{"id":552,"date":"2016-10-18T22:26:19","date_gmt":"2016-10-18T22:26:19","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&#038;p=552"},"modified":"2017-04-03T22:48:09","modified_gmt":"2017-04-03T22:48:09","slug":"why-it-matters-algebra-essentials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/why-it-matters-algebra-essentials\/","title":{"raw":"Why It Matters: Algebra Essentials","rendered":"Why It Matters: Algebra Essentials"},"content":{"raw":"<h2>Why learn about the essentials of algebra?<\/h2>\r\n[caption id=\"attachment_1557\" align=\"alignright\" width=\"395\"]<img class=\" wp-image-1557\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/28235201\/Yuan_dynasty_iron_magic_square-300x273.jpg\" alt=\"Iron plate showing persian\/ arabic numbers from teh Yuan dynasty in china circa 1271 - 1368.\" width=\"395\" height=\"359\" \/> Yuan Dynasty iron magic square showing Persian\/ Arabic numbers (ca. 1271 - 1368)[\/caption]\r\n\r\nIt is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Farmers, cattlemen, and tradesmen used tokens, stones, or markers to signify a single quantity\u2014a sheaf of grain, a head of livestock, or a fixed length of cloth, for example. Doing so made commerce possible, leading to improved communications and the spread of civilization.\r\n\r\nThree to four thousand years ago, Egyptians introduced fractions. They first used them to show reciprocals. Later, they used them to represent the amount when a quantity was divided into equal parts.\r\n\r\nBut what if there were no cattle to trade or an entire crop of grain was lost in a flood? How could someone indicate the existence of nothing? From earliest times, people had thought of a \"base state\" while counting and used various symbols to represent this null condition. However, it was not until about the fifth century A.D. in India that zero was added to the number system and used as a numeral in calculations.\r\n\r\nClearly, there was also a need for numbers to represent loss or debt. In India, in the seventh century A.D., negative numbers were used as solutions to mathematical equations and commercial debts. The opposites of the counting numbers expanded the number system even further.\r\n\r\n&nbsp;\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nReal Numbers\r\n<ul>\r\n \t<li class=\"li2\"><span class=\"s1\">Classify a real number<\/span><\/li>\r\n \t<li class=\"li2\"><span class=\"s1\">Perform calculations using order of operations<\/span><\/li>\r\n \t<li class=\"li2\"><span class=\"s1\">Use the properties of real numbers<\/span><\/li>\r\n \t<li class=\"li2\"><span class=\"s1\">Evaluate and simplify algebraic expressions<\/span><\/li>\r\n<\/ul>\r\nExponents and Scientific Notation\r\n<ul>\r\n \t<li class=\"li2\"><span class=\"s1\">Use the rules of exponents to simplify exponential expressions<\/span><\/li>\r\n \t<li class=\"li2\"><span class=\"s1\">Use scientific notation<\/span><\/li>\r\n<\/ul>\r\nRadicals and Rational Exponents\r\n<ul>\r\n \t<li class=\"li2\"><span class=\"s1\">Evaluate and simplify square roots<\/span><\/li>\r\n \t<li class=\"li2\"><span class=\"s1\">Rationalize a denominator that contains a square root<\/span><\/li>\r\n \t<li class=\"li3\"><span class=\"s4\">Rewrite a radical expression using rational exponents<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;","rendered":"<h2>Why learn about the essentials of algebra?<\/h2>\n<div id=\"attachment_1557\" style=\"width: 405px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1557\" class=\"wp-image-1557\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/28235201\/Yuan_dynasty_iron_magic_square-300x273.jpg\" alt=\"Iron plate showing persian\/ arabic numbers from teh Yuan dynasty in china circa 1271 - 1368.\" width=\"395\" height=\"359\" \/><\/p>\n<p id=\"caption-attachment-1557\" class=\"wp-caption-text\">Yuan Dynasty iron magic square showing Persian\/ Arabic numbers (ca. 1271 &#8211; 1368)<\/p>\n<\/div>\n<p>It is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Farmers, cattlemen, and tradesmen used tokens, stones, or markers to signify a single quantity\u2014a sheaf of grain, a head of livestock, or a fixed length of cloth, for example. Doing so made commerce possible, leading to improved communications and the spread of civilization.<\/p>\n<p>Three to four thousand years ago, Egyptians introduced fractions. They first used them to show reciprocals. Later, they used them to represent the amount when a quantity was divided into equal parts.<\/p>\n<p>But what if there were no cattle to trade or an entire crop of grain was lost in a flood? How could someone indicate the existence of nothing? From earliest times, people had thought of a &#8220;base state&#8221; while counting and used various symbols to represent this null condition. However, it was not until about the fifth century A.D. in India that zero was added to the number system and used as a numeral in calculations.<\/p>\n<p>Clearly, there was also a need for numbers to represent loss or debt. In India, in the seventh century A.D., negative numbers were used as solutions to mathematical equations and commercial debts. The opposites of the counting numbers expanded the number system even further.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Real Numbers<\/p>\n<ul>\n<li class=\"li2\"><span class=\"s1\">Classify a real number<\/span><\/li>\n<li class=\"li2\"><span class=\"s1\">Perform calculations using order of operations<\/span><\/li>\n<li class=\"li2\"><span class=\"s1\">Use the properties of real numbers<\/span><\/li>\n<li class=\"li2\"><span class=\"s1\">Evaluate and simplify algebraic expressions<\/span><\/li>\n<\/ul>\n<p>Exponents and Scientific Notation<\/p>\n<ul>\n<li class=\"li2\"><span class=\"s1\">Use the rules of exponents to simplify exponential expressions<\/span><\/li>\n<li class=\"li2\"><span class=\"s1\">Use scientific notation<\/span><\/li>\n<\/ul>\n<p>Radicals and Rational Exponents<\/p>\n<ul>\n<li class=\"li2\"><span class=\"s1\">Evaluate and simplify square roots<\/span><\/li>\n<li class=\"li2\"><span class=\"s1\">Rationalize a denominator that contains a square root<\/span><\/li>\n<li class=\"li3\"><span class=\"s4\">Rewrite a radical expression using rational exponents<\/span><\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/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-552\">\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>Why It Matters: Algebra Essentials. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Yuan Dynasty iron magic square showing Persian\/ Arabic numbers (ca. 1271 - 1368). <strong>Authored by<\/strong>: By BabelStone - Own work. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/commons.wikimedia.org\/w\/index.php?curid=16206206\">https:\/\/commons.wikimedia.org\/w\/index.php?curid=16206206<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/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":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Yuan Dynasty iron magic square showing Persian\/ Arabic numbers (ca. 1271 - 1368)\",\"author\":\"By BabelStone - Own work\",\"organization\":\"\",\"url\":\"https:\/\/commons.wikimedia.org\/w\/index.php?curid=16206206\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Why It Matters: Algebra Essentials\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"c6a6901e-5908-4294-9bca-7f375485c5a7","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-552","chapter","type-chapter","status-publish","hentry"],"part":55,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/552","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/552\/revisions"}],"predecessor-version":[{"id":3937,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/552\/revisions\/3937"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/55"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/552\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/media?parent=552"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=552"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/contributor?post=552"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/license?post=552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}