{"id":23,"date":"2004-04-20T16:27:57","date_gmt":"2004-04-20T16:27:57","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=23"},"modified":"2004-04-20T16:27:57","modified_gmt":"2004-04-20T16:27:57","slug":"cancelling","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=23","title":{"rendered":"Cancelling"},"content":{"rendered":"<p>Students love to cancel wherever they can, so much so that the book <a href=\"http:\/\/www.amazon.co.uk\/exec\/obidos\/ASIN\/1857480074\/qid=1082473925\/sr=1-1\/ref=sr_1_8_1\/202-7622383-2888606\" target=\"_blank\">Comic Sections<\/a> (now out of print) had the following joke:<\/p>\n<ul><i>The student law of universal cancellation: If the same symbol x occurs in any two different places on the one page it may be cancelled<\/i><\/ul>\n<p>So you get horrors like <img src='\/maths\/latexrender\/pictures\/a0d160860f2f567ede36df642dbcd116.gif' title='\\dfrac{\\sin x}{n}=\\dfrac{\\text{si}\\hspace{-1mm}\\not{n}\\hspace{1mm} x}{\\not n}=$ six$' alt='\\dfrac{\\sin x}{n}=\\dfrac{\\text{si}\\hspace{-1mm}\\not{n}\\hspace{1mm} x}{\\not n}=$ six$' align=absmiddle> \ud83d\ude2e<\/p>\n<p>And yet strange things can happen. It is true that <img src='\/maths\/latexrender\/pictures\/0dbed526e0ea17d41652000f0ba45a78.gif' title='\\frac{2666}{6665}=\\frac{266}{665}=\\frac{2}{5}' alt='\\frac{2666}{6665}=\\frac{266}{665}=\\frac{2}{5}' align=absmiddle>.<br \/>\nWhat is remarkable is that you can have as many sixes as you like and cancel them as many times as you like so, for example, <img src='\/maths\/latexrender\/pictures\/0961c706146eea93b8744f508a4f54eb.gif' title='\\frac{26666666}{66666665}=\\frac{266}{665}' alt='\\frac{26666666}{66666665}=\\frac{266}{665}' align=absmiddle>. Can you prove this is true? Can you find 3 other similar fractions?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students love to cancel wherever they can, so much so that the book Comic Sections (now out of print) had the following joke: The student law of universal cancellation: If the same symbol x occurs in any two different places on the one page it may be cancelled So you get horrors like \ud83d\ude2e And [&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-23","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/23","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=23"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/23\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}