) is [latex]1[\/latex] degree below [latex]0[\/latex]. A minus sign is shown before a number to indicate that it is negative. The figure of a thermometer below&nbsp;shows [latex]-20^\\circ F[\/latex], which is [latex]20[\/latex] degrees below [latex]0[\/latex].<\/p>\n<p>Temperatures below zero are described by negative numbers.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220056\/CNX_BMath_Figure_03_01_002.png\" alt=\"This figure is a thermometer scaled in degrees Fahrenheit. The thermometer has a reading of 20 degrees.\" \/><br \/>\nTemperatures are not the only negative numbers. A bank overdraft is another example of a negative number. If a person writes a check for more than he has in his account, his balance will be negative.<\/p>\n<p>Elevations can also be represented by negative numbers. The elevation at sea level is [latex]0[\/latex] feet. Elevations above sea level are positive and elevations below sea level are negative. The elevation of the Dead Sea, which borders Israel and Jordan, is about [latex]1,302[\/latex] feet below sea level, so the elevation of the Dead Sea can be represented as [latex]-1,302[\/latex] feet. Refer to the image below for a depiction.<\/p>\n<p>The surface of the Mediterranean Sea has an elevation of [latex]0[\/latex] ft. The diagram shows that nearby mountains have higher (positive) elevations whereas the Dead Sea has a lower (negative) elevation.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220057\/CNX_BMath_Figure_03_01_003.png\" alt=\"This figure is a drawing of a side view of the coast of Israel, showing different elevations. The Mediterranean Sea is labeled 0 feet elevation and the Dead Sea is labeled negative 1302 feet elevation. The country of Jordan is also labeled in the figure.\" \/><br \/>\nDepths below the ocean surface are also described by negative numbers. A submarine, for example, might descend to a depth of [latex]500[\/latex] feet. Its position would then be [latex]-500[\/latex] feet as labeled in the image below.<\/p>\n<p>Depths below sea level are described by negative numbers. A submarine [latex]500[\/latex] ft below sea level is at [latex]-500[\/latex] ft.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220058\/CNX_BMath_Figure_03_01_004.png\" alt=\"This figure is a drawing of a submarine underwater. In the water is also a vertical number line, scaled in feet. The number line has 0 feet at the surface and negative 500 feet below the water where the submarine is located.\" \/><br \/>\nBoth positive and negative numbers can be represented on a number line. Recall that the number line created in Add Whole Numbers started at [latex]0[\/latex] and showed the counting numbers increasing to the right as shown in the number line below. The counting numbers [latex](1, 2, 3, \\ldots )[\/latex] on the number line are all positive. We could write a plus sign, [latex]+[\/latex], before a positive number such as [latex]+2[\/latex] or [latex]+3[\/latex], but it is customary to omit the plus sign and write only the number. If there is no sign, the number is assumed to be positive.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220100\/CNX_BMath_Figure_03_01_005.png\" alt=\"This figure is a number line scaled from 0 to 6.\" \/><br \/>\nNow we need to extend the number line to include negative numbers. We mark several units to the left of zero, keeping the intervals the same width as those on the positive side. We label the marks with negative numbers, starting with [latex]-1[\/latex] at the first mark to the left of [latex]0,-2[\/latex] at the next mark, and so on. Refer to the number line below for reference.<\/p>\n<p>On a number line, positive numbers are to the right of zero. Negative numbers are to the left of zero. What about zero? Zero is neither positive nor negative.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220102\/CNX_BMath_Figure_03_01_006.png\" alt=\"This figure is a number line with 0 in the middle. Then, the scaling has positive numbers 1 to 4 to the right of 0 and negative numbers, negative 1 to negative 4 to the left of 0.\" \/><br \/>\nThe arrows at either end of the line indicate that the number line extends forever in each direction. There is no greatest positive number and there is no smallest negative number.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Plot the numbers on a number line:<\/p>\n<ol>\n<li>[latex]3[\/latex]<\/li>\n<li>[latex]-3[\/latex]<\/li>\n<li>[latex]-2[\/latex]<\/li>\n<\/ol>\n<p>Solution<br \/>\nDraw a number line. Mark [latex]0[\/latex] in the center and label several units to the left and right.<\/p>\n<p>1. To plot [latex]3[\/latex], start at [latex]0[\/latex] and count three units to the right. Place a point as shown in the number line below.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220104\/CNX_BMath_Figure_03_01_007.png\" alt=\"This figure is a number line scaled from negative 4 to 4, with the point 3 labeled with a dot.\" \/><\/p>\n<p>2. To plot [latex]-3[\/latex], start at [latex]0[\/latex] and count three units to the left. Place a point as shown in&nbsp;the number line below.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220107\/CNX_BMath_Figure_03_01_008.png\" alt=\"This figure is a number line scaled from negative 4 to 4, with the point negative 3 labeled with a dot.\" \/><\/p>\n<p>3. To plot [latex]-2[\/latex], start at [latex]0[\/latex] and count two units to the left. Place a point as shown in the number line below.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220109\/CNX_BMath_Figure_03_01_009.png\" alt=\"This figure is a number line scaled from negative 4 to 4, with the point negative 2 labeled with a dot.\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144924\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144924&#38;theme=oea&#38;iframe_resize_id=ohm144924&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the video below we show more examples of how to plot integers on a number line.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Plot Integers on the Number Line\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/jlc-m5sXNug?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Order Positive and Negative Numbers<\/h2>\n<p>We can use the number line to compare and order positive and negative numbers. Going from left to right, numbers increase in value. Going from right to left, numbers decrease in value. See the number line below.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220114\/CNX_BMath_Figure_03_01_012.png\" alt=\"This figure is a number line. Above the number line there is an arrow pointing to the right labeled increasing. Below the number line there is an arrow pointing to the left labeled decreasing.\" \/><br \/>\nJust as we did with positive numbers, we can use inequality symbols to show the ordering of positive and negative numbers. Remember that we use the notation [latex]a<b[\/latex] (read [latex]a[\/latex] <em>is less than<\/em> [latex]b[\/latex] ) when [latex]a[\/latex] is to the left of [latex]b[\/latex] on the number line. We write [latex]a>b[\/latex] (read [latex]a[\/latex] <em>is greater than<\/em> [latex]b[\/latex] ) when [latex]a[\/latex] is to the right of [latex]b[\/latex] on the number line. This is shown for the numbers [latex]3[\/latex] and [latex]5[\/latex] in the image below.<\/p>\n<p>The number [latex]3[\/latex] is to the left of [latex]5[\/latex] on the number line. So [latex]3[\/latex] is less than [latex]5[\/latex], and [latex]5[\/latex] is greater than [latex]3[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220116\/CNX_BMath_Figure_03_01_013.png\" alt=\"This figure is a number line with points 3 and 5 labeled with dots. Below the number line is the statements 3 is less than 5 and 5 is greater than 3.\" \/><br \/>\nThe numbers lines to follow show a few more examples.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220118\/CNX_BMath_Figure_03_01_014a_img.png\" alt=\"This figure is a number line with points 1 and 4 labeled with dots.\" \/><br \/>\n[latex]4[\/latex] is to the right of [latex]1[\/latex] on the number line, so [latex]4>1[\/latex].<br \/>\n[latex]1[\/latex] is to the left of [latex]4[\/latex] on the number line, so [latex]1<4[\/latex].\n\n&nbsp;\n\n<img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220120\/CNX_BMath_Figure_03_01_014b_img.png\" alt=\"This figure is a number line with points negative 2 and 1 labeled with dots.\" \/><br \/>\n[latex]-2[\/latex] is to the left of [latex]1[\/latex] on the number line, so [latex]-2<1[\/latex].\n[latex]1[\/latex] is to the right of [latex]-2[\/latex] on the number line, so [latex]1>-2[\/latex].<\/p>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220122\/CNX_BMath_Figure_03_01_014c_img.png\" alt=\"This figure is a number line with points negative 3 and negative 1 labeled with dots.\" \/><br \/>\n[latex]-1[\/latex] is to the right of [latex]-3[\/latex] on the number line, so [latex]-1>-3[\/latex].<br \/>\n[latex]-3[\/latex] is to the left of [latex]-1[\/latex] on the number line, so [latex]-3<-1[\/latex].\n\n\n\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Order each of the following pairs of numbers using [latex]&lt[\/latex]; or [latex]\\text{>:}[\/latex]<\/p>\n<p>[latex]14[\/latex]___[latex]6[\/latex]<br \/>\n[latex]-1[\/latex]___[latex]9[\/latex]<br \/>\n[latex]-1[\/latex]___ [latex]- 4[\/latex]<br \/>\n[latex]2[\/latex]___ [latex]- 20[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q157184\">Show Solution<\/span><\/p>\n<div id=\"q157184\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nBegin by plotting the numbers on a number line as shown in the number line below.<\/p>\n<p><img decoding=\"async\" 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=\"This figure is a number line with points negative 20, negative 4, negative 1, 2, 6, 9, and 14 labeled with dots.\" \/><\/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___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___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___ - 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___ - 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<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm144925\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144925&#38;theme=oea&#38;iframe_resize_id=ohm144925&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the video below we show more examples of how to use inequality symbols to compare integers.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Compare Integers Using An Inequality Symbol\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/YzTGfD6kw-s?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-6388\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Plot Integers on the Number Line. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/jlc-m5sXNug\">https:\/\/youtu.be\/jlc-m5sXNug<\/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: Compare Integers Using An Inequality Symbol. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/YzTGfD6kw-s\">https:\/\/youtu.be\/YzTGfD6kw-s<\/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: 144924, 144925. <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":21,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Plot Integers on the Number Line\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/jlc-m5sXNug\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Compare Integers Using An Inequality Symbol\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/YzTGfD6kw-s\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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