Gavin and his three friends want to share (1)\/(3) of a cake equally. Gavin says that each friend will get (1)\/(9) of the cake. Use the drop-down menus to explain whether or not Gavin is correct.<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n Answer:<\/strong><\/p>\n\n\n\n Gavin is not correct<\/strong>. Let\u2019s break the problem down step-by-step to understand why Gavin\u2019s answer is incorrect and how to find the correct one.<\/p>\n\n\n\n Gavin and his three friends are sharing $\\frac{1}{3}$<\/strong> of a cake. That means they are not sharing the entire cake\u2014only a third of it. Also, there are four people total<\/strong> (Gavin + 3 friends), and they are dividing that one-third of a cake equally<\/strong> among themselves.<\/p>\n\n\n\n We are trying to divide $\\frac{1}{3}$ by 4 (since four people are sharing it equally).<\/p>\n\n\n\n In mathematical terms:<\/p>\n\n\n\n $$ So, each person gets $\\frac{1}{12}$ of the whole cake.<\/p>\n\n\n\n Gavin claims that each person gets $\\frac{1}{9}$ of the cake. That would imply that:<\/p>\n\n\n\n $$ This means they would be eating almost half the cake ($\\frac{4}{9}$), which is more than the $\\frac{1}{3}$<\/strong> they were supposed to share. So Gavin’s estimate is too large.<\/p>\n\n\n\n Let\u2019s multiply the correct portion per person by 4 people:<\/p>\n\n\n\n $$ This confirms that dividing $\\frac{1}{3}$ into four equal parts gives $\\frac{1}{12}$ per person.<\/p>\n\n\n\n Gavin is incorrect. Each of the four people should receive $\\frac{1}{12}$<\/strong> of the whole cake when $\\frac{1}{3}$ of it is shared equally among them. This result ensures that the total amount shared still adds up to $\\frac{1}{3}$ of the cake. <\/p>\n","protected":false},"excerpt":{"rendered":" Gavin and his three friends want to share (1)\/(3) of a cake equally. Gavin says that each friend will get (1)\/(9) of the cake. Use the drop-down menus to explain whether or not Gavin is correct. The correct answer and explanation is : Answer: Gavin is not correct.Each friend will actually get $\\frac{1}{12}$ of the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-1007","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/1007","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=1007"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/1007\/revisions"}],"predecessor-version":[{"id":1008,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/1007\/revisions\/1008"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=1007"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=1007"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=1007"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Each friend will actually get $\\frac{1}{12}$<\/strong> of the cake.<\/p>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/strong><\/h3>\n\n\n\n
Step 1: Understand the Situation<\/strong><\/h4>\n\n\n\n
Step 2: Divide the Fraction<\/strong><\/h4>\n\n\n\n
\\frac{1}{3} \\div 4 = \\frac{1}{3} \\times \\frac{1}{4} = \\frac{1}{12}
$$<\/p>\n\n\n\nStep 3: Why Gavin is Incorrect<\/strong><\/h4>\n\n\n\n
\\frac{1}{9} \\times 4 = \\frac{4}{9}
$$<\/p>\n\n\n\nStep 4: Double-Check the Correct Answer<\/strong><\/h4>\n\n\n\n
\\frac{1}{12} \\times 4 = \\frac{4}{12} = \\frac{1}{3}
$$<\/p>\n\n\n\n
\n\n\n\nFinal Conclusion<\/strong><\/h3>\n\n\n\n