{"id":37568,"date":"2025-06-26T02:39:42","date_gmt":"2025-06-26T02:39:42","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=37568"},"modified":"2025-06-26T02:39:43","modified_gmt":"2025-06-26T02:39:43","slug":"gary-applied-the-distributive-property-using-the-greatest-common-factor-to-determine-the-expression-that-is-equivalent-to-66-36","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/gary-applied-the-distributive-property-using-the-greatest-common-factor-to-determine-the-expression-that-is-equivalent-to-66-36\/","title":{"rendered":"Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36."},"content":{"rendered":"\n<p>Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36. His work is shown below. Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66 Factors of 36: 1, 2, <\/p>\n\n\n\n<p>3, 4, 6, 9, 12, 18, 36 66 + 36 = 3 (22 + 12<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>Gary made a mistake. The correct expression using the <strong>greatest common factor (GCF)<\/strong> and the distributive property is:<\/p>\n\n\n\n<p><strong>66 + 36 = 6(11 + 6)<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation (300 words):<\/strong><\/p>\n\n\n\n<p>Gary attempted to apply the distributive property using the greatest common factor (GCF) to factor the expression 66 + 36. The distributive property states that for any numbers a, b, and c:<\/p>\n\n\n\n<p><strong>a \u00d7 (b + c) = a \u00d7 b + a \u00d7 c<\/strong><\/p>\n\n\n\n<p>This can be used in reverse to factor expressions by identifying a common factor. In this case, we want to express 66 + 36 as:<\/p>\n\n\n\n<p><strong>GCF \u00d7 (some expression)<\/strong><\/p>\n\n\n\n<p>First, identify the common factors of 66 and 36.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Factors of 66:<\/strong> 1, 2, 3, 6, 11, 22, 33, 66<\/li>\n\n\n\n<li><strong>Factors of 36:<\/strong> 1, 2, 3, 4, 6, 9, 12, 18, 36<\/li>\n<\/ul>\n\n\n\n<p>From this list, the <strong>greatest common factor<\/strong> of 66 and 36 is <strong>6<\/strong>.<\/p>\n\n\n\n<p>Now divide each number by the GCF:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>66 \u00f7 6 = 11<\/li>\n\n\n\n<li>36 \u00f7 6 = 6<\/li>\n<\/ul>\n\n\n\n<p>So we rewrite the expression using the distributive property:<\/p>\n\n\n\n<p><strong>66 + 36 = 6 \u00d7 (11 + 6)<\/strong><br><strong>66 + 36 = 6(17)<\/strong><\/p>\n\n\n\n<p>Gary incorrectly chose 3 as the common factor and wrote:<\/p>\n\n\n\n<p><strong>66 + 36 = 3(22 + 12)<\/strong><\/p>\n\n\n\n<p>While it is mathematically true that 3(22 + 12) = 66 + 36 = 102, it does <strong>not<\/strong> use the <strong>greatest<\/strong> common factor. The goal was to find the GCF, which is 6, and factor it out.<\/p>\n\n\n\n<p>Using the GCF makes the resulting expression more simplified and useful for factoring or mental math. This method is often used in algebra to factor polynomials or simplify numeric expressions.<\/p>\n\n\n\n<p>)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-920.jpeg\" alt=\"\" class=\"wp-image-37569\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-920.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-920-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-920-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36. His work is shown below. Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 66 + 36 = 3 (22 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37568","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37568","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37568"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37568\/revisions"}],"predecessor-version":[{"id":37570,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37568\/revisions\/37570"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37568"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37568"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}