{"id":550,"date":"2021-08-03T12:29:31","date_gmt":"2021-08-03T12:29:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=550"},"modified":"2022-01-18T20:03:46","modified_gmt":"2022-01-18T20:03:46","slug":"summary-review-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-review-2\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<strong>To add numbers with the same sign (both positive or both negative)<\/strong>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Add their absolute values (without the + or -).<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Give the sum the same sign.<\/li>\r\n<\/ul>\r\n<strong>To add numbers with different signs (one positive, one negative)<\/strong>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Find the difference of their absolute values. (Note that when you find the difference of the absolute values, you always subtract the lesser absolute value from the greater one.)<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Give the sum the same sign as the number with the greater absolute value.<\/li>\r\n<\/ul>\r\nTo subtract signed numbers, change any subtraction of a number to the addition of its negative.\r\n\r\n<strong>The product or quotient of numbers with different signs (one positive, one negative) is negative.<\/strong>\r\n\r\n<strong>The product or quotient of numbers with the same sign (both positive or both negative) is positive.<\/strong>\r\n\r\n<strong>Order of Operations<\/strong>\r\n<ul>\r\n \t<li>Perform operations within grouping symbols: [latex]\\{\\}, [], ()[\/latex]<\/li>\r\n \t<li>Evaluate exponents and radicals<\/li>\r\n \t<li>Multiply and divide, left to right<\/li>\r\n \t<li>Add and subtract, left to right<\/li>\r\n<\/ul>\r\n<strong>Steps for plotting an ordered pair (<em>x<\/em>,\u00a0<em>y<\/em>) in the coordinate plane:<\/strong>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Beginning at the origin, move horizontally (the direction of the [latex]x[\/latex]-axis) the distance given by the [latex]x[\/latex]-coordinate. If the [latex]x[\/latex]-coordinate is positive, move to the right; if the [latex]x[\/latex]-coordinate is negative, move to the left.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Beginning at the [latex]x[\/latex]-coordinate, move vertically (the direction of the [latex]y[\/latex]-axis) the distance given by the [latex]y[\/latex]-coordinate. If the [latex]y[\/latex]-coordinate\u00a0is positive, move up; if the [latex]y[\/latex]-coordinate is negative, move down.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Draw a point at the ending location. Label the point with the ordered pair.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>absolute value:<\/strong> a number\u2019s distance from zero; it\u2019s always positive\r\n\r\n<strong>axis:\u00a0<\/strong>an element of a coordinate plane. Includes a horizontal axis and a vertical axis, or number lines that intersect at right angles. The horizontal axis is called the [latex]x[\/latex]-axis. The vertical axis is called the [latex]y[\/latex]-axis.\r\n\r\n<strong>base:\u00a0<\/strong>an element of an exponential notation. In\u00a0[latex]2^{3}, 2[\/latex] is the base.\r\n\r\n<strong>difference:<\/strong> the result of subtraction\r\n\r\n<strong>exploratory data analysis:<\/strong>\u00a0a method of creating graphs and numerical summaries based on data gathered from a sample of the population to investigate the answer to a research question\r\n\r\n<strong>exponent<\/strong>\u00a0(power): an element of an exponential notation.\u00a0In [latex]2^{3}, [latex]3[\/latex] is the exponent.\r\n\r\n<strong>exponential notation:\u00a0<\/strong>a simplified method to represent repeated multiplication\r\n\r\n<strong>expression:<\/strong>\u00a0combines numbers and variables with mathematical operations such as addition, subtraction, multiplication, and addition. For example, [latex]2+8 \\cdot 5[\/latex] is an expression.\r\n\r\n<strong>integers:<\/strong> counting numbers like 1, 2, 3, etc., including negatives and zero\r\n\r\n<strong>order of operations \/ PEMDAS:\u00a0<\/strong>the order in which a mathematical equation should be solved. The order is\u00a0parenthesis, exponents, multiplications and divisions, additions, and subtractions, or PEMDAS.\r\n\r\n<strong>ordered pair:<\/strong>\u00a0[latex](x,y)[\/latex] describes the location of a point relative to the horizontal [latex]x[\/latex]-axis (the first value of the ordered pair) and relative to the vertical [latex]y[\/latex]\u2212axis (the second value of the ordered pair).\r\n\r\n<strong>origin:\u00a0<\/strong>the point at which the two axes intersect on a coordinate plane\r\n\r\n<strong>product:<\/strong> the result of multiplication\r\n\r\n<strong>quotient:<\/strong> the result of division\r\n\r\n<strong>real number:<\/strong> fractions, negative numbers, decimals, integers, and zero are all real numbers\r\n\r\n<strong>reciprocal:<\/strong>\u00a0another name for the multiplicative inverse (just as opposite is another name for additive inverse). A number and its reciprocal have the same sign.\r\n\r\n<strong>sign:<\/strong> this refers to whether a number is positive or negative, + for positive (to the right of zero on the number line) and \u2212 for negative (to the left of zero on the number line)\r\n\r\n<strong>sum:<\/strong> the result of addition","rendered":"<h2>Key Concepts<\/h2>\n<p><strong>To add numbers with the same sign (both positive or both negative)<\/strong><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Add their absolute values (without the + or -).<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Give the sum the same sign.<\/li>\n<\/ul>\n<p><strong>To add numbers with different signs (one positive, one negative)<\/strong><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Find the difference of their absolute values. (Note that when you find the difference of the absolute values, you always subtract the lesser absolute value from the greater one.)<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Give the sum the same sign as the number with the greater absolute value.<\/li>\n<\/ul>\n<p>To subtract signed numbers, change any subtraction of a number to the addition of its negative.<\/p>\n<p><strong>The product or quotient of numbers with different signs (one positive, one negative) is negative.<\/strong><\/p>\n<p><strong>The product or quotient of numbers with the same sign (both positive or both negative) is positive.<\/strong><\/p>\n<p><strong>Order of Operations<\/strong><\/p>\n<ul>\n<li>Perform operations within grouping symbols: [latex]\\{\\}, [], ()[\/latex]<\/li>\n<li>Evaluate exponents and radicals<\/li>\n<li>Multiply and divide, left to right<\/li>\n<li>Add and subtract, left to right<\/li>\n<\/ul>\n<p><strong>Steps for plotting an ordered pair (<em>x<\/em>,\u00a0<em>y<\/em>) in the coordinate plane:<\/strong><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Beginning at the origin, move horizontally (the direction of the [latex]x[\/latex]-axis) the distance given by the [latex]x[\/latex]-coordinate. If the [latex]x[\/latex]-coordinate is positive, move to the right; if the [latex]x[\/latex]-coordinate is negative, move to the left.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Beginning at the [latex]x[\/latex]-coordinate, move vertically (the direction of the [latex]y[\/latex]-axis) the distance given by the [latex]y[\/latex]-coordinate. If the [latex]y[\/latex]-coordinate\u00a0is positive, move up; if the [latex]y[\/latex]-coordinate is negative, move down.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Draw a point at the ending location. Label the point with the ordered pair.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>absolute value:<\/strong> a number\u2019s distance from zero; it\u2019s always positive<\/p>\n<p><strong>axis:\u00a0<\/strong>an element of a coordinate plane. Includes a horizontal axis and a vertical axis, or number lines that intersect at right angles. The horizontal axis is called the [latex]x[\/latex]-axis. The vertical axis is called the [latex]y[\/latex]-axis.<\/p>\n<p><strong>base:\u00a0<\/strong>an element of an exponential notation. In\u00a0[latex]2^{3}, 2[\/latex] is the base.<\/p>\n<p><strong>difference:<\/strong> the result of subtraction<\/p>\n<p><strong>exploratory data analysis:<\/strong>\u00a0a method of creating graphs and numerical summaries based on data gathered from a sample of the population to investigate the answer to a research question<\/p>\n<p><strong>exponent<\/strong>\u00a0(power): an element of an exponential notation.\u00a0In [latex]2^{3}, [latex]3[\/latex] is the exponent.<\/p>\n<p><strong>exponential notation:\u00a0<\/strong>a simplified method to represent repeated multiplication<\/p>\n<p><strong>expression:<\/strong>\u00a0combines numbers and variables with mathematical operations such as addition, subtraction, multiplication, and addition. For example, [latex]2+8 \\cdot 5[\/latex] is an expression.<\/p>\n<p><strong>integers:<\/strong> counting numbers like 1, 2, 3, etc., including negatives and zero<\/p>\n<p><strong>order of operations \/ PEMDAS:\u00a0<\/strong>the order in which a mathematical equation should be solved. The order is\u00a0parenthesis, exponents, multiplications and divisions, additions, and subtractions, or PEMDAS.<\/p>\n<p><strong>ordered pair:<\/strong>\u00a0[latex](x,y)[\/latex] describes the location of a point relative to the horizontal [latex]x[\/latex]-axis (the first value of the ordered pair) and relative to the vertical [latex]y[\/latex]\u2212axis (the second value of the ordered pair).<\/p>\n<p><strong>origin:\u00a0<\/strong>the point at which the two axes intersect on a coordinate plane<\/p>\n<p><strong>product:<\/strong> the result of multiplication<\/p>\n<p><strong>quotient:<\/strong> the result of division<\/p>\n<p><strong>real number:<\/strong> fractions, negative numbers, decimals, integers, and zero are all real numbers<\/p>\n<p><strong>reciprocal:<\/strong>\u00a0another name for the multiplicative inverse (just as opposite is another name for additive inverse). A number and its reciprocal have the same sign.<\/p>\n<p><strong>sign:<\/strong> this refers to whether a number is positive or negative, + for positive (to the right of zero on the number line) and \u2212 for negative (to the left of zero on the number line)<\/p>\n<p><strong>sum:<\/strong> the result of addition<\/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-550\">\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><strong>Provided 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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-550","chapter","type-chapter","status-publish","hentry"],"part":31,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/550","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":12,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/550\/revisions"}],"predecessor-version":[{"id":3361,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/550\/revisions\/3361"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/31"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/550\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=550"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=550"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=550"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=550"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}