{"id":1220,"date":"2017-12-05T03:42:28","date_gmt":"2017-12-05T03:42:28","guid":{"rendered":"https:\/\/kellyfish.me\/?p=1220"},"modified":"2018-11-04T00:47:23","modified_gmt":"2018-11-04T00:47:23","slug":"more-magic-tables","status":"publish","type":"post","link":"https:\/\/kellyfish.me\/index.php\/2017\/12\/05\/more-magic-tables\/","title":{"rendered":"More Magic Tables"},"content":{"rendered":"

[latexpage]<\/span><\/p>\n

Fun Math for Girls
\n<\/span>By Kelly Tan<\/span><\/span><\/p>\n

\"\"<\/span><\/p>\n

Here are more magic tables filled with fun patterns to share with your friends or write down in your notebooks yourself.<\/span><\/p>\n

\u00a0 \u00a01\u00b7 1 = 1<\/span><\/p>\n

\u00a011\u00b7 11 = 121<\/span><\/p>\n

\u00a0111\u00b7 111 = 12321<\/span><\/p>\n

\u00a0 1111\u00b7 1111 = 1234321<\/span><\/p>\n

\u00a011111\u00b7 11111 = 123454321<\/span><\/p>\n

\u00a0111111\u00b7 111111 = 12345654321<\/span><\/p>\n

\u00a0 1111111\u00b7 1111111 = 1234567654321<\/span><\/p>\n

\u00a0 11111111\u00b7 11111111 = 123456787654321<\/span><\/p>\n

\u00a0 \u00a0 111111111\u00b7 111111111 = 12345678987654321<\/span><\/p>\n

The table is symmetric on both sides of the equation. But exactly how does the underlying algebra work? As usual, let’s look at the third row.<\/span><\/p>\n

111\u00b7111<\/span><\/p>\n

=($10^2$<\/span>+$10^1$<\/span>$+10^0$<\/span>)\u00b7$(10^2+10^1+10^0)$<\/span><\/span><\/p>\n

$=(10^2$+$10^1$$+10^0)$\u00b7$10^2+(10^2+10^1+10^0)$\u00b7$10^1+(10^2+10^1+10^0)$\u00b7$10^0$\u00a0<\/span>\u00a0\u00a0— distributive law<\/span><\/span><\/p>\n

$=(10^4+10^3+10^2)+(10^3+10^2+10^1)+(10^2+10^1+10^0)$ \u00a0\u00a0— distributive law<\/span><\/p>\n

=$1$\u00b7$10^4+2$\u00b7$10^3+3$\u00b7$10^2+2$\u00b7$10^1+1$\u00b7$10^0$ \u00a0\u00a0— Combining like terms<\/span><\/p>\n

$=12321$<\/span><\/p>\n

You see, the mathematics is actually not very complicated, you just have to remember to combine terms with the same exponents.<\/span><\/p>\n

Here is another symmetric table for multiplication of 9’s instead of 1’s.<\/span><\/p>\n

\u00a0 9 \u00b7 9 = 81<\/span><\/p>\n

\u00a099 \u00b7 99 = 9801<\/span><\/p>\n

\u00a0 999 \u00b7 999 = 998001<\/span><\/p>\n

\u00a0\u00a09999 \u00b7 9999 = 99980001<\/span><\/p>\n

\u00a099999 \u00b7 99999 = 9999800001<\/span><\/p>\n

999999 \u00b7 999999\u00a0 = 999998000001<\/span><\/p>\n

9999999 \u00b7 9999999 = 99999980000001<\/span><\/p>\n

If you think about it, each factor on the left hand side in this table (the second table) is simply 9 times the factor on the left hand side of the first table in this article. So for the third term, $111$\u00b7$9 = 999$. In this table, since there are two factors on the left hand side, each row is 81 (9\u00b79) times the previous table. For the third term, for example, $12321$\u00b7$81=998001$. By multiplying 81 times the result of the right hand side of the first table, you get the same numbers as the results on the right hand side of the second table. You will get:<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a081\u00b71 = 81<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a081\u00b7121 = 9801<\/span><\/p>\n

\u00a0\u00a0\u00a081\u00b712321 = 998001<\/span><\/p>\n

\u00a0\u00a081\u00b71234321 = 99980001<\/span><\/p>\n

\u00a081\u00b7123454321 = 9999800001<\/span><\/p>\n

81\u00b712345654321 \u00a0= 999998000001<\/span><\/p>\n

81\u00b71234567654321 = 99999980000001<\/span><\/p>\n

So, you actually can combine tables to create new tables. There are endless possibilities for you to design new patterns to draw out.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

[latexpage] Fun Math for Girls By Kelly Tan Here are more magic tables filled with fun patterns to share with your friends or write down in your notebooks yourself. \u00a0 \u00a01\u00b7 1 = 1 \u00a011\u00b7 11 = 121 \u00a0111\u00b7 111 = 12321 \u00a0 1111\u00b7 1111 = 1234321 \u00a011111\u00b7 11111 = 123454321 \u00a0111111\u00b7 111111 = 12345654321 […]<\/p>\n","protected":false},"author":1,"featured_media":1259,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[28],"tags":[],"class_list":["post-1220","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-articles"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/kellyfish.me\/wp-content\/uploads\/2017\/12\/e21516-0920-1.jpg?fit=1000%2C1000&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1220","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/comments?post=1220"}],"version-history":[{"count":12,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1220\/revisions"}],"predecessor-version":[{"id":1290,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/posts\/1220\/revisions\/1290"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media\/1259"}],"wp:attachment":[{"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/media?parent=1220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/categories?post=1220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kellyfish.me\/index.php\/wp-json\/wp\/v2\/tags?post=1220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}