{"id":9209,"date":"2017-05-02T16:41:17","date_gmt":"2017-05-02T16:41:17","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9209"},"modified":"2020-01-08T23:48:22","modified_gmt":"2020-01-08T23:48:22","slug":"summary-using-the-language-of-algebra","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/summary-using-the-language-of-algebra\/","title":{"raw":"Summary: Using the Language of Algebra","rendered":"Summary: Using the Language of Algebra"},"content":{"raw":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,\r\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\r\n<h2 data-type=\"title\">Key Concepts<\/h2>\r\n<table id=\"eip-id1168265095050\" class=\"unnumbered\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled \" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"left\"><strong>Operation<\/strong><\/th>\r\n<th data-align=\"left\"><strong>Notation<\/strong><\/th>\r\n<th data-align=\"left\"><strong>Say:<\/strong><\/th>\r\n<th data-align=\"left\"><strong>The result is\u2026<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Addition<\/td>\r\n<td data-align=\"left\">[latex]a+b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] plus [latex]b[\/latex]<\/td>\r\n<td data-align=\"left\">the sum of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Multiplication<\/td>\r\n<td data-align=\"left\">[latex]a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] times [latex]b[\/latex]<\/td>\r\n<td data-align=\"left\">the product of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Subtraction<\/td>\r\n<td data-align=\"left\">[latex]a-b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] minus [latex]b[\/latex]<\/td>\r\n<td data-align=\"left\">the difference of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Division<\/td>\r\n<td data-align=\"left\">[latex]a\\div b,a\/b,\\frac{a}{b},b\\overline{)a}[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] divided by [latex]b[\/latex]<\/td>\r\n<td data-align=\"left\">the quotient of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ul id=\"eip-740\">\r\n \t<li><strong>Equality Symbol<\/strong>\r\n<ul id=\"eip-id1168262501679\">\r\n \t<li>[latex]a=b[\/latex] is read as [latex]a[\/latex] is equal to [latex]b[\/latex]<\/li>\r\n \t<li>The symbol [latex]=[\/latex] is called the equal sign.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Inequality<\/strong>\r\n<ul id=\"eip-id1168263909662\">\r\n \t<li>[latex]a&lt;b[\/latex] is read [latex]a[\/latex] is less than [latex]b[\/latex]<\/li>\r\n \t<li>[latex]a[\/latex] is to the left of [latex]b[\/latex] on the number line<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215805\/CNX_BMath_Figure_02_01_018_img.png\" alt=\"..\" data-media-type=\"image\/png\" \/><\/li>\r\n \t<li>[latex]a&gt;b[\/latex] is read [latex]a[\/latex] is greater than [latex]b[\/latex]<\/li>\r\n \t<li>[latex]a[\/latex] is to the right of [latex]b[\/latex] on the number line<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215806\/CNX_BMath_Figure_02_01_019_img.png\" alt=\"..\" data-media-type=\"image\/png\" \/><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<table id=\"eip-455\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"center\">Algebraic Notation<\/th>\r\n<th data-align=\"center\">Say<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a=b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is equal to [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a\\ne b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is not equal to [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a&lt;b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is less than [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a&gt;b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is greater than [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a\\le b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is less than or equal to [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">[latex]a\\ge b[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]a[\/latex] is greater than or equal to [latex]b[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ul id=\"eip-910\">\r\n \t<li><strong>Exponential Notation<\/strong>\r\n<ul id=\"eip-id1168266330675\">\r\n \t<li>For any expression [latex]{a}^{n}[\/latex] is a factor multiplied by itself [latex]n[\/latex] times, if [latex]n[\/latex] is a positive integer.<\/li>\r\n \t<li>[latex]{a}^{n}[\/latex] means multiply [latex]n[\/latex] factors of [latex]a[\/latex]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215807\/CNX_BMath_Figure_02_01_020_img.png\" alt=\"..\" data-media-type=\"image\/png\" \/><\/li>\r\n \t<li>The expression of [latex]{a}^{n}[\/latex] is read [latex]a[\/latex] to the [latex]n[\/latex]th power.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<strong>Order of Operations<\/strong> When simplifying mathematical expressions perform the operations in the following order:\r\n<ol>\r\n \t<li><strong>Parentheses<\/strong> and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\r\n \t<li><strong>Exponents<\/strong>: Simplify all expressions with exponents.<\/li>\r\n \t<li><strong>Multiplication and Division<\/strong>: Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\r\n \t<li><strong>Addition and Subtraction<\/strong>: Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\r\n<\/ol>\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id2645686\" class=\"definition\">\r\n \t<dt><strong>expressions<\/strong><\/dt>\r\n \t<dd id=\"fs-id2645692\">An expression is a number, a variable, or a combination of numbers and variables and operation symbols.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id2645696\" class=\"definition\">\r\n \t<dt><strong>equation<\/strong><\/dt>\r\n \t<dd id=\"fs-id2645701\">An equation is made up of two expressions connected by an equal sign.<\/dd>\r\n<\/dl>\r\n&nbsp;","rendered":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,<br \/>\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\n<h2 data-type=\"title\">Key Concepts<\/h2>\n<table id=\"eip-id1168265095050\" class=\"unnumbered\" summary=\"This table has five rows and four columns. The first row is a header row. Each column is labeled accordingly: the first is labeled\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"left\"><strong>Operation<\/strong><\/th>\n<th data-align=\"left\"><strong>Notation<\/strong><\/th>\n<th data-align=\"left\"><strong>Say:<\/strong><\/th>\n<th data-align=\"left\"><strong>The result is\u2026<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Addition<\/td>\n<td data-align=\"left\">[latex]a+b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] plus [latex]b[\/latex]<\/td>\n<td data-align=\"left\">the sum of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Multiplication<\/td>\n<td data-align=\"left\">[latex]a\\cdot b,\\left(a\\right)\\left(b\\right),\\left(a\\right)b,a\\left(b\\right)[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] times [latex]b[\/latex]<\/td>\n<td data-align=\"left\">the product of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Subtraction<\/td>\n<td data-align=\"left\">[latex]a-b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] minus [latex]b[\/latex]<\/td>\n<td data-align=\"left\">the difference of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">Division<\/td>\n<td data-align=\"left\">[latex]a\\div b,a\/b,\\frac{a}{b},b\\overline{)a}[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] divided by [latex]b[\/latex]<\/td>\n<td data-align=\"left\">the quotient of [latex]a[\/latex] and [latex]b[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul id=\"eip-740\">\n<li><strong>Equality Symbol<\/strong>\n<ul id=\"eip-id1168262501679\">\n<li>[latex]a=b[\/latex] is read as [latex]a[\/latex] is equal to [latex]b[\/latex]<\/li>\n<li>The symbol [latex]=[\/latex] is called the equal sign.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Inequality<\/strong>\n<ul id=\"eip-id1168263909662\">\n<li>[latex]a<b[\/latex] is read [latex]a[\/latex] is less than [latex]b[\/latex]<\/li>\n<li>[latex]a[\/latex] is to the left of [latex]b[\/latex] on the number line<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215805\/CNX_BMath_Figure_02_01_018_img.png\" alt=\"..\" data-media-type=\"image\/png\" \/><\/li>\n<li>[latex]a>b[\/latex] is read [latex]a[\/latex] is greater than [latex]b[\/latex]<\/li>\n<li>[latex]a[\/latex] is to the right of [latex]b[\/latex] on the number line<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215806\/CNX_BMath_Figure_02_01_019_img.png\" alt=\"..\" data-media-type=\"image\/png\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<table id=\"eip-455\" summary=\"This table has seven rows and two columns. The first row is a header row and it labels each column. The first column is labeled\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"center\">Algebraic Notation<\/th>\n<th data-align=\"center\">Say<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a=b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is equal to [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a\\ne b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is not equal to [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a<b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is less than [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a>b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is greater than [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a\\le b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is less than or equal to [latex]b[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\">[latex]a\\ge b[\/latex]<\/td>\n<td data-align=\"left\">[latex]a[\/latex] is greater than or equal to [latex]b[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul id=\"eip-910\">\n<li><strong>Exponential Notation<\/strong>\n<ul id=\"eip-id1168266330675\">\n<li>For any expression [latex]{a}^{n}[\/latex] is a factor multiplied by itself [latex]n[\/latex] times, if [latex]n[\/latex] is a positive integer.<\/li>\n<li>[latex]{a}^{n}[\/latex] means multiply [latex]n[\/latex] factors of [latex]a[\/latex]<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215807\/CNX_BMath_Figure_02_01_020_img.png\" alt=\"..\" data-media-type=\"image\/png\" \/><\/li>\n<li>The expression of [latex]{a}^{n}[\/latex] is read [latex]a[\/latex] to the [latex]n[\/latex]th power.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Order of Operations<\/strong> When simplifying mathematical expressions perform the operations in the following order:<\/p>\n<ol>\n<li><strong>Parentheses<\/strong> and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\n<li><strong>Exponents<\/strong>: Simplify all expressions with exponents.<\/li>\n<li><strong>Multiplication and Division<\/strong>: Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\n<li><strong>Addition and Subtraction<\/strong>: Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\n<\/ol>\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id2645686\" class=\"definition\">\n<dt><strong>expressions<\/strong><\/dt>\n<dd id=\"fs-id2645692\">An expression is a number, a variable, or a combination of numbers and variables and operation symbols.<\/dd>\n<\/dl>\n<dl id=\"fs-id2645696\" class=\"definition\">\n<dt><strong>equation<\/strong><\/dt>\n<dd id=\"fs-id2645701\">An equation is made up of two expressions connected by an equal sign.<\/dd>\n<\/dl>\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-9209\">\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":6,"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":"d130a620-0240-4c9b-b841-898720a5b9e6","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9209","chapter","type-chapter","status-publish","hentry"],"part":13769,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9209","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9209\/revisions"}],"predecessor-version":[{"id":16074,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9209\/revisions\/16074"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/parts\/13769"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9209\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/media?parent=9209"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9209"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/contributor?post=9209"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/license?post=9209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}