{"id":623044,"date":"2023-06-20T22:37:16","date_gmt":"2023-06-20T17:07:16","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=623044"},"modified":"2024-07-05T11:12:33","modified_gmt":"2024-07-05T05:42:33","slug":"commutative-property-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/formulas\/commutative-property-formula\/","title":{"rendered":"Commutative Property Formula\u00a0"},"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\/formulas\/commutative-property-formula\/#Introduction_to_Commutative_Property_Formula\" title=\"Introduction to Commutative Property Formula\">Introduction to Commutative Property Formula<\/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\/formulas\/commutative-property-formula\/#What_is_the_Commutative_Property_of_Multiplication\" title=\"What is the Commutative Property of Multiplication?\">What is the Commutative Property of Multiplication?<\/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\/formulas\/commutative-property-formula\/#Commutative_Property_of_Multiplication_Formula\" title=\"Commutative Property of Multiplication Formula\">Commutative Property of Multiplication Formula<\/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\/formulas\/commutative-property-formula\/#Commutative_Property_of_Multiplication_and_Addition\" title=\"Commutative Property of Multiplication and Addition\">Commutative Property of Multiplication and Addition<\/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\/formulas\/commutative-property-formula\/#Tips_on_the_Commutative_Property_of_Multiplication\" title=\"Tips on the Commutative Property of Multiplication:\">Tips on the Commutative Property of 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\/formulas\/commutative-property-formula\/#Solved_Examples_on_Commutative_Property_of_Multiplication\" title=\"Solved Examples on Commutative Property of Multiplication\">Solved Examples on Commutative Property of Multiplication<\/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\/formulas\/commutative-property-formula\/#Frequently_Asked_Questions_on_Commutative_Property_of_Multiplication\" title=\"Frequently Asked Questions on Commutative Property of Multiplication\">Frequently Asked Questions on Commutative Property of Multiplication<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/commutative-property-formula\/#What_is_the_Commutative_Property_of_Multiplication-2\" title=\"What is the Commutative Property of Multiplication? \">What is the Commutative Property of Multiplication? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/commutative-property-formula\/#How_do_you_find_the_Commutative_Property_of_Multiplication\" title=\"How do you find the Commutative Property of Multiplication? \">How do you find the Commutative Property of Multiplication? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/commutative-property-formula\/#What_is_an_Example_of_Commutative_Property_of_Multiplication\" title=\"What is an Example of Commutative Property of Multiplication? \">What is an Example of Commutative Property of Multiplication? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/commutative-property-formula\/#What_is_the_Commutative_Property_of_Multiplication_for_the_Numbers_7_and_6\" title=\"What is the Commutative Property of Multiplication for the Numbers 7 and 6? \">What is the Commutative Property of Multiplication for the Numbers 7 and 6? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/commutative-property-formula\/#What_is_the_Commutative_Property_of_Multiplication_for_Rational_Numbers\" title=\"What is the Commutative Property of Multiplication for Rational Numbers? \">What is the Commutative Property of Multiplication for Rational Numbers? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/commutative-property-formula\/#What_is_the_Commutative_Property_of_Multiplication_for_Fractions\" title=\"What is the Commutative Property of Multiplication for Fractions? \">What is the Commutative Property of Multiplication for Fractions? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/commutative-property-formula\/#What_is_the_Commutative_Property_of_Multiplication_for_Integers\" title=\" What is the Commutative Property of Multiplication for Integers? \"> What is the Commutative Property of Multiplication for Integers? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/commutative-property-formula\/#What_is_the_Difference_between_the_Associative_and_Commutative_Property_of_Multiplication\" title=\"What is the Difference between the Associative and Commutative Property of Multiplication? \">What is the Difference between the Associative and Commutative Property of Multiplication? <\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Commutative_Property_Formula\"><\/span>Introduction to Commutative Property Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">The commutative property of multiplication states that the product of two or more numbers remains the same irrespective of the order in which they are placed. For example, 3 \u00d7 4 = 4 \u00d7 3 = 12. Let us study more about the commutative property of multiplication in this article.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_the_Commutative_Property_of_Multiplication\"><\/span>What is the Commutative Property of Multiplication?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">According to the commutative law of multiplication, if two or more numbers are multiplied, we get the same result irrespective of the order of the numbers. Here, the order of the numbers refers to the way in which they are arranged in the given expression. Observe the following example to understand the concept of the commutative property of multiplication.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">5 \u00d7 6 = 6 \u00d7 5<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">30 = 30<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Here, we can observe that even when the order of the numbers is changed, the product remains the same. This means 5 \u00d7 6 = 30; and 6 \u00d7 5 = 30.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Commutative_Property_of_Multiplication_Formula\"><\/span>Commutative Property of Multiplication Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">The commutative property formula for multiplication shows that the order of the numbers does not affect the product. The commutative property of multiplication applies to integers, fractions, and decimals.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The Commutative property multiplication formula is expressed as:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">A \u00d7 B = B \u00d7 A<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">According to the commutative property of multiplication, the order in which we multiply the numbers does not change the final product.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">This can be applied to two or more numbers and the order of the numbers can be shuffled and arranged in any way.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Example: 5 \u00d7 3 \u00d7 2 \u00d7 10 = 10 \u00d7 2 \u00d7 5 \u00d7 3 = 300. We can see that even after we shuffle the order of the numbers, the product remains the same.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Commutative_Property_of_Multiplication_and_Addition\"><\/span>Commutative Property of Multiplication and Addition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">The commutative property is applicable to multiplication and addition.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">For Addition: The Commutative law for addition is expressed as A + B = B + A. For example, (7 + 4) = (4 + 7) = 11. This shows that even after we change the order of the numbers, 7 and 4, the sum remains the same.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"1\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">For Multiplication: The Commutative law of multiplication is expressed as A \u00d7 B = B \u00d7 A. For example, (7 \u00d7 4) = (4 \u00d7 7) = 28. Here, we can see that the product of the numbers remains the same even when the order of the numbers is changed.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">It should be noted that the Commutative property of multiplication is not applicable to subtraction and division.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Tips_on_the_Commutative_Property_of_Multiplication\"><\/span>Tips on the Commutative Property of Multiplication:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">Here are a few important points related to the Commutative property of multiplication.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">The commutative property of multiplication and addition is only applicable to addition and multiplication. It cannot be applied to division and subtraction.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/li>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" data-list-defn-props=\"{&quot;335552541&quot;:1,&quot;335559684&quot;:-2,&quot;335559685&quot;:720,&quot;335559991&quot;:360,&quot;469769226&quot;:&quot;Symbol&quot;,&quot;469769242&quot;:[8226],&quot;469777803&quot;:&quot;left&quot;,&quot;469777804&quot;:&quot;\uf0b7&quot;,&quot;469777815&quot;:&quot;hybridMultilevel&quot;}\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">The commutative property of multiplication and addition can be applied to 2 or more numbers.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"><br \/>\n<\/span><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Examples_on_Commutative_Property_of_Multiplication\"><\/span>Solved Examples on Commutative Property of Multiplication<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><b><span data-contrast=\"auto\">Example 1: <\/span><\/b><span data-contrast=\"auto\">Fill in the missing number using the commutative property of multiplication: 6 \u00d7 4 = __ \u00d7 6.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">According to the commutative property of multiplication formula, A \u00d7 B = B \u00d7 A. So, let us substitute the given values in this formula and check.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">(6 \u00d7 4) = (4 \u00d7 6) = 24. Hence, the missing number is 4.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">Example 2:<\/span><\/b><span data-contrast=\"auto\"> Shimon&#8217;s mother asked him whether p \u00d7 q = q \u00d7 p is an example of the commutative property of multiplication. Can you help Shimon to find out whether it is commutative or not?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">We know that the commutative property for multiplication states that changing the order of the multiplicands does not change the value of the product.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">pq = qp<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">So, we see that changing the order will not alter the product value.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">So this is an example of the commutative property.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">Example 3:<\/span><\/b><span data-contrast=\"auto\"> Which of the expressions follows the commutative property of multiplication?<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">a.) 7 \u00d7 8 \u00d7 5 \u00d7 6<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">b.) 4 \u00d7 (- 2)<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Solution:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">a.) Let us find the product of the given expression. It comes to 7 \u00d7 8 \u00d7 5 \u00d7 6 = 1680.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Now, let us reverse the order of the numbers and find the product of the numbers. It comes to 6 \u00d7 5 \u00d7 8 \u00d7 7 = 1680.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Both the products are the same. Therefore, the given expression follows the commutative property of multiplication because it shows that even when we changed the order of the numbers the product remains the same.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">b.) Let us find the product of the given expression, 4 \u00d7 (- 2) = -8. Now, let us reverse the order of the numbers and check, (- 2) \u00d7 4 = -8. This shows that the given expression follows the commutative property of multiplication.<\/span><\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" style=\"width: 55.6278%;\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td style=\"text-align: center; width: 99.7409%;\" colspan=\"2\"><strong>Also Check<br \/>\n<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.5544%;\"><a href=\"https:\/\/infinitylearn.com\/surge\/english\/speech\/how-to-write-and-deliver-welcome-speech\/\"><strong>How to Write and Deliver a Welcome Speech<\/strong><\/a><\/td>\n<td style=\"width: 48.1865%;\"><a href=\"https:\/\/infinitylearn.com\/surge\/english\/speech\/welcome-speech-for-freshers-party\/\"><strong>Welcome Speech for Fresher\u2019s Party<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 51.5544%;\"><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/english\/speech\/welcome-speech-for-seminar\/\"><strong>Welcome Speech for Seminar<\/strong><\/a><\/td>\n<td style=\"width: 48.1865%;\"><a href=\"https:\/\/infinitylearn.com\/surge\/english\/speech\/welcome-speech-on-teachers-day-by-students\/\"><strong>Welcome Speech on Teachers\u2019 Day by Students<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions_on_Commutative_Property_of_Multiplication\"><\/span>Frequently Asked Questions on Commutative Property of Multiplication<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_Commutative_Property_of_Multiplication-2\"><\/span>What is the Commutative Property of Multiplication? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe commutative law of multiplication states that the product of two or more numbers remains the same, irrespective of the order of the operands. For multiplication, the commutative property formula is expressed as (A \u00d7 B) = (B \u00d7 A). The commutative property of multiplication applies to integers, fractions, and decimals.  \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_do_you_find_the_Commutative_Property_of_Multiplication\"><\/span>How do you find the Commutative Property of Multiplication? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe commutative property of multiplication states that if 'a' and 'b' are two numbers, then a \u00d7 b = b \u00d7 a. If the product of the values on the Left-hand side (LHS) and the product of the values on the right-hand side (RHS) terms is equal, then it can be said that the given expression follows the commutative property of multiplication.  \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_an_Example_of_Commutative_Property_of_Multiplication\"><\/span>What is an Example of Commutative Property of Multiplication? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tAn example of the commutative property of multiplication can be seen as follows. We know that (A \u00d7 B) = (B \u00d7 A). Let us substitute the value of A = 8 and B = 9. On substituting these values in the formula. we get 8 \u00d7 9 = 9 \u00d7 8 = 72. Hence it is proved that the product of both the numbers is the same even when we change the order of the numbers. This means, if we have expressions such as, 6 \u00d7 8, or 9 \u00d7 7 \u00d7 10, we know that the commutative property of multiplication will be applicable to it.  \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_Commutative_Property_of_Multiplication_for_the_Numbers_7_and_6\"><\/span>What is the Commutative Property of Multiplication for the Numbers 7 and 6? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tLet us arrange the given numbers as per the general equation of commutative law that is (A \u00d7 B) = (B \u00d7 A). Here A = 7 and B = 6. After substituting the values in the formula, we get 7 \u00d7 6 = 6 \u00d7 7 = 42. Hence, 6 \u00d7 7 follows the commutative property of multiplication.  \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_Commutative_Property_of_Multiplication_for_Rational_Numbers\"><\/span>What is the Commutative Property of Multiplication for Rational Numbers? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe commutative property of multiplication for rational numbers can be expressed as (P \u00d7 Q) = (Q \u00d7 P). Here the values of P, Q are in form of a\/b, where b \u2260 0. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_Commutative_Property_of_Multiplication_for_Fractions\"><\/span>What is the Commutative Property of Multiplication for Fractions? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe commutative property of multiplication for fractions can be expressed as (P \u00d7 Q) = (Q \u00d7 P). Let us substitute the values of P, Q in the form of a\/b.  For example, if, P = 7\/8 and Q = 5\/2. On substituting the values in (P \u00d7 Q) = (Q \u00d7 P) we get, (7\/8 \u00d7 5\/2) = (5\/2 \u00d7 7\/8) = 35\/16. Hence, the commutative property of multiplication is applicable to fractions.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_Commutative_Property_of_Multiplication_for_Integers\"><\/span> What is the Commutative Property of Multiplication for Integers? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe commutative property of multiplication for integers can be expressed as (P \u00d7 Q) = (Q \u00d7 P). For example, let us substitute the value of P = -3 and Q = -9. On substituting the values in the formula, we get (-3 \u00d7 -9) = (-9 \u00d7 -3) = 27. Hence, the commutative property of multiplication is applicable to integers.  \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_Difference_between_the_Associative_and_Commutative_Property_of_Multiplication\"><\/span>What is the Difference between the Associative and Commutative Property of Multiplication? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe associative property of multiplication states that the product of the numbers remains the same even when the grouping of the numbers is changed. The associative property of multiplication is expressed as (A \u00d7 B) \u00d7 C = A \u00d7 (B \u00d7 C). The commutative property of multiplication states that the product of two or more numbers remains the same even if the order of the numbers is changed. The commutative property of multiplication is expressed as A \u00d7 B \u00d7 C = C \u00d7 B \u00d7 A. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the Commutative Property of Multiplication? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The commutative law of multiplication states that the product of two or more numbers remains the same, irrespective of the order of the operands. For multiplication, the commutative property formula is expressed as (A \u00d7 B) = (B \u00d7 A). The commutative property of multiplication applies to integers, fractions, and decimals.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you find the Commutative Property of Multiplication? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The commutative property of multiplication states that if 'a' and 'b' are two numbers, then a \u00d7 b = b \u00d7 a. If the product of the values on the Left-hand side (LHS) and the product of the values on the right-hand side (RHS) terms is equal, then it can be said that the given expression follows the commutative property of multiplication.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is an Example of Commutative Property of Multiplication? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"An example of the commutative property of multiplication can be seen as follows. We know that (A \u00d7 B) = (B \u00d7 A). Let us substitute the value of A = 8 and B = 9. On substituting these values in the formula. we get 8 \u00d7 9 = 9 \u00d7 8 = 72. Hence it is proved that the product of both the numbers is the same even when we change the order of the numbers. This means, if we have expressions such as, 6 \u00d7 8, or 9 \u00d7 7 \u00d7 10, we know that the commutative property of multiplication will be applicable to it.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the Commutative Property of Multiplication for the Numbers 7 and 6? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Let us arrange the given numbers as per the general equation of commutative law that is (A \u00d7 B) = (B \u00d7 A). Here A = 7 and B = 6. After substituting the values in the formula, we get 7 \u00d7 6 = 6 \u00d7 7 = 42. Hence, 6 \u00d7 7 follows the commutative property of multiplication.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the Commutative Property of Multiplication for Rational Numbers? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The commutative property of multiplication for rational numbers can be expressed as (P \u00d7 Q) = (Q \u00d7 P). Here the values of P, Q are in form of a\/b, where b \u2260 0.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the Commutative Property of Multiplication for Fractions? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The commutative property of multiplication for fractions can be expressed as (P \u00d7 Q) = (Q \u00d7 P). Let us substitute the values of P, Q in the form of a\/b.  For example, if, P = 7\/8 and Q = 5\/2. On substituting the values in (P \u00d7 Q) = (Q \u00d7 P) we get, (7\/8 \u00d7 5\/2) = (5\/2 \u00d7 7\/8) = 35\/16. Hence, the commutative property of multiplication is applicable to fractions.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \" What is the Commutative Property of Multiplication for Integers? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The commutative property of multiplication for integers can be expressed as (P \u00d7 Q) = (Q \u00d7 P). For example, let us substitute the value of P = -3 and Q = -9. On substituting the values in the formula, we get (-3 \u00d7 -9) = (-9 \u00d7 -3) = 27. Hence, the commutative property of multiplication is applicable to integers.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the Difference between the Associative and Commutative Property of Multiplication? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The associative property of multiplication states that the product of the numbers remains the same even when the grouping of the numbers is changed. The associative property of multiplication is expressed as (A \u00d7 B) \u00d7 C = A \u00d7 (B \u00d7 C). The commutative property of multiplication states that the product of two or more numbers remains the same even if the order of the numbers is changed. The commutative property of multiplication is expressed as A \u00d7 B \u00d7 C = C \u00d7 B \u00d7 A.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Commutative Property Formula The commutative property of multiplication states that the product of two or more numbers remains [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Commutative Property Formula\u00a0","_yoast_wpseo_title":"Commutative Property Formula\u00a0with Example - Infinity learn","_yoast_wpseo_metadesc":"Learn how the commutative property allows you to change the order of numbers in addition and multiplication without changing the result.","custom_permalink":"formulas\/commutative-property-formula\/"},"categories":[8438,8536],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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