{"id":6328,"date":"2013-09-18T04:30:08","date_gmt":"2013-09-18T04:30:08","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6328"},"modified":"2014-12-02T08:26:58","modified_gmt":"2014-12-02T08:26:58","slug":"math-review-of-commutative-and-associative-properties","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-commutative-and-associative-properties\/","title":{"rendered":"Math Review of Commutative and Associative Properties"},"content":{"rendered":"

Overview:\u00a0 Properties of Addition and Multiplication<\/strong>
\nThe commutative and associative properties of addition and multiplication are useful within operations.\u00a0 Both properties help students to arrange and group numbers more effectively.\u00a0 However, these properties do not hold for either subtraction or division.<\/p>\n

What Is the Commutative Property?<\/strong>
\nThe commutative property of addition and multiplication states that \u00a0any numbers a and b can be added (or multiplied) in any order to equal the same amount.\u00a0 In other words (or symbols) , a + b = b + a. \u00a0\u00a0For example, 4 + 5\u00a0 = 5 +4.\u00a0 It forms a shortcut for basic addition facts.<\/p>\n

What Is the Associative Property?<\/strong>
\nWhile the commutative property states that order that numbers are added doesn’t matter, the associative property states that the way numbers are grouped doesn’t matter, as long as everything is being added.\u00a0 Therefore, (a + b) + c = a + (b +c).\u00a0\u00a0 If a equals 4, b equals 5, and c equals 3 , (4 + 5) +3 = 4 +(5 +3).<\/p>\n

How Are the Properties Used Together?<\/strong>
\nThe properties can be used together to solve problems.\u00a0 For example, if the order doesn’t matter when adding numbers together, and the way numbers are grouped doesn’t matter, one can use shortcuts when adding.\u00a0 In fact, both properties are used when adding two-digit numbers without much thought.\u00a0 For example 46 +33 = 79.\u00a0 That is the same as (40 + 6) + (30 + 3) = (40 +30) + (6 + 3) or 70 +9 = 79.\u00a0 The numbers have been expanded into what they mean, grouped together, and rearranged.<\/p>\n

Why Are They True for Multiplication?<\/strong>
\nThe commutative and associative properties are true for multiplication, because one definition for multiplication is repeated addition.\u00a0 If 3 X 3 means the same thing as 3 + 3 + 3, then multiplication is a shortcut that involves grouping numbers differently.\u00a0 For example, 24 X 36 = 864 , which equals \u00a0(24 X 30) + (24 X 6) = 720 + 144 = 864.<\/p>\n

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Overview:\u00a0 Properties of Addition and Multiplication The commutative and associative properties of addition and multiplication are useful within operations.\u00a0 Both properties help students to arrange and group numbers more effectively.\u00a0 However, these properties do not hold for either subtraction or division. What Is the Commutative Property? The commutative property of addition and multiplication states that […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[13],"tags":[50,151,327,1159],"class_list":["post-6328","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-addition","tag-associative-property","tag-commutative-property","tag-multiplication"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6328","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6328"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6328\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}