{"id":154872,"date":"2022-03-26T00:01:03","date_gmt":"2022-03-25T18:31:03","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/operations-on-real-numbers\/"},"modified":"2022-12-31T15:33:31","modified_gmt":"2022-12-31T10:03:31","slug":"operations-on-real-numbers","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/","title":{"rendered":"Operations on Real Numbers"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#What_is_a_Real_Number\" title=\"What is a Real Number?\">What is a Real Number?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#What_are_Mathematical_Operations\" title=\"What are Mathematical Operations?\">What are Mathematical Operations?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Addition_of_Two_Rational_Numbers\" title=\"Addition of Two Rational Numbers\">Addition of Two Rational Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Subtraction_of_Two_Rational_Numbers\" title=\"Subtraction of Two Rational Numbers\">Subtraction of Two Rational Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Multiplication_of_Two_Rational_Numbers\" title=\"Multiplication of Two Rational Numbers\">Multiplication of Two Rational Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Division_of_Two_Rational_Numbers\" title=\"Division of Two Rational Numbers\">Division of Two Rational Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Addition_of_Two_Irrational_Numbers\" title=\"Addition of Two Irrational Numbers\">Addition of Two Irrational Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Subtraction_of_Two_Irrational_Numbers\" title=\"Subtraction of Two Irrational Numbers\">Subtraction of Two Irrational Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Multiplication_of_Two_Irrational_Numbers\" title=\"Multiplication of Two Irrational Numbers\">Multiplication of Two Irrational Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Division_of_Two_Irrational_Numbers\" title=\"Division of Two Irrational Numbers\">Division of Two Irrational Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Addition_of_an_Irrational_and_a_Rational_Number\" title=\"Addition of an Irrational and a Rational Number\">Addition of an Irrational and a Rational Number<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Subtraction_of_an_Irrational_and_a_Rational_Number\" title=\"Subtraction of an Irrational and a Rational Number\">Subtraction of an Irrational and a Rational Number<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Multiplication_of_an_Irrational_and_a_Rational_Number\" title=\"Multiplication of an Irrational and a Rational Number\">Multiplication of an Irrational and a Rational Number<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Division_of_an_Irrational_Number_with_a_Rational_Number\" title=\"Division of an Irrational Number with a Rational Number\">Division of an Irrational Number with a Rational Number<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Operations_on_Real_Numbers_Worksheet\" title=\"Operations on Real Numbers Worksheet\">Operations on Real Numbers Worksheet<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/#Summary\" title=\"Summary\">Summary<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Real_Number\"><\/span>What is a Real Number?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A real number is a number that can be represented in decimal notation, and that is not a complex number. Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154871 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/operations-on-real-numbers.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/operations-on-real-numbers.jpg?v=1648233059 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/operations-on-real-numbers-300x212.jpg?v=1648233059 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Mathematical_Operations\"><\/span>What are Mathematical Operations?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Mathematical operations are the basic arithmetic and algebraic manipulations that are used to solve mathematical problems. The most common operations are addition, subtraction, multiplication, and division, but there are many others, including exponents, roots, and logarithms. These operations can be performed on numbers, variables, and other mathematical expressions.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Addition_of_Two_Rational_Numbers\"><\/span>Addition of Two Rational Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The sum of two rational numbers is another rational number. To find the sum of two rational numbers, add the two numbers together and keep the denominator the same.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Subtraction_of_Two_Rational_Numbers\"><\/span>Subtraction of Two Rational Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To subtract two rational numbers, subtract the numerators and subtract the denominators.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Multiplication_of_Two_Rational_Numbers\"><\/span>Multiplication of Two Rational Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To multiply two rational numbers, multiply the numerators and multiply the denominators.<\/p>\n<p>For example, to multiply 3 and 5, multiply 3&#215;5=15 and 5&#215;3=15. The product is 15\/15=1.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Division_of_Two_Rational_Numbers\"><\/span>Division of Two Rational Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The division of two rational numbers can be done by using the division algorithm.<\/p>\n<p>The division algorithm states that to divide two rational numbers, divide the numerator by the denominator.<\/p>\n<p>For example, to divide 5 by 2, divide 5 by 2 to get 2.5.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Addition_of_Two_Irrational_Numbers\"><\/span>Addition of Two Irrational Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Let&#8217;s add two irrational numbers together. We&#8217;ll use the irrational number \u03c0 and the irrational number 2.<\/p>\n<p>We&#8217;ll start by writing out the two irrational numbers.<\/p>\n<p>\u03c0<br \/>\n2<\/p>\n<p>Next, we&#8217;ll add the two numbers together.<\/p>\n<p>\u03c0 + 2<\/p>\n<p>We get the answer 3.14159.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Subtraction_of_Two_Irrational_Numbers\"><\/span>Subtraction of Two Irrational Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To subtract two irrational numbers, subtract the numerators and subtract the denominators.<\/p>\n<p>\\frac{1}{2} &#8211; \\frac{1}{3} = \\frac{1}{6}<\/p>\n<p>-\\frac{\\sqrt{3}}{2} = -\\frac{1}{2}<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Multiplication_of_Two_Irrational_Numbers\"><\/span>Multiplication of Two Irrational Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To multiply two irrational numbers, one must use the following steps:<\/p>\n<p>1. Convert the irrational numbers to decimals.<\/p>\n<p>2. Multiply the decimals.<\/p>\n<p>3. Convert the answer back to irrational numbers.<\/p>\n<p>For example, to multiply \u221a2 and \u03c0, the steps would be:<\/p>\n<p>1. Convert \u221a2 to 1.41421356<\/p>\n<p>2. Multiply 1.41421356 by 3.14159265<\/p>\n<p>3. Convert the answer back to \u221a2.<\/p>\n<p>The answer is 4.7123889<\/p>\n<p>Another example, to multiply \u221a3 and \u03c0\/2, the steps would be:<\/p>\n<p>1. Convert \u221a3 to 1.73205081<\/p>\n<p>2. Multiply 1.73205081 by 1.5<\/p>\n<p>3. Convert the answer back to \u221a3.<\/p>\n<p>The answer is 2.618033988<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Division_of_Two_Irrational_Numbers\"><\/span>Division of Two Irrational Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The division of two irrational numbers is not a rational operation.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Addition_of_an_Irrational_and_a_Rational_Number\"><\/span>Addition of an Irrational and a Rational Number<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The sum of an irrational and a rational number is always irrational.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Subtraction_of_an_Irrational_and_a_Rational_Number\"><\/span>Subtraction of an Irrational and a Rational Number<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To subtract an irrational number from a rational number, simply subtract the numerators and subtract the denominators.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Multiplication_of_an_Irrational_and_a_Rational_Number\"><\/span>Multiplication of an Irrational and a Rational Number<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>When multiplying two irrational numbers, the result will be irrational. For example, when multiplying \\(\\sqrt{2}\\) and \\(\\sqrt{3}\\), the result will be irrational. When multiplying a rational number and an irrational number, the result will be irrational. For example, when multiplying 3 and \\(\\sqrt{2}\\), the result will be irrational.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Division_of_an_Irrational_Number_with_a_Rational_Number\"><\/span>Division of an Irrational Number with a Rational Number<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To divide an irrational number with a rational number, divide the numerator and denominator of the rational number by the root of the irrational number.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Operations_on_Real_Numbers_Worksheet\"><\/span>Operations on Real Numbers Worksheet<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. Add 3.14 and 5.<\/p>\n<p>3.14 + 5 = 8.14<\/p>\n<p>2. Subtract 5.14 from 8.<\/p>\n<p>8.14 &#8211; 5.14 = 3<\/p>\n<p>3. Multiply 3.14 by 2.<\/p>\n<p>3.14 * 2 = 6.28<\/p>\n<p>4. Divide 8.14 by 2.<\/p>\n<p>8.14 \/ 2 = 4.07<\/p>\n<p>5. Find the square root of 64.<\/p>\n<p>64 = 8.<\/p>\n<p>6. Find the cube root of 125.<\/p>\n<p>125 = 5.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Summary\"><\/span>Summary<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The article &#8220;The Negative Effects of Social Media on Society&#8221; discusses the various ways in which social media can have a negative impact on society. The article cites examples of how social media can lead to cyberbullying, social isolation, and an increase in the spread of misinformation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is a Real Number? A real number is a number that can be represented in decimal notation, and that [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Operations on Real Numbers","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Operations on Real Numbers topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/operations-on-real-numbers\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Operations on Real Numbers - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Operations on Real Numbers topic of Maths in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/operations-on-real-numbers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Operations on Real Numbers - 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