{"id":8979,"date":"2017-04-27T21:59:17","date_gmt":"2017-04-27T21:59:17","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=8979"},"modified":"2017-09-23T20:36:26","modified_gmt":"2017-09-23T20:36:26","slug":"putting-it-together-integers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/putting-it-together-integers\/","title":{"raw":"Putting It Together: Integers","rendered":"Putting It Together: Integers"},"content":{"raw":"At the beginning of this module, we met Beatrice and her team of scientists who were collecting lava at different elevations both above and below sea level. Some of the questions they asked included:\r\n<ul>\r\n \t<li>What's the total elevation change between samples of rock?<\/li>\r\n \t<li>They notice that the lava samples from [latex]23[\/latex] feet below sea level and [latex]518[\/latex] feet above sea level are very similar. What's their vertical distance from each other?<\/li>\r\n<\/ul>\r\nTo answer these questions, we can use integers. If we set up a number line like those we saw in the module, we can place the samples of rock at different \"elevations\" and answer the questions.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/04\/14223828\/Screen-Shot-2017-08-14-at-3.37.53-PM.png\"><img class=\"wp-image-14798 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/04\/14223828\/Screen-Shot-2017-08-14-at-3.37.53-PM-300x94.png\" alt=\"Number line with 110 feet below sea level, sea level, 518 feet above sea level and 10,679 feet above sea level labeled.\" width=\"523\" height=\"164\" \/><\/a>\r\n\r\nWe will align sea level with zero on the number line, such that depths below sea level are negative numbers, and heights above sea level are positive numbers. Now we can answer the questions the scientists asked.\r\n\r\nWhat is the total elevation change between the samples of rock? We are being asked the difference between the greatest elevation above and below sea level where samples were taken. \u00a0In the module, we learned that difference means subtract, so we can subtract the \u00a0elevation below sea level from the elevation above:\r\n<p style=\"text-align: center;\">[latex]10,679-(-110) = 10,889[\/latex]<\/p>\r\n<p style=\"text-align: center;\">The total elevation change is [latex]10,889[\/latex] ft.<\/p>\r\nThe next question asks what is the vertical distance between the sample taken at 23 feet below sea level and the sample taken 518 feet above sea level. We can think of distance from sea level as absolute value, so we can take the sum of the absolute values of the distances.\r\n<p style=\"text-align: center;\">[latex]|-23|+|518| = 23+518=541[\/latex].<\/p>\r\n<p style=\"text-align: center;\">The vertical distance between the two samples is [latex]541[\/latex] feet.<\/p>\r\nIntegers have helped us orient ourselves in space to answer questions that a scientist would want to know.","rendered":"<p>At the beginning of this module, we met Beatrice and her team of scientists who were collecting lava at different elevations both above and below sea level. Some of the questions they asked included:<\/p>\n<ul>\n<li>What&#8217;s the total elevation change between samples of rock?<\/li>\n<li>They notice that the lava samples from [latex]23[\/latex] feet below sea level and [latex]518[\/latex] feet above sea level are very similar. What&#8217;s their vertical distance from each other?<\/li>\n<\/ul>\n<p>To answer these questions, we can use integers. If we set up a number line like those we saw in the module, we can place the samples of rock at different &#8220;elevations&#8221; and answer the questions.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/04\/14223828\/Screen-Shot-2017-08-14-at-3.37.53-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-14798 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/04\/14223828\/Screen-Shot-2017-08-14-at-3.37.53-PM-300x94.png\" alt=\"Number line with 110 feet below sea level, sea level, 518 feet above sea level and 10,679 feet above sea level labeled.\" width=\"523\" height=\"164\" \/><\/a><\/p>\n<p>We will align sea level with zero on the number line, such that depths below sea level are negative numbers, and heights above sea level are positive numbers. Now we can answer the questions the scientists asked.<\/p>\n<p>What is the total elevation change between the samples of rock? We are being asked the difference between the greatest elevation above and below sea level where samples were taken. \u00a0In the module, we learned that difference means subtract, so we can subtract the \u00a0elevation below sea level from the elevation above:<\/p>\n<p style=\"text-align: center;\">[latex]10,679-(-110) = 10,889[\/latex]<\/p>\n<p style=\"text-align: center;\">The total elevation change is [latex]10,889[\/latex] ft.<\/p>\n<p>The next question asks what is the vertical distance between the sample taken at 23 feet below sea level and the sample taken 518 feet above sea level. We can think of distance from sea level as absolute value, so we can take the sum of the absolute values of the distances.<\/p>\n<p style=\"text-align: center;\">[latex]|-23|+|518| = 23+518=541[\/latex].<\/p>\n<p style=\"text-align: center;\">The vertical distance between the two samples is [latex]541[\/latex] feet.<\/p>\n<p>Integers have helped us orient ourselves in space to answer questions that a scientist would want to know.<\/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-8979\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><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":17533,"menu_order":28,"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\"}]","CANDELA_OUTCOMES_GUID":"3b40e62b-98ca-4a99-a0dc-0fac979267c8","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-8979","chapter","type-chapter","status-publish","hentry"],"part":6350,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/8979","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/8979\/revisions"}],"predecessor-version":[{"id":15755,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/8979\/revisions\/15755"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/6350"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/8979\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=8979"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=8979"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=8979"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=8979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}