{"id":866,"date":"2022-05-17T17:45:17","date_gmt":"2022-05-17T17:45:17","guid":{"rendered":"http:\/\/meatpie\/?p=866"},"modified":"2023-05-01T17:50:32","modified_gmt":"2023-05-01T17:50:32","slug":"fun-with-numbers","status":"publish","type":"post","link":"https:\/\/snersbots.co.uk\/index.php\/fun-with-numbers\/","title":{"rendered":"Fun With Numbers"},"content":{"rendered":"\n<p>I love little number tricks. This page is to help me remember them.<\/p>\n\n\n\n<p>They&#8217;re very difficult to describe in words, and I don&#8217;t have any nice mathematical or graphical tools, so it is a bit hard to follow some of them. But go practice. They&#8217;re a lot of fun once you get the hang of them.<\/p>\n\n\n\n<p>If you are genuinely interested and want something explained better, or if you have any more neat tricks for me., please leave a message below. But if you are a robot, don&#8217;t bother, I have a robot policing this site for spam \ud83d\ude09<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\" id=\"number-divisible-by-3\">Number Divisible by 3?<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Add all the digits of the number<\/li>\n\n\n\n<li>If the result is greater than 10, add the digits of the result<\/li>\n\n\n\n<li>When you get down to a one-digit number, if the number is 3, 6 or 9, <\/li>\n\n\n\n<li>Then the original number is divisible by 3<\/li>\n<\/ul>\n\n\n\n<p>eg 123456789 <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>digits total 45<\/li>\n\n\n\n<li>4 + 5 = 9<\/li>\n\n\n\n<li>therefore it is divisible by 3<\/li>\n<\/ul>\n\n\n\n<p>eg 1236262<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>digits total 22<\/li>\n\n\n\n<li>2 + 2 = 4<\/li>\n\n\n\n<li>therefore it is not divisible by 3<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"multiply-by-5\">Multiply by 5<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Divide the number by 2.<\/li>\n\n\n\n<li>Multiply the answer by 10.<\/li>\n<\/ul>\n\n\n\n<p>eg 234 * 5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>234 \/ 2 = 117<\/li>\n\n\n\n<li>117 * 10 = 1170<\/li>\n\n\n\n<li>therefore the answer is 1170<\/li>\n<\/ul>\n\n\n\n<p>eg 751 * 5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>751 \/ 2 = 375.5<\/li>\n\n\n\n<li>375.5 * 10 = 3755<\/li>\n\n\n\n<li>therefore the answer is 3755<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"divide-by-5\">Divide by 5<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply the number by 2<\/li>\n\n\n\n<li>Divide the answer by 10.<\/li>\n<\/ul>\n\n\n\n<p>eg 2340 \/ 5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2340 * 2 = 4680<\/li>\n\n\n\n<li>4680 \/ 10 = 468<\/li>\n\n\n\n<li>therefore the answer is 468<\/li>\n<\/ul>\n\n\n\n<p>eg 7515 \/ 5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7515 * 2 = 15030<\/li>\n\n\n\n<li>15030 \/ 10 = 1503<\/li>\n\n\n\n<li>therefore the answer is 1503<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"square-a-number-ending-in-5\">Square a Number Ending in 5<\/h2>\n\n\n\n<p>Multiply the number that precedes the 5 by the next number higher than it, and then tack on 25.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Remove the 5<\/li>\n\n\n\n<li>Multiply what is left by (itself + 1)<\/li>\n\n\n\n<li>Append 25<\/li>\n<\/ul>\n\n\n\n<p>eg 75 squared<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>the number without the 5 is 7<\/li>\n\n\n\n<li>7 * 8 = 56<\/li>\n\n\n\n<li>therefore the answer is 5625<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"number-divisible-by-3\">Number Divisible by 9?<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Add all the digits of the number<\/li>\n\n\n\n<li>If the result is greater than 10, add the digits of the result<\/li>\n\n\n\n<li>When you get down to a one-digit number, if the number is 9, <\/li>\n\n\n\n<li>Then the original number is divisible by 3<\/li>\n<\/ul>\n\n\n\n<p>eg 123456789 <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>digits total 45<\/li>\n\n\n\n<li>4 + 5 = 9<\/li>\n\n\n\n<li>therefore it is divisible by 9<\/li>\n<\/ul>\n\n\n\n<p>eg 1236262<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>digits total 22<\/li>\n\n\n\n<li>2 + 2 = 4<\/li>\n\n\n\n<li>therefore it is not divisible by 9<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"multiply-by-11\">Multiply by 11<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Take any number<\/li>\n\n\n\n<li>The digits of the number is as follows:\n<ul class=\"wp-block-list\">\n<li>If the number has digits abcde<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>The answer has digits as follows:\n<ul class=\"wp-block-list\">\n<li>a(a+b)(b+c)(c+d)(d+e)e<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>If any single calculation is greater than 10<\/li>\n\n\n\n<li>Carry the one as per normal rules of addition<\/li>\n<\/ul>\n\n\n\n<p>Another way of saying it is, working right to left:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The right-most digit is the last digit of the original number<\/li>\n\n\n\n<li>Add each number to the digit immediately preceding it<\/li>\n\n\n\n<li>Write down the answer<\/li>\n\n\n\n<li>If the answer is greater than 10, then carry one to the next sum to the left<\/li>\n\n\n\n<li>When there is only one number left, write that down, optionally adding any carried one<\/li>\n<\/ul>\n\n\n\n<p>eg 12342 * 11<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1(1+2)(2+3)(3+4)(4+2)2<\/li>\n\n\n\n<li>simplifies to 135762<\/li>\n\n\n\n<li>therefore the answer is 135762<\/li>\n<\/ul>\n\n\n\n<p>eg 75382 * 11<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7(7+5)(5+3)(3+8)(8+2)2<\/li>\n\n\n\n<li>simplifies to 7(2 carry 1)(8)(1 carry 1)(0 carry 1) 2<\/li>\n\n\n\n<li>move the carries left gives (7+1)(2)(8+1)(1+1)(0)2<\/li>\n\n\n\n<li>and the answer is 829202<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"number-divisible-by-11\">Number Divisible by 11?<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For any number with more than 1 digit<\/li>\n\n\n\n<li>Add up all the digits in positions 1, 3, 5 etc<\/li>\n\n\n\n<li>Add up all the digits in positions 2, 4, 6 etc<\/li>\n\n\n\n<li>If the two answers are equal, then the number is divisible by 11<\/li>\n\n\n\n<li>If the two numbers are not equal, subtract one from the other. <\/li>\n\n\n\n<li>If the result is divisible by 11, then the original number is divisible by 11<\/li>\n<\/ul>\n\n\n\n<p>eg <strong>5<\/strong>8<strong>9<\/strong>6<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 + 9 = 14<\/li>\n\n\n\n<li>8 + 6 = 14<\/li>\n\n\n\n<li>therefore it is divisible by 11<\/li>\n<\/ul>\n\n\n\n<p>eg <strong>6<\/strong>2<strong>3<\/strong>5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>6 + 3 = 9<\/li>\n\n\n\n<li>2 + 5 = 7<\/li>\n\n\n\n<li>9 &#8211; 7 = 2<\/li>\n\n\n\n<li>therefore it is not divisible by 11<\/li>\n<\/ul>\n\n\n\n<p>eg <strong>7<\/strong>4<strong>6<\/strong>8<strong>8<\/strong>6<strong>3<\/strong>6<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7 + 6 + 8 + 3 = 24<\/li>\n\n\n\n<li>4 + 8 + 6 + 6 = 24<\/li>\n\n\n\n<li>therefore it is divisible by 11<\/li>\n<\/ul>\n\n\n\n<p>eg<strong> 7<\/strong>4<strong>6<\/strong>8<strong>8<\/strong>6<strong>4<\/strong>1<strong>5<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7 + 6 + 8 + 4 + 5 = 30<\/li>\n\n\n\n<li>4 + 8 + 6 + 1 = 19<\/li>\n\n\n\n<li>30 &#8211; 19 = 11<\/li>\n\n\n\n<li>therefore it is divisible by 11<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"multiplication-in-your-head\">Multiplication in your head<\/h2>\n\n\n\n<p>Working right to left:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply the rightmost digits together<\/li>\n\n\n\n<li>Write the last digit of the answer, carry the 10s<\/li>\n\n\n\n<li>In your mind, draw an X over the last two digits of both numbers<\/li>\n\n\n\n<li>Multiply the digit at top left corner with the digit at bottom right corner of the X<\/li>\n\n\n\n<li>Multiply the digit at the right corner with the digit at bottom left corner of the X<\/li>\n\n\n\n<li>Add the two numbers above<\/li>\n\n\n\n<li>Add any carries<\/li>\n\n\n\n<li>Right down the last digit and carry the 10s<\/li>\n\n\n\n<li>eg abCD * efGH &#8211; the result is (C * H) + (D * G)<\/li>\n\n\n\n<li>Move the X 1 place to the left, and repeat until you reach the end of the number<\/li>\n\n\n\n<li>Finally multiply the two digits on the left, and add the carries. <\/li>\n\n\n\n<li>If your final answer is greater than 10, now put in the carries.<\/li>\n<\/ul>\n\n\n\n<p>If you&#8217;re doing this as a party trick, keep the digits low. It&#8217;s the carries that fall out of your head more than anything else.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I love little number tricks. This page is to help me remember them. They&#8217;re very difficult to describe in words, and I don&#8217;t have any nice mathematical or graphical tools, so it is a bit hard to follow some of them. But go practice. They&#8217;re a lot of fun once you get the hang of <a class=\"read-more\" href=\"https:\/\/snersbots.co.uk\/index.php\/fun-with-numbers\/\">The full story here&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[37],"tags":[],"class_list":["post-866","post","type-post","status-publish","format-standard","hentry","category-tips"],"_links":{"self":[{"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/posts\/866","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/comments?post=866"}],"version-history":[{"count":13,"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/posts\/866\/revisions"}],"predecessor-version":[{"id":957,"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/posts\/866\/revisions\/957"}],"wp:attachment":[{"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/media?parent=866"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/categories?post=866"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/snersbots.co.uk\/index.php\/wp-json\/wp\/v2\/tags?post=866"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}