{"id":154702,"date":"2022-03-25T23:49:42","date_gmt":"2022-03-25T18:19:42","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/properties-of-multiplication-of-integers\/"},"modified":"2022-12-31T15:48:54","modified_gmt":"2022-12-31T10:18:54","slug":"properties-of-multiplication-of-integers","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/","title":{"rendered":"Properties of Multiplication of Integers"},"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\/properties-of-multiplication-of-integers\/#Properties_of_Multiplication_of_Integer\" title=\"Properties of Multiplication of Integer\">Properties of Multiplication of Integer<\/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\/properties-of-multiplication-of-integers\/#What_Is_The_Meaning_of_An_Integer\" title=\"What Is The Meaning of An Integer?\">What Is The Meaning of An Integer?<\/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\/properties-of-multiplication-of-integers\/#Basic_Properties_of_the_Integers\" title=\"Basic Properties of the Integers\">Basic Properties of the Integers<\/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\/properties-of-multiplication-of-integers\/#Closure_Property\" title=\"Closure Property\">Closure Property<\/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\/properties-of-multiplication-of-integers\/#Closure_Property_Under_Multiplication\" title=\"Closure Property Under Multiplication:\">Closure Property Under Multiplication:<\/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\/properties-of-multiplication-of-integers\/#Commutative_Property\" title=\"Commutative Property\">Commutative Property<\/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\/properties-of-multiplication-of-integers\/#Multiplication_is_commutative_for_integer_numbers\" title=\"Multiplication is commutative for integer numbers.\">Multiplication is commutative for integer 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\/properties-of-multiplication-of-integers\/#Associative_Property\" title=\"Associative Property\">Associative Property<\/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\/properties-of-multiplication-of-integers\/#Associative_property_under_multiplication\" title=\"Associative property under multiplication:\">Associative property under multiplication:<\/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\/properties-of-multiplication-of-integers\/#Distributive_Property\" title=\"Distributive Property\">Distributive Property<\/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\/properties-of-multiplication-of-integers\/#Distributive_Property_of_Multiplication_Over_Addition\" title=\"Distributive Property of Multiplication Over Addition:\">Distributive Property of Multiplication Over Addition:<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Multiplication_of_Integer\"><\/span>Properties of Multiplication of Integer<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The product of two integers is always an integer.<\/p>\n<p>The product of two negative integers is always a negative integer.<\/p>\n<p>The product of two positive integers is always a positive integer.<\/p>\n<p>The product of a positive and a negative integer is always a negative integer.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154701 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/properties-of-multiplication-of-integers.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/properties-of-multiplication-of-integers.jpg?v=1648232379 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/properties-of-multiplication-of-integers-300x212.jpg?v=1648232379 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_Is_The_Meaning_of_An_Integer\"><\/span>What Is The Meaning of An Integer?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An integer is a number that can be written without a decimal point and has no fractional parts. Integers include the natural numbers (1, 2, 3,&#8230;) and their negatives (-1, -2, -3,&#8230;).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Basic_Properties_of_the_Integers\"><\/span>Basic Properties of the Integers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Integers are whole numbers and their opposites. The set of all integers is denoted by \\mathbb{Z}. The first few integers are:<\/p>\n<p>\\mathbb{Z} = {&#8230;, -3, -2, -1, 0, 1, 2, 3, &#8230;}<\/p>\n<p>Integers have the following properties:<\/p>\n<p>They are whole numbers.<\/p>\n<p>Their opposites are also integers.<\/p>\n<p>Integers can be added, subtracted, multiplied, and divided.<\/p>\n<p>Integers are closed under addition, subtraction, multiplication, and division. This means that the sum, difference, product, and quotient of two integers is always another integer.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Closure_Property\"><\/span>Closure Property<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Closed property indicates whether the text box is currently closed.<\/p>\n<p>public bool Closed { get; }<\/p>\n<p>The Closed property is a bool that indicates whether the text box is currently closed.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Closure_Property_Under_Multiplication\"><\/span>Closure Property Under Multiplication:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If a and b are two positive real numbers and a*b = c, then c is also a positive real number.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Commutative_Property\"><\/span>Commutative Property<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>of Addition<\/p>\n<p>The commutative property of addition states that the order of addition does not affect the result. In other words, a + b is the same as b + a.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Multiplication_is_commutative_for_integer_numbers\"><\/span>Multiplication is commutative for integer numbers.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>This means that the order of multiplication does not affect the result: a\u00d7b=b\u00d7a.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Associative_Property\"><\/span>Associative Property<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The associative property states that when two or more items are combined, the order of the items does not matter. For example, if you are adding three numbers together, the order in which you add them does not matter.<\/p>\n<p>3 + 4 + 5 = 12<\/p>\n<p>12 + 3 = 15<\/p>\n<p>15 + 4 = 19<\/p>\n<p>19 + 5 = 24<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Associative_property_under_multiplication\"><\/span>Associative property under multiplication:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>For all real numbers a, b, and c,<\/p>\n<p>a(bc) = (ab)c.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Distributive_Property\"><\/span>Distributive Property<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The distributive property states that for any real numbers a, b, and c,<\/p>\n<p>a(b+c) = ab+ac.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Distributive_Property_of_Multiplication_Over_Addition\"><\/span>Distributive Property of Multiplication Over Addition:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>For any real numbers a, b, and c,<\/p>\n<p>(a + b) * c = a * c + b * c.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Properties of Multiplication of Integer The product of two integers is always an integer. The product of two negative integers [&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":"Properties of Multiplication of Integers","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Properties of Multiplication of Integers topic of Maths in details explained by subject experts on infinitylearn.com","custom_permalink":"maths\/properties-of-multiplication-of-integers\/"},"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>Properties of Multiplication of Integers - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Properties of Multiplication of Integers 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\/properties-of-multiplication-of-integers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Properties of Multiplication of Integers - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"Learn about Properties of Multiplication of Integers topic of Maths in details explained by subject experts on infinitylearn.com\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-25T18:19:42+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-12-31T10:18:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/properties-of-multiplication-of-integers.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"vipin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Properties of Multiplication of Integers - Infinity Learn by Sri Chaitanya","description":"Learn about Properties of Multiplication of Integers topic of Maths in details explained by subject experts on infinitylearn.com","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/","og_locale":"en_US","og_type":"article","og_title":"Properties of Multiplication of Integers - Infinity Learn by Sri Chaitanya","og_description":"Learn about Properties of Multiplication of Integers topic of Maths in details explained by subject experts on infinitylearn.com","og_url":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2022-03-25T18:19:42+00:00","article_modified_time":"2022-12-31T10:18:54+00:00","og_image":[{"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/properties-of-multiplication-of-integers.jpg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"vipin","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/#primaryimage","inLanguage":"en-US","url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/properties-of-multiplication-of-integers.jpg?v=1648232379","contentUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/properties-of-multiplication-of-integers.jpg?v=1648232379","width":606,"height":428},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/","name":"Properties of Multiplication of Integers - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"primaryImageOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/#primaryimage"},"datePublished":"2022-03-25T18:19:42+00:00","dateModified":"2022-12-31T10:18:54+00:00","description":"Learn about Properties of Multiplication of Integers topic of Maths in details explained by subject experts on infinitylearn.com","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Properties of Multiplication of Integers"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2"},"headline":"Properties of Multiplication of Integers","datePublished":"2022-03-25T18:19:42+00:00","dateModified":"2022-12-31T10:18:54+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/#webpage"},"wordCount":378,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/properties-of-multiplication-of-integers\/#primaryimage"},"thumbnailUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/properties-of-multiplication-of-integers.jpg","articleSection":["Maths"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2","name":"vipin","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","caption":"vipin"},"sameAs":["http:\/\/surge.infinitylearn.com"],"url":"https:\/\/infinitylearn.com\/surge\/author\/vipin\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/154702"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=154702"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/154702\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=154702"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=154702"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=154702"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=154702"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}