{"id":57,"date":"2023-06-05T15:29:38","date_gmt":"2023-06-05T15:29:38","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/converting-between-bases\/"},"modified":"2024-01-16T00:04:46","modified_gmt":"2024-01-16T00:04:46","slug":"converting-between-bases","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/converting-between-bases\/","title":{"raw":"Adding and Subtracting in Other Bases","rendered":"Adding and Subtracting in Other Bases"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Add two numbers from a base other than 10<\/li>\r\n \t<li>Subtract two numbers from a base other than 10<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Adding Basic Time Units<\/h3>\r\n<span style=\"font-size: 1em;\">Think about the number of seconds in a minute and minutes in an hour.\u00a0 What base does this follow?\u00a0 If you said sixty, you are correct! Further, if you add 2 hours 20 minutes 35 seconds and 1 hour 45 minutes\u00a0 50 seconds, is the answer 3 hours 65 minutes 85 seconds?\u00a0 Technically, this is true, but we wouldn't keep this format.\u00a0 Once we reach 60 or higher in an unit, we convert 60 it to one in the next higher unit.\u00a0 You would follow these steps,\u00a0<\/span><span style=\"font-size: 1em;\">65 minutes is equal to 1 hour 5 minutes and\u00a0<\/span><span style=\"font-size: 1em; text-align: initial;\">85 seconds is equal to 1 minute 15 seconds.\u00a0 Thus, 3 hours 65 minutes 85 seconds is roughly 3 hours + 1 hour 5 minutes + 1 minute 15 seconds and simplifies to 4 hours 6 minutes 15 seconds.\u00a0 Adding non-decimal (not base 10) numbers uses similar steps to adding different time units.<\/span>\r\n<h3>Understanding the Process of Adding in Decimal Numbers<\/h3>\r\nBefore we try adding in other bases let's review the steps to adding two base 10 numbers.\u00a0 Add these two numbers without a calculator:\r\n<p style=\"text-align: center;\">536\r\n<span style=\"text-decoration: underline;\">+ 398<\/span><\/p>\r\nThis problem requires carrying to get the correct answer.\u00a0 Majority of the population can show the steps necessary to get the answer to the above addition problem, but fewer can explain why we carry?\u00a0 This video answers the question of why carrying works and will prepare you for adding in a base other than 10.\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=O9zSHs1TWMM[\/embed]\r\n<h3>Adding in Other Bases<\/h3>\r\n<p id=\"para-00004\">When you think back to when you first learned addition, it is very likely you learned the addition table. Once you knew the addition table, you moved on to addition of numbers with more than one digit. The same process holds for addition in other bases. We begin with an addition table, and then move on to adding numbers with two or more digits.<\/p>\r\n<p id=\"para-00094\">Here\u2019s the beginning of the base 6 addition table:<\/p>\r\n\r\n<div id=\"table-00001\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00001\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>5<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<td>?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00006\">Many of the cells are not filled out. The ones filled in are values that never get past 5, which is the largest legal symbol in base 6, so they are acceptable symbols. But what do we do with 5 + 3 in base 6? We can\u2019t represent the answer as \u201c8\u201d since \u201c8\u201d is not a symbol available to us. Let\u2019s look at the list of first 36 numbers we have for base 6.<\/p>\r\n\r\n<div id=\"table-00002\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00002\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>10<\/td>\r\n<td>11<\/td>\r\n<td>12<\/td>\r\n<td>13<\/td>\r\n<td>14<\/td>\r\n<td>15<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>20<\/td>\r\n<td>21<\/td>\r\n<td>22<\/td>\r\n<td>23<\/td>\r\n<td>24<\/td>\r\n<td>25<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>30<\/td>\r\n<td>31<\/td>\r\n<td>32<\/td>\r\n<td>33<\/td>\r\n<td>34<\/td>\r\n<td>35<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>40<\/td>\r\n<td>41<\/td>\r\n<td>42<\/td>\r\n<td>43<\/td>\r\n<td>44<\/td>\r\n<td>45<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>50<\/td>\r\n<td>51<\/td>\r\n<td>52<\/td>\r\n<td>53<\/td>\r\n<td>54<\/td>\r\n<td>55<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00007\">So, what is 5 + 1 equal to in base 6? Well, start at the 5, and jump ahead one step. You land on 10.<\/p>\r\n\r\n<div id=\"fig-00002\" class=\"os-figure\">\r\n<figure class=\"unnumbered\" data-id=\"fig-00002\"><span data-type=\"media\" data-alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. An arrow points from 5 to 10\"><img class=\"\" src=\"https:\/\/openstax.org\/apps\/archive\/20231109.173216\/resources\/d617577ab67883f6cbf28e2f65395ef9524ae6d7\" alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. An arrow points from 5 to 10\" width=\"613\" height=\"451\" data-media-type=\"image\/jpg\" \/><\/span><\/figure>\r\n<div class=\"os-caption-container\"><\/div>\r\n<\/div>\r\n<div id=\"fig-00003\" class=\"os-figure\">\r\n<figure class=\"unnumbered\" data-id=\"fig-00003\"><span data-type=\"media\" data-alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. A callout pointing to 10 reads, The 10 is one step past the 5.\"><img src=\"https:\/\/openstax.org\/apps\/archive\/20231109.173216\/resources\/44c907e6ec6e016c93d861341f785e5074719bf5\" alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. A callout pointing to 10 reads, The 10 is one step past the 5.\" width=\"1154\" height=\"553\" data-media-type=\"image\/jpg\" \/><\/span><\/figure>\r\n<div class=\"os-caption-container\"><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">This means that, in base 6, 5 + 1 = 10.<\/span><\/div>\r\n<\/div>\r\n<p id=\"para-00009\">So, what is 5 + 2 in base 6? Well, 5 + 2 = 5 + 1 + 1, so 10 + 1\u2026jump one more space and you land on 11. So, 5 + 2 = 11 in base 6.<\/p>\r\n\r\n<div id=\"fig-00004\" class=\"os-figure\">\r\n<figure class=\"unnumbered\" data-id=\"fig-00004\"><span data-type=\"media\" data-alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. Arrows point from 5 to 10 and from 10 to 11.\"><img src=\"https:\/\/openstax.org\/apps\/archive\/20231109.173216\/resources\/04042152447efc5a78a550dbe02b2b0dcb0d1c17\" alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. Arrows point from 5 to 10 and from 10 to 11.\" width=\"706\" height=\"539\" data-media-type=\"image\/jpg\" \/><\/span><\/figure>\r\n<div class=\"os-caption-container\"><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">And so it goes. Using that process, stepping one more along the list, we can fill in the remainder of the base 6 addition table<\/span><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">.<\/span><\/div>\r\n<\/div>\r\n<div id=\"table-00006\" class=\"os-table\">\r\n<table data-id=\"table-00006\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td><strong>10<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td><strong>10<\/strong><\/td>\r\n<td><strong>11<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td><strong>10<\/strong><\/td>\r\n<td><strong>11<\/strong><\/td>\r\n<td><strong>12<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td><strong>10<\/strong><\/td>\r\n<td><strong>11<\/strong><\/td>\r\n<td><strong>12<\/strong><\/td>\r\n<td><strong>13<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>5<\/td>\r\n<td><strong>10<\/strong><\/td>\r\n<td><strong>11<\/strong><\/td>\r\n<td><strong>12<\/strong><\/td>\r\n<td><strong>13<\/strong><\/td>\r\n<td><strong>14<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><\/div>\r\n<\/div>\r\n<p id=\"para-00011\">With this table, and with our understanding of \u201ccarrying the one,\u201d we can then use the addition table to do addition in base 6 for numbers with two or more digits, using the same processes you learned for addition when you did it by hand.<\/p>\r\n\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\n<p data-type=\"title\"><strong>Adding in Base 6<\/strong><\/p>\r\n\r\n<div id=\"exer-00001\" class=\"unnumbered\" data-type=\"exercise\"><header><\/header><section>\r\n<div id=\"prob-00001\" data-type=\"problem\">\r\n<div class=\"os-problem-container\">\r\n<p id=\"para-00012\">Calculate 251<sub>6<\/sub>\u00a0+ 133<sub>6<\/sub>.<\/p>\r\n[reveal-answer q=\"462788\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"462788\"]\r\n<p id=\"para-00013\"><strong>Step 1:<\/strong>\u00a0Let\u2019s set up the addition using columns.<\/p>\r\n\r\n<div id=\"table-00007\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00007\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>2<\/td>\r\n<td>5<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>1<\/td>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00014\"><strong>Step 2:<\/strong>\u00a0Let\u2019s do the one\u2019s place first. According to the base 6 addition table, 1 + 3 = 4.<\/p>\r\n\r\n<div id=\"table-00008\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00008\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>2<\/td>\r\n<td>5<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>1<\/td>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><strong>4<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00015\"><strong>Step 3:<\/strong>\u00a0Now, we do the \u201ctens\u201d place (it\u2019s really the sixes place). According to the base 6 addition table, we have 5 + 3 = 12. So, like in base 10, we use the 2 and carry the 1.<\/p>\r\n\r\n<div id=\"table-00009\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00009\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><strong>1<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>2<\/td>\r\n<td>5<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>1<\/td>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><strong>2<\/strong><\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00016\"><strong>Step 4:<\/strong>\u00a0Now the \u201chundreds\u201d place (really, thirty-sixes place). There, we have 1 + 2 + 1 = 3 + 1 = 4.<\/p>\r\n\r\n<div id=\"table-00010\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00010\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>2<\/td>\r\n<td>5<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>1<\/td>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><strong>4<\/strong><\/td>\r\n<td>2<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00017\">So, 251<sub>6<\/sub>\u00a0+ 133<sub>6<\/sub>\u00a0= 424<sub>6<\/sub>.<\/p>\r\n<p id=\"para-00018\">As you can see, the process is the same as when you learned base 10 addition, just a different symbol set.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<div id=\"exam-00001\" class=\"ui-has-child-title\" data-type=\"example\"><header><\/header><section>\r\n<div class=\"body\">\r\n<div id=\"exer-00001\" class=\"unnumbered\" data-type=\"exercise\"><section>\r\n<div id=\"prob-00001\" data-type=\"problem\">\r\n<div class=\"os-problem-container\">\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nCalculate 453<sub>6<\/sub>\u00a0+ 345<sub>6<\/sub>.\r\n\r\n[reveal-answer q=\"148410\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"148410\"]\r\n\r\n1242<sub>6<\/sub>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<p id=\"para-00024\">To summarize the creation of the addition tables for a given base, do the following.<\/p>\r\n<p id=\"para-00095\"><strong>Step 1:<\/strong>\u00a0Set up the table.<\/p>\r\n<p id=\"para-00096\"><strong>Step 2:<\/strong>\u00a0Fill in all the additions that use the \u201clegal\u201d symbols for the base. The diagonal that goes from upper left to lower right that is immediately next to the filled boxes all get the value 10, regardless of base.<\/p>\r\n<p id=\"para-00097\"><strong>Step 3:<\/strong>\u00a0Enter the values that are in the \u201cteens.\u201d This can all be done on one table without creating multiple copies of previously done work.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Examples<\/h3>\r\n<h4 data-type=\"title\">Creating an Addition Table for a Base Lower Than 10<\/h4>\r\n<div id=\"exer-00003\" class=\"unnumbered\" data-type=\"exercise\"><header><\/header><section>\r\n<div id=\"prob-00003\" data-type=\"problem\">\r\n<div class=\"os-problem-container\">\r\n<ol id=\"list-00002\" type=\"1\">\r\n \t<li>Create the addition table for base 7.<\/li>\r\n \t<li>Create the addition table for base 2.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"186862\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"186862\"]\r\n<ol id=\"list-00003\" type=\"1\">\r\n \t<li>We begin with the table below.<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"table-00011\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00011\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00020\">In base 7, the number that follows 6 is 10 (since we\u2019ve run out of symbols!). So, 6<sub>7<\/sub>\u00a0+ 1<sub>7<\/sub>\u00a0= 10<sub>7<\/sub>. Once that is established, 6<sub>7<\/sub>\u00a0+ 2<sub>7<\/sub>\u00a0will be two numbers past 6, which is 11 in base 7.<\/p>\r\n\r\n<div id=\"table-00012\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00012\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><strong>10<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<td><strong>11<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>6<\/td>\r\n<td><strong>10<\/strong><\/td>\r\n<td><strong>11<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00021\">Continuing, we can fill in the rows as we would in base 10, but being aware that we are working in base 7.<\/p>\r\n\r\n<div id=\"table-00013\" class=\"os-table\">\r\n<table data-id=\"table-00013\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>10<\/td>\r\n<td>11<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>10<\/td>\r\n<td>11<\/td>\r\n<td>12<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>10<\/td>\r\n<td>11<\/td>\r\n<td>12<\/td>\r\n<td>13<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>10<\/td>\r\n<td>11<\/td>\r\n<td>12<\/td>\r\n<td>13<\/td>\r\n<td>14<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6<\/td>\r\n<td>6<\/td>\r\n<td>10<\/td>\r\n<td>11<\/td>\r\n<td>12<\/td>\r\n<td>13<\/td>\r\n<td>14<\/td>\r\n<td>15<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><span class=\"os-title-label\">Table<\/span>\u00a0<span class=\"os-number\">4.5<\/span>\u00a0<span class=\"os-caption\">Base 7 Addition Table<\/span><\/div>\r\n<\/div><\/li>\r\n \t<li>We revisit base 2 here. Begin with the table:<span data-type=\"newline\">\r\n<\/span>\r\n<div id=\"table-00014\" class=\"os-table\">\r\n<table data-id=\"table-00014\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><span class=\"os-title-label\">Table<\/span>\u00a0<span class=\"os-number\">4.6<\/span>\u00a0<span class=\"os-caption\">Base 2 Addition Table<\/span><\/div>\r\n<\/div>\r\n<p id=\"para-00022\">In base 2, the number that follows 1 is 10 (since we\u2019ve run out of symbols!). So, 1<sub>2<\/sub>\u00a0+ 1<sub>2<\/sub>\u00a0= 10<sub>2<\/sub>. The complete table for base two then is below.<\/p>\r\n\r\n<div id=\"table-00036\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00036\"><colgroup> <col data-width=\"1*\" \/> <col data-width=\"1*\" \/> <col data-width=\"1*\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>10<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<span data-type=\"newline\">\r\n<\/span>This demonstrates that the rules necessary for base 2 addition are as small as possible: four rules.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nCreate the addition table for base 4.\r\n\r\n[reveal-answer q=\"290694\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"290694\"]\r\n<div class=\"os-solution-container has-first-element\">\r\n<div class=\"os-table first-element\">\r\n<table class=\"unnumbered\">\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>10<\/td>\r\n<td>11<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<td>10<\/td>\r\n<td>11<\/td>\r\n<td>12<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><span class=\"os-caption\">Base 4 Addition Table<\/span><\/div>\r\n<\/div>\r\n<\/div>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\n<h4 data-type=\"title\"><strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">Adding in Base 7<\/span><\/strong><\/h4>\r\n<div id=\"exer-00005\" class=\"unnumbered\" data-type=\"exercise\"><section>\r\n<div id=\"prob-00005\" data-type=\"problem\">\r\n<div class=\"os-problem-container\">\r\n\r\nCalculate 536<sub>7<\/sub>\u00a0+ 433<sub>7<\/sub>.\r\n\r\n[reveal-answer q=\"186863\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"186863\"]\r\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\r\n<div class=\"os-solution-container\">\r\n<p id=\"para-00026\"><strong>Step 1:<\/strong>\u00a0Let\u2019s set up the addition using columns.<\/p>\r\n\r\n<div id=\"table-00015\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00015\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>5<\/td>\r\n<td>3<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>4<\/td>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00027\"><strong>Step 2:<\/strong>\u00a0Let\u2019s do the one\u2019s place first. According to the base 7 addition table, 6 + 3 = 12. We will carry the 1.<\/p>\r\n\r\n<div id=\"table-00016\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00016\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><strong>1<\/strong><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>5<\/td>\r\n<td>3<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>4<\/td>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><strong>2<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00028\"><strong>Step 3:<\/strong>\u00a0Now, we do the \u201ctens\u201d place (it\u2019s really the sevens place). According to the base 7 addition table, we have 1 + 3 + 3 = 10. So, like in base 10, we use the 0 and carry the 1.<\/p>\r\n\r\n<div id=\"table-00017\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00017\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><strong>1<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>5<\/td>\r\n<td>3<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>4<\/td>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><strong>0<\/strong><\/td>\r\n<td>2<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00029\"><strong>Step 4:<\/strong>\u00a0Now the \u201chundreds\u201d place (really, forty-ninths place). There, we have 1 + 5 + 4 = 6 + 4 = 13.<\/p>\r\n\r\n<div id=\"table-00018\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00018\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>5<\/td>\r\n<td>3<\/td>\r\n<td>6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>4<\/td>\r\n<td>3<\/td>\r\n<td>3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>1<\/strong><\/td>\r\n<td><strong>3<\/strong><\/td>\r\n<td>0<\/td>\r\n<td>2<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00030\">So, 536<sub>7<\/sub>\u00a0+ 333<sub>7<\/sub>\u00a0= 1302<sub>7<\/sub>.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nCalculate 461<sub>7<\/sub>\u00a0+ 142<sub>7<\/sub>.\r\n\r\n[reveal-answer q=\"148411\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"148411\"]\r\n\r\n633<sub>7<\/sub>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<span style=\"font-size: 1rem; text-align: initial;\">As seen previously, when performing addition in another base, set up the problem exactly as you would for addition in base 10. At each step, check the addition table for the base. As in base 10 addition, move right to left, adding down the columns using the rules in the addition table. When necessary and just as in base 10, be sure to carry the 1.<\/span>\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=HSB7_Noy8Vg[\/embed]\r\n\r\n<span style=\"font-size: 1rem; text-align: initial;\">The following video shows how to add in base 5 and 8.\r\n<\/span>\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=U-19aiF2pbg[\/embed]\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=RgklPQ8rbkg[\/embed]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\n<strong>Adding in Base 2 - Binary System<\/strong>\r\n\r\nWe return to base 2, the base used by computers.\u00a0 Calculate 1001<sub>2<\/sub> + 11011<sub>2<\/sub>.\r\n\r\n[reveal-answer q=\"290696\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"290696\"]\r\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\r\n<div class=\"os-solution-container\">\r\n<p id=\"para-00046\"><strong>Step 1:<\/strong>\u00a0Using the process established in the earlier addition problem, set up the columns.<\/p>\r\n\r\n<div id=\"table-00024\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00024\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>1<\/td>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00047\"><strong>Step 2:<\/strong>\u00a0Being careful to carry the 1 when necessary (and shown at the top of the grid), we get the following:<\/p>\r\n\r\n<div id=\"table-00025\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00025\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>1<\/td>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00048\"><strong>Step 3:<\/strong>\u00a0Calculate 1001<sub>2<\/sub>\u00a0+ 11011<sub>2<\/sub>\u00a0= 100100<sub>2<\/sub>.<\/p>\r\n<p id=\"para-00074\">So, 1001<sub>2<\/sub>\u00a0+ 11011<sub>2<\/sub>\u00a0= 100100<sub>2<\/sub>.<\/p>\r\n\r\n<\/div>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nCalculate 1100011<sub>2<\/sub><span style=\"font-size: 1rem; text-align: initial;\">\u00a0+ 101111<\/span><sub style=\"text-align: initial;\">2<\/sub><span style=\"font-size: 1rem; text-align: initial;\">.<\/span>\r\n\r\n[reveal-answer q=\"290695\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"290695\"]\r\n\r\n10010010<sub>2<\/sub>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\n<strong>Creating an Addition Table for a Base Higher Than 10<\/strong>\r\n\r\nCreate the addition table for base 12.\r\n\r\n[reveal-answer q=\"290697\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"290697\"]\r\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\r\n<div class=\"os-solution-container\">\r\n<p id=\"para-00034\"><strong>Step 1:<\/strong>\u00a0Recall, in base 12, the symbol set is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, and B. So, the addition table begins as shown below.<\/p>\r\n\r\n<div id=\"table-00019\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00019\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td><strong>0<\/strong><\/td>\r\n<td><strong>1<\/strong><\/td>\r\n<td><strong>2<\/strong><\/td>\r\n<td><strong>3<\/strong><\/td>\r\n<td><strong>4<\/strong><\/td>\r\n<td><strong>5<\/strong><\/td>\r\n<td><strong>6<\/strong><\/td>\r\n<td><strong>7<\/strong><\/td>\r\n<td><strong>8<\/strong><\/td>\r\n<td><strong>9<\/strong><\/td>\r\n<td><strong>A<\/strong><\/td>\r\n<td><strong>B<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>0<\/strong><\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>1<\/strong><\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>2<\/strong><\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>3<\/strong><\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>4<\/strong><\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>5<\/strong><\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>6<\/strong><\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>7<\/strong><\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>8<\/strong><\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>9<\/strong><\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>A<\/strong><\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>B<\/strong><\/td>\r\n<td>B<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00035\"><strong>Step 2:<\/strong>\u00a0The diagonal immediately to the right of the filled in boxes is where the 10 goes for this base.<\/p>\r\n\r\n<div id=\"table-00020\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00020\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td>+<\/td>\r\n<td><strong>0<\/strong><\/td>\r\n<td><strong>1<\/strong><\/td>\r\n<td><strong>2<\/strong><\/td>\r\n<td><strong>3<\/strong><\/td>\r\n<td><strong>4<\/strong><\/td>\r\n<td><strong>5<\/strong><\/td>\r\n<td><strong>6<\/strong><\/td>\r\n<td><strong>7<\/strong><\/td>\r\n<td><strong>8<\/strong><\/td>\r\n<td><strong>9<\/strong><\/td>\r\n<td><strong>A<\/strong><\/td>\r\n<td><strong>B<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>0<\/strong><\/td>\r\n<td>0<\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>1<\/strong><\/td>\r\n<td>1<\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>2<\/strong><\/td>\r\n<td>2<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>3<\/strong><\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>4<\/strong><\/td>\r\n<td>4<\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>5<\/strong><\/td>\r\n<td>5<\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>6<\/strong><\/td>\r\n<td>6<\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>7<\/strong><\/td>\r\n<td>7<\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>8<\/strong><\/td>\r\n<td>8<\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>9<\/strong><\/td>\r\n<td>9<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>A<\/strong><\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>B<\/strong><\/td>\r\n<td>B<\/td>\r\n<td>10<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00036\"><strong>Step 3:<\/strong>\u00a0Using the pattern we\u2019re familiar with, and counting in base 12, we can fill in the other cells.<\/p>\r\n\r\n<div id=\"table-00021\" class=\"os-table\">\r\n<table data-id=\"table-00021\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 31px;\">+<\/td>\r\n<td style=\"width: 27px;\"><strong>0<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>1<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>2<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>3<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>4<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>5<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>6<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>7<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>8<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>9<\/strong><\/td>\r\n<td style=\"width: 37px;\"><strong>A<\/strong><\/td>\r\n<td style=\"width: 39px;\"><strong>B<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>0<\/strong><\/td>\r\n<td style=\"width: 27px;\">0<\/td>\r\n<td style=\"width: 37px;\">1<\/td>\r\n<td style=\"width: 37px;\">2<\/td>\r\n<td style=\"width: 37px;\">3<\/td>\r\n<td style=\"width: 37px;\">4<\/td>\r\n<td style=\"width: 37px;\">5<\/td>\r\n<td style=\"width: 37px;\">6<\/td>\r\n<td style=\"width: 37px;\">7<\/td>\r\n<td style=\"width: 37px;\">8<\/td>\r\n<td style=\"width: 37px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 39px;\">B<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>1<\/strong><\/td>\r\n<td style=\"width: 27px;\">1<\/td>\r\n<td style=\"width: 37px;\">2<\/td>\r\n<td style=\"width: 37px;\">3<\/td>\r\n<td style=\"width: 37px;\">4<\/td>\r\n<td style=\"width: 37px;\">5<\/td>\r\n<td style=\"width: 37px;\">6<\/td>\r\n<td style=\"width: 37px;\">7<\/td>\r\n<td style=\"width: 37px;\">8<\/td>\r\n<td style=\"width: 37px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 39px;\">10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>2<\/strong><\/td>\r\n<td style=\"width: 27px;\">2<\/td>\r\n<td style=\"width: 37px;\">3<\/td>\r\n<td style=\"width: 37px;\">4<\/td>\r\n<td style=\"width: 37px;\">5<\/td>\r\n<td style=\"width: 37px;\">6<\/td>\r\n<td style=\"width: 37px;\">7<\/td>\r\n<td style=\"width: 37px;\">8<\/td>\r\n<td style=\"width: 37px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 39px;\">11<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>3<\/strong><\/td>\r\n<td style=\"width: 27px;\">3<\/td>\r\n<td style=\"width: 37px;\">4<\/td>\r\n<td style=\"width: 37px;\">5<\/td>\r\n<td style=\"width: 37px;\">6<\/td>\r\n<td style=\"width: 37px;\">7<\/td>\r\n<td style=\"width: 37px;\">8<\/td>\r\n<td style=\"width: 37px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 37px;\">11<\/td>\r\n<td style=\"width: 39px;\">12<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>4<\/strong><\/td>\r\n<td style=\"width: 27px;\">4<\/td>\r\n<td style=\"width: 37px;\">5<\/td>\r\n<td style=\"width: 37px;\">6<\/td>\r\n<td style=\"width: 37px;\">7<\/td>\r\n<td style=\"width: 37px;\">8<\/td>\r\n<td style=\"width: 37px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 37px;\">11<\/td>\r\n<td style=\"width: 37px;\">12<\/td>\r\n<td style=\"width: 39px;\">13<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>5<\/strong><\/td>\r\n<td style=\"width: 27px;\">5<\/td>\r\n<td style=\"width: 37px;\">6<\/td>\r\n<td style=\"width: 37px;\">7<\/td>\r\n<td style=\"width: 37px;\">8<\/td>\r\n<td style=\"width: 37px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 37px;\">11<\/td>\r\n<td style=\"width: 37px;\">12<\/td>\r\n<td style=\"width: 37px;\">13<\/td>\r\n<td style=\"width: 39px;\">14<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>6<\/strong><\/td>\r\n<td style=\"width: 27px;\">6<\/td>\r\n<td style=\"width: 37px;\">7<\/td>\r\n<td style=\"width: 37px;\">8<\/td>\r\n<td style=\"width: 37px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 37px;\">11<\/td>\r\n<td style=\"width: 37px;\">12<\/td>\r\n<td style=\"width: 37px;\">13<\/td>\r\n<td style=\"width: 37px;\">14<\/td>\r\n<td style=\"width: 39px;\">15<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>7<\/strong><\/td>\r\n<td style=\"width: 27px;\">7<\/td>\r\n<td style=\"width: 37px;\">8<\/td>\r\n<td style=\"width: 37px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 37px;\">11<\/td>\r\n<td style=\"width: 37px;\">12<\/td>\r\n<td style=\"width: 37px;\">13<\/td>\r\n<td style=\"width: 37px;\">14<\/td>\r\n<td style=\"width: 37px;\">15<\/td>\r\n<td style=\"width: 39px;\">16<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>8<\/strong><\/td>\r\n<td style=\"width: 27px;\">8<\/td>\r\n<td style=\"width: 37px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 37px;\">11<\/td>\r\n<td style=\"width: 37px;\">12<\/td>\r\n<td style=\"width: 37px;\">13<\/td>\r\n<td style=\"width: 37px;\">14<\/td>\r\n<td style=\"width: 37px;\">15<\/td>\r\n<td style=\"width: 37px;\">16<\/td>\r\n<td style=\"width: 39px;\">17<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>9<\/strong><\/td>\r\n<td style=\"width: 27px;\">9<\/td>\r\n<td style=\"width: 37px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 37px;\">11<\/td>\r\n<td style=\"width: 37px;\">12<\/td>\r\n<td style=\"width: 37px;\">13<\/td>\r\n<td style=\"width: 37px;\">14<\/td>\r\n<td style=\"width: 37px;\">15<\/td>\r\n<td style=\"width: 37px;\">16<\/td>\r\n<td style=\"width: 37px;\">17<\/td>\r\n<td style=\"width: 39px;\">18<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>A<\/strong><\/td>\r\n<td style=\"width: 27px;\">A<\/td>\r\n<td style=\"width: 37px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 37px;\">11<\/td>\r\n<td style=\"width: 37px;\">12<\/td>\r\n<td style=\"width: 37px;\">13<\/td>\r\n<td style=\"width: 37px;\">14<\/td>\r\n<td style=\"width: 37px;\">15<\/td>\r\n<td style=\"width: 37px;\">16<\/td>\r\n<td style=\"width: 37px;\">17<\/td>\r\n<td style=\"width: 37px;\">18<\/td>\r\n<td style=\"width: 39px;\">19<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 31px;\"><strong>B<\/strong><\/td>\r\n<td style=\"width: 27px;\">B<\/td>\r\n<td style=\"width: 37px;\">10<\/td>\r\n<td style=\"width: 37px;\">11<\/td>\r\n<td style=\"width: 37px;\">12<\/td>\r\n<td style=\"width: 37px;\">13<\/td>\r\n<td style=\"width: 37px;\">14<\/td>\r\n<td style=\"width: 37px;\">15<\/td>\r\n<td style=\"width: 37px;\">16<\/td>\r\n<td style=\"width: 37px;\">17<\/td>\r\n<td style=\"width: 37px;\">18<\/td>\r\n<td style=\"width: 37px;\">19<\/td>\r\n<td style=\"width: 39px;\">1A<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><span class=\"os-caption\">Base 12 addition table<\/span><\/div>\r\n<\/div>\r\n&nbsp;\r\n<p id=\"para-00037\">Notice that the lower-right entry is 1A<sub>12<\/sub>, as this is the number one past 19<sub>12<\/sub>.<\/p>\r\n\r\n<\/div>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\n<strong>Adding in Base 12<\/strong>\r\n\r\nCalculate\u00a03A7<sub>12<\/sub>\u00a0+ 9BA<sub>12<\/sub>.\r\n\r\n[reveal-answer q=\"290698\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"290698\"]\r\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\r\n<div class=\"os-solution-container\">\r\n<p id=\"para-00040\"><strong>Step 1:<\/strong>\u00a0Using the process established in the earlier addition problem, set up the columns.<\/p>\r\n\r\n<div id=\"table-00022\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00022\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>3<\/td>\r\n<td>A<\/td>\r\n<td>7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>+<\/td>\r\n<td>9<\/td>\r\n<td>B<\/td>\r\n<td>A<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00041\"><strong>Step 2:<\/strong>\u00a0Using the rules from the base 12 addition table, and being careful to carry the 1 when necessary, we get the following:<\/p>\r\n\r\n<div id=\"table-00023\" class=\"os-table\">\r\n<table class=\"unnumbered\" style=\"height: 48px;\" data-id=\"table-00023\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"height: 12px; width: 102.963px;\"><\/td>\r\n<td style=\"height: 12px; width: 100.887px;\">1<\/td>\r\n<td style=\"height: 12px; width: 109.025px;\">1<\/td>\r\n<td style=\"height: 12px; width: 109.05px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"height: 12px; width: 102.963px;\"><\/td>\r\n<td style=\"height: 12px; width: 100.887px;\">3<\/td>\r\n<td style=\"height: 12px; width: 109.025px;\">A<\/td>\r\n<td style=\"height: 12px; width: 109.05px;\">7<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"height: 12px; width: 102.963px;\">+<\/td>\r\n<td style=\"height: 12px; width: 100.887px;\">9<\/td>\r\n<td style=\"height: 12px; width: 109.025px;\">B<\/td>\r\n<td style=\"height: 12px; width: 109.05px;\">A<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"height: 12px; width: 102.963px;\"><strong>1<\/strong><\/td>\r\n<td style=\"height: 12px; width: 100.887px;\"><strong>1<\/strong><\/td>\r\n<td style=\"height: 12px; width: 109.025px;\">A<\/td>\r\n<td style=\"height: 12px; width: 109.05px;\">5<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00042\">The ones that were carried are located over the columns.<\/p>\r\n<p id=\"para-00043\">So, 3A7<sub>12<\/sub>\u00a0+ 9BA<sub>12<\/sub>= 11A5<sub>12<\/sub>.<\/p>\r\n\r\n<\/div>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nCalculate 4B3<sub>12<\/sub>\u00a0+ B06<sub>12<\/sub>.\r\n\r\n[reveal-answer q=\"290699\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"290699\"]\r\n\r\n13B9<sub>12<\/sub>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n[embed]https:\/\/www.youtube.com\/watch?v=rF8eKBQNXDc[\/embed]\r\n<h3>Subtracting in Other Bases<\/h3>\r\nSometimes carrying is necessary when adding numbers. Likewise, sometimes borrowing is necessary when subtracting numbers.\u00a0 As you view these two videos, pay close attention to the steps and understanding what it means to borrow.\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=9T3AAn-Cw3g[\/embed]\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=3lHBgFvr3yE[\/embed]\r\n\r\n<span id=\"term-00001\" data-type=\"term\">Subtraction in bases<\/span>\u00a0other than base 10 follow the same processes as base 10 subtraction, but, as with addition, using the addition table for the base.\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\n<strong>Subtracting in Base 6<\/strong>\r\n\r\nCalculate\u00a052<sub>6<\/sub>\u00a0\u2212 34<sub>6<\/sub>.\r\n\r\n[reveal-answer q=\"290700\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"290700\"]\r\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\r\n<div class=\"os-solution-container\">\r\n<p id=\"para-00052\"><strong>Step 1:<\/strong>\u00a0Let\u2019s set up the subtraction using columns.<\/p>\r\n\r\n<div id=\"table-00026\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00026\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>5<\/td>\r\n<td>2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u2212<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00053\"><strong>Step 2:<\/strong>\u00a0Just as we might do in base 10, we borrow a 1 from the 5 for the ones digit. The 1 borrowed represents a group of 6.<\/p>\r\n\r\n<div id=\"table-00027\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00027\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"MathJax-Element-161-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;inline&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/mrow&gt;&lt;annotation-xml encoding=&quot;MathML-Content&quot;&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/annotation-xml&gt;&lt;\/semantics&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-3240\" class=\"math\"><span id=\"MathJax-Span-3241\" class=\"mrow\"><span id=\"MathJax-Span-3242\" class=\"semantics\"><span id=\"MathJax-Span-3243\" class=\"mrow\"><span id=\"MathJax-Span-3244\" class=\"mrow\"><span id=\"MathJax-Span-3245\" class=\"menclose\"><del><span id=\"MathJax-Span-3246\" class=\"mrow\"><span id=\"MathJax-Span-3247\" class=\"mn\">5\u00a0<\/span><\/span><\/del><\/span><span id=\"MathJax-Span-3248\" class=\"mn\">\u00a04<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\r\n<td><strong>12<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u2212<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00054\"><strong>Step 3:<\/strong>\u00a0Referring to the base 6 addition table, we see that 4 + 4 = 12, so 12<sub>6<\/sub>\u00a0\u2212 4<sub>6<\/sub>\u00a0is 4<sub>6<\/sub>.<\/p>\r\n\r\n<div id=\"table-00028\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00028\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"MathJax-Element-161-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;inline&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/mrow&gt;&lt;annotation-xml encoding=&quot;MathML-Content&quot;&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/annotation-xml&gt;&lt;\/semantics&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-3240\" class=\"math\"><span id=\"MathJax-Span-3241\" class=\"mrow\"><span id=\"MathJax-Span-3242\" class=\"semantics\"><span id=\"MathJax-Span-3243\" class=\"mrow\"><span id=\"MathJax-Span-3244\" class=\"mrow\"><span id=\"MathJax-Span-3245\" class=\"menclose\"><del><span id=\"MathJax-Span-3246\" class=\"mrow\"><span id=\"MathJax-Span-3247\" class=\"mn\">5\u00a0<\/span><\/span><\/del><\/span><span id=\"MathJax-Span-3248\" class=\"mn\">\u00a04<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\r\n<td><strong>1<\/strong>2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u2212<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><strong>4<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00055\"><strong>Step 4:<\/strong>\u00a0Now we deal with the \u201ctens\u201d (really, sixes) digit, 4<sub>6<\/sub>\u00a0\u2212 3<sub>6<\/sub>, which equals 1<sub>6<\/sub>\u00a0according to the base 6 addition table.<\/p>\r\n\r\n<div id=\"table-00029\" class=\"os-table\">\r\n<table class=\"unnumbered\" data-id=\"table-00029\"><colgroup> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/> <col data-width=\"1pt\" \/><\/colgroup>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"MathJax-Element-161-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;inline&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/mrow&gt;&lt;annotation-xml encoding=&quot;MathML-Content&quot;&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/annotation-xml&gt;&lt;\/semantics&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-3240\" class=\"math\"><span id=\"MathJax-Span-3241\" class=\"mrow\"><span id=\"MathJax-Span-3242\" class=\"semantics\"><span id=\"MathJax-Span-3243\" class=\"mrow\"><span id=\"MathJax-Span-3244\" class=\"mrow\"><span id=\"MathJax-Span-3245\" class=\"menclose\"><del><span id=\"MathJax-Span-3246\" class=\"mrow\"><span id=\"MathJax-Span-3247\" class=\"mn\">5\u00a0<\/span><\/span><\/del><\/span><span id=\"MathJax-Span-3248\" class=\"mn\">\u00a04<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\r\n<td><strong>1<\/strong>2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u2212<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><strong>1<\/strong><\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"para-00056\">So, 52<sub>6<\/sub>\u00a0\u2212 34<sub>6<\/sub>\u00a0= 14<sub>6<\/sub>.<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nCalculate 115<sub>6<\/sub>\u00a0\u2212 43<sub>6<\/sub>.\r\n\r\n[reveal-answer q=\"290701\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"290701\"]\r\n\r\n32<sub>6<\/sub>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nYou will see two different approaches to representing the value borrowed:\r\n1. Writing the borrowed amount by adding the digit 1 (like above example) keeping all values in the problem in the given base.\r\n2. Writing the borrowed amount in base 10 since it's \"scratch paper\" as in the videos below.\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=1O3DG2UShGI[\/embed]\r\n\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Add two numbers from a base other than 10<\/li>\n<li>Subtract two numbers from a base other than 10<\/li>\n<\/ul>\n<\/div>\n<h3>Adding Basic Time Units<\/h3>\n<p><span style=\"font-size: 1em;\">Think about the number of seconds in a minute and minutes in an hour.\u00a0 What base does this follow?\u00a0 If you said sixty, you are correct! Further, if you add 2 hours 20 minutes 35 seconds and 1 hour 45 minutes\u00a0 50 seconds, is the answer 3 hours 65 minutes 85 seconds?\u00a0 Technically, this is true, but we wouldn&#8217;t keep this format.\u00a0 Once we reach 60 or higher in an unit, we convert 60 it to one in the next higher unit.\u00a0 You would follow these steps,\u00a0<\/span><span style=\"font-size: 1em;\">65 minutes is equal to 1 hour 5 minutes and\u00a0<\/span><span style=\"font-size: 1em; text-align: initial;\">85 seconds is equal to 1 minute 15 seconds.\u00a0 Thus, 3 hours 65 minutes 85 seconds is roughly 3 hours + 1 hour 5 minutes + 1 minute 15 seconds and simplifies to 4 hours 6 minutes 15 seconds.\u00a0 Adding non-decimal (not base 10) numbers uses similar steps to adding different time units.<\/span><\/p>\n<h3>Understanding the Process of Adding in Decimal Numbers<\/h3>\n<p>Before we try adding in other bases let&#8217;s review the steps to adding two base 10 numbers.\u00a0 Add these two numbers without a calculator:<\/p>\n<p style=\"text-align: center;\">536<br \/>\n<span style=\"text-decoration: underline;\">+ 398<\/span><\/p>\n<p>This problem requires carrying to get the correct answer.\u00a0 Majority of the population can show the steps necessary to get the answer to the above addition problem, but fewer can explain why we carry?\u00a0 This video answers the question of why carrying works and will prepare you for adding in a base other than 10.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Adding: why carrying works | Addition and subtraction | Arithmetic | Khan Academy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/O9zSHs1TWMM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Adding in Other Bases<\/h3>\n<p id=\"para-00004\">When you think back to when you first learned addition, it is very likely you learned the addition table. Once you knew the addition table, you moved on to addition of numbers with more than one digit. The same process holds for addition in other bases. We begin with an addition table, and then move on to adding numbers with two or more digits.<\/p>\n<p id=\"para-00094\">Here\u2019s the beginning of the base 6 addition table:<\/p>\n<div id=\"table-00001\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00001\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>+<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>?<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>5<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00006\">Many of the cells are not filled out. The ones filled in are values that never get past 5, which is the largest legal symbol in base 6, so they are acceptable symbols. But what do we do with 5 + 3 in base 6? We can\u2019t represent the answer as \u201c8\u201d since \u201c8\u201d is not a symbol available to us. Let\u2019s look at the list of first 36 numbers we have for base 6.<\/p>\n<div id=\"table-00002\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00002\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>11<\/td>\n<td>12<\/td>\n<td>13<\/td>\n<td>14<\/td>\n<td>15<\/td>\n<\/tr>\n<tr>\n<td>20<\/td>\n<td>21<\/td>\n<td>22<\/td>\n<td>23<\/td>\n<td>24<\/td>\n<td>25<\/td>\n<\/tr>\n<tr>\n<td>30<\/td>\n<td>31<\/td>\n<td>32<\/td>\n<td>33<\/td>\n<td>34<\/td>\n<td>35<\/td>\n<\/tr>\n<tr>\n<td>40<\/td>\n<td>41<\/td>\n<td>42<\/td>\n<td>43<\/td>\n<td>44<\/td>\n<td>45<\/td>\n<\/tr>\n<tr>\n<td>50<\/td>\n<td>51<\/td>\n<td>52<\/td>\n<td>53<\/td>\n<td>54<\/td>\n<td>55<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00007\">So, what is 5 + 1 equal to in base 6? Well, start at the 5, and jump ahead one step. You land on 10.<\/p>\n<div id=\"fig-00002\" class=\"os-figure\">\n<figure class=\"unnumbered\" data-id=\"fig-00002\"><span data-type=\"media\" data-alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. An arrow points from 5 to 10\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/openstax.org\/apps\/archive\/20231109.173216\/resources\/d617577ab67883f6cbf28e2f65395ef9524ae6d7\" alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. An arrow points from 5 to 10\" width=\"613\" height=\"451\" data-media-type=\"image\/jpg\" \/><\/span><\/figure>\n<div class=\"os-caption-container\"><\/div>\n<\/div>\n<div id=\"fig-00003\" class=\"os-figure\">\n<figure class=\"unnumbered\" data-id=\"fig-00003\"><span data-type=\"media\" data-alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. A callout pointing to 10 reads, The 10 is one step past the 5.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/openstax.org\/apps\/archive\/20231109.173216\/resources\/44c907e6ec6e016c93d861341f785e5074719bf5\" alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. A callout pointing to 10 reads, The 10 is one step past the 5.\" width=\"1154\" height=\"553\" data-media-type=\"image\/jpg\" \/><\/span><\/figure>\n<div class=\"os-caption-container\"><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">This means that, in base 6, 5 + 1 = 10.<\/span><\/div>\n<\/div>\n<p id=\"para-00009\">So, what is 5 + 2 in base 6? Well, 5 + 2 = 5 + 1 + 1, so 10 + 1\u2026jump one more space and you land on 11. So, 5 + 2 = 11 in base 6.<\/p>\n<div id=\"fig-00004\" class=\"os-figure\">\n<figure class=\"unnumbered\" data-id=\"fig-00004\"><span data-type=\"media\" data-alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. Arrows point from 5 to 10 and from 10 to 11.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/openstax.org\/apps\/archive\/20231109.173216\/resources\/04042152447efc5a78a550dbe02b2b0dcb0d1c17\" alt=\"A table with numbers 0 to 5, 10 to 15, 20 to 25, 30 to 35, 40 to 45, 50 to 55. Arrows point from 5 to 10 and from 10 to 11.\" width=\"706\" height=\"539\" data-media-type=\"image\/jpg\" \/><\/span><\/figure>\n<div class=\"os-caption-container\"><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">And so it goes. Using that process, stepping one more along the list, we can fill in the remainder of the base 6 addition table<\/span><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">.<\/span><\/div>\n<\/div>\n<div id=\"table-00006\" class=\"os-table\">\n<table data-id=\"table-00006\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>+<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td><strong>10<\/strong><\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td><strong>10<\/strong><\/td>\n<td><strong>11<\/strong><\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td><strong>10<\/strong><\/td>\n<td><strong>11<\/strong><\/td>\n<td><strong>12<\/strong><\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td><strong>10<\/strong><\/td>\n<td><strong>11<\/strong><\/td>\n<td><strong>12<\/strong><\/td>\n<td><strong>13<\/strong><\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>5<\/td>\n<td><strong>10<\/strong><\/td>\n<td><strong>11<\/strong><\/td>\n<td><strong>12<\/strong><\/td>\n<td><strong>13<\/strong><\/td>\n<td><strong>14<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><\/div>\n<\/div>\n<p id=\"para-00011\">With this table, and with our understanding of \u201ccarrying the one,\u201d we can then use the addition table to do addition in base 6 for numbers with two or more digits, using the same processes you learned for addition when you did it by hand.<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p data-type=\"title\"><strong>Adding in Base 6<\/strong><\/p>\n<div id=\"exer-00001\" class=\"unnumbered\" data-type=\"exercise\">\n<header><\/header>\n<section>\n<div id=\"prob-00001\" data-type=\"problem\">\n<div class=\"os-problem-container\">\n<p id=\"para-00012\">Calculate 251<sub>6<\/sub>\u00a0+ 133<sub>6<\/sub>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q462788\">Show Solution<\/span><\/p>\n<div id=\"q462788\" class=\"hidden-answer\" style=\"display: none\">\n<p id=\"para-00013\"><strong>Step 1:<\/strong>\u00a0Let\u2019s set up the addition using columns.<\/p>\n<div id=\"table-00007\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00007\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td>2<\/td>\n<td>5<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>1<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00014\"><strong>Step 2:<\/strong>\u00a0Let\u2019s do the one\u2019s place first. According to the base 6 addition table, 1 + 3 = 4.<\/p>\n<div id=\"table-00008\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00008\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td>2<\/td>\n<td>5<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>1<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><strong>4<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00015\"><strong>Step 3:<\/strong>\u00a0Now, we do the \u201ctens\u201d place (it\u2019s really the sixes place). According to the base 6 addition table, we have 5 + 3 = 12. So, like in base 10, we use the 2 and carry the 1.<\/p>\n<div id=\"table-00009\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00009\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td><strong>1<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>2<\/td>\n<td>5<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>1<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><strong>2<\/strong><\/td>\n<td>4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00016\"><strong>Step 4:<\/strong>\u00a0Now the \u201chundreds\u201d place (really, thirty-sixes place). There, we have 1 + 2 + 1 = 3 + 1 = 4.<\/p>\n<div id=\"table-00010\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00010\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td>1<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>2<\/td>\n<td>5<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>1<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><strong>4<\/strong><\/td>\n<td>2<\/td>\n<td>4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00017\">So, 251<sub>6<\/sub>\u00a0+ 133<sub>6<\/sub>\u00a0= 424<sub>6<\/sub>.<\/p>\n<p id=\"para-00018\">As you can see, the process is the same as when you learned base 10 addition, just a different symbol set.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<div id=\"exam-00001\" class=\"ui-has-child-title\" data-type=\"example\">\n<header><\/header>\n<section>\n<div class=\"body\">\n<div id=\"exer-00001\" class=\"unnumbered\" data-type=\"exercise\">\n<section>\n<div id=\"prob-00001\" data-type=\"problem\">\n<div class=\"os-problem-container\">\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Calculate 453<sub>6<\/sub>\u00a0+ 345<sub>6<\/sub>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q148410\">Show Solution<\/span><\/p>\n<div id=\"q148410\" class=\"hidden-answer\" style=\"display: none\">\n<p>1242<sub>6<\/sub><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<p id=\"para-00024\">To summarize the creation of the addition tables for a given base, do the following.<\/p>\n<p id=\"para-00095\"><strong>Step 1:<\/strong>\u00a0Set up the table.<\/p>\n<p id=\"para-00096\"><strong>Step 2:<\/strong>\u00a0Fill in all the additions that use the \u201clegal\u201d symbols for the base. The diagonal that goes from upper left to lower right that is immediately next to the filled boxes all get the value 10, regardless of base.<\/p>\n<p id=\"para-00097\"><strong>Step 3:<\/strong>\u00a0Enter the values that are in the \u201cteens.\u201d This can all be done on one table without creating multiple copies of previously done work.<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Examples<\/h3>\n<h4 data-type=\"title\">Creating an Addition Table for a Base Lower Than 10<\/h4>\n<div id=\"exer-00003\" class=\"unnumbered\" data-type=\"exercise\">\n<header><\/header>\n<section>\n<div id=\"prob-00003\" data-type=\"problem\">\n<div class=\"os-problem-container\">\n<ol id=\"list-00002\" type=\"1\">\n<li>Create the addition table for base 7.<\/li>\n<li>Create the addition table for base 2.<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q186862\">Show Solution<\/span><\/p>\n<div id=\"q186862\" class=\"hidden-answer\" style=\"display: none\">\n<ol id=\"list-00003\" type=\"1\">\n<li>We begin with the table below.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"table-00011\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00011\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>+<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>6<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00020\">In base 7, the number that follows 6 is 10 (since we\u2019ve run out of symbols!). So, 6<sub>7<\/sub>\u00a0+ 1<sub>7<\/sub>\u00a0= 10<sub>7<\/sub>. Once that is established, 6<sub>7<\/sub>\u00a0+ 2<sub>7<\/sub>\u00a0will be two numbers past 6, which is 11 in base 7.<\/p>\n<div id=\"table-00012\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00012\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>+<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><strong>10<\/strong><\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><\/td>\n<td><strong>11<\/strong><\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>6<\/td>\n<td><strong>10<\/strong><\/td>\n<td><strong>11<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00021\">Continuing, we can fill in the rows as we would in base 10, but being aware that we are working in base 7.<\/p>\n<div id=\"table-00013\" class=\"os-table\">\n<table data-id=\"table-00013\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>+<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>10<\/td>\n<td>11<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>10<\/td>\n<td>11<\/td>\n<td>12<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>10<\/td>\n<td>11<\/td>\n<td>12<\/td>\n<td>13<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>10<\/td>\n<td>11<\/td>\n<td>12<\/td>\n<td>13<\/td>\n<td>14<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>6<\/td>\n<td>10<\/td>\n<td>11<\/td>\n<td>12<\/td>\n<td>13<\/td>\n<td>14<\/td>\n<td>15<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><span class=\"os-title-label\">Table<\/span>\u00a0<span class=\"os-number\">4.5<\/span>\u00a0<span class=\"os-caption\">Base 7 Addition Table<\/span><\/div>\n<\/div>\n<\/li>\n<li>We revisit base 2 here. Begin with the table:<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<div id=\"table-00014\" class=\"os-table\">\n<table data-id=\"table-00014\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>+<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><span class=\"os-title-label\">Table<\/span>\u00a0<span class=\"os-number\">4.6<\/span>\u00a0<span class=\"os-caption\">Base 2 Addition Table<\/span><\/div>\n<\/div>\n<p id=\"para-00022\">In base 2, the number that follows 1 is 10 (since we\u2019ve run out of symbols!). So, 1<sub>2<\/sub>\u00a0+ 1<sub>2<\/sub>\u00a0= 10<sub>2<\/sub>. The complete table for base two then is below.<\/p>\n<div id=\"table-00036\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00036\">\n<colgroup>\n<col data-width=\"1*\" \/>\n<col data-width=\"1*\" \/>\n<col data-width=\"1*\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>+<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><span data-type=\"newline\"><br \/>\n<\/span>This demonstrates that the rules necessary for base 2 addition are as small as possible: four rules.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Create the addition table for base 4.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q290694\">Show Solution<\/span><\/p>\n<div id=\"q290694\" class=\"hidden-answer\" style=\"display: none\">\n<div class=\"os-solution-container has-first-element\">\n<div class=\"os-table first-element\">\n<table class=\"unnumbered\">\n<tbody>\n<tr>\n<td>+<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>10<\/td>\n<td>11<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>3<\/td>\n<td>10<\/td>\n<td>11<\/td>\n<td>12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><span class=\"os-caption\">Base 4 Addition Table<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<h4 data-type=\"title\"><strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial;\">Adding in Base 7<\/span><\/strong><\/h4>\n<div id=\"exer-00005\" class=\"unnumbered\" data-type=\"exercise\">\n<section>\n<div id=\"prob-00005\" data-type=\"problem\">\n<div class=\"os-problem-container\">\n<p>Calculate 536<sub>7<\/sub>\u00a0+ 433<sub>7<\/sub>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q186863\">Show Solution<\/span><\/p>\n<div id=\"q186863\" class=\"hidden-answer\" style=\"display: none\">\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\n<div class=\"os-solution-container\">\n<p id=\"para-00026\"><strong>Step 1:<\/strong>\u00a0Let\u2019s set up the addition using columns.<\/p>\n<div id=\"table-00015\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00015\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td>5<\/td>\n<td>3<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>4<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00027\"><strong>Step 2:<\/strong>\u00a0Let\u2019s do the one\u2019s place first. According to the base 7 addition table, 6 + 3 = 12. We will carry the 1.<\/p>\n<div id=\"table-00016\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00016\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><strong>1<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>5<\/td>\n<td>3<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>4<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><strong>2<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00028\"><strong>Step 3:<\/strong>\u00a0Now, we do the \u201ctens\u201d place (it\u2019s really the sevens place). According to the base 7 addition table, we have 1 + 3 + 3 = 10. So, like in base 10, we use the 0 and carry the 1.<\/p>\n<div id=\"table-00017\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00017\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td><strong>1<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>5<\/td>\n<td>3<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>4<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><strong>0<\/strong><\/td>\n<td>2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00029\"><strong>Step 4:<\/strong>\u00a0Now the \u201chundreds\u201d place (really, forty-ninths place). There, we have 1 + 5 + 4 = 6 + 4 = 13.<\/p>\n<div id=\"table-00018\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00018\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td>1<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>5<\/td>\n<td>3<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>4<\/td>\n<td>3<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>3<\/strong><\/td>\n<td>0<\/td>\n<td>2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00030\">So, 536<sub>7<\/sub>\u00a0+ 333<sub>7<\/sub>\u00a0= 1302<sub>7<\/sub>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Calculate 461<sub>7<\/sub>\u00a0+ 142<sub>7<\/sub>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q148411\">Show Solution<\/span><\/p>\n<div id=\"q148411\" class=\"hidden-answer\" style=\"display: none\">\n<p>633<sub>7<\/sub><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><span style=\"font-size: 1rem; text-align: initial;\">As seen previously, when performing addition in another base, set up the problem exactly as you would for addition in base 10. At each step, check the addition table for the base. As in base 10 addition, move right to left, adding down the columns using the rules in the addition table. When necessary and just as in base 10, be sure to carry the 1.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Adding in base 4 and base 7\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/HSB7_Noy8Vg?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><span style=\"font-size: 1rem; text-align: initial;\">The following video shows how to add in base 5 and 8.<br \/>\n<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Addition in Bases other than Base-10 127-2.3\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/U-19aiF2pbg?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Adding in binary | Applying mathematical reasoning | Pre-Algebra | Khan Academy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/RgklPQ8rbkg?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p><strong>Adding in Base 2 &#8211; Binary System<\/strong><\/p>\n<p>We return to base 2, the base used by computers.\u00a0 Calculate 1001<sub>2<\/sub> + 11011<sub>2<\/sub>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q290696\">Show Solution<\/span><\/p>\n<div id=\"q290696\" class=\"hidden-answer\" style=\"display: none\">\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\n<div class=\"os-solution-container\">\n<p id=\"para-00046\"><strong>Step 1:<\/strong>\u00a0Using the process established in the earlier addition problem, set up the columns.<\/p>\n<div id=\"table-00024\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00024\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00047\"><strong>Step 2:<\/strong>\u00a0Being careful to carry the 1 when necessary (and shown at the top of the grid), we get the following:<\/p>\n<div id=\"table-00025\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00025\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td>1<\/td>\n<td><\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00048\"><strong>Step 3:<\/strong>\u00a0Calculate 1001<sub>2<\/sub>\u00a0+ 11011<sub>2<\/sub>\u00a0= 100100<sub>2<\/sub>.<\/p>\n<p id=\"para-00074\">So, 1001<sub>2<\/sub>\u00a0+ 11011<sub>2<\/sub>\u00a0= 100100<sub>2<\/sub>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Calculate 1100011<sub>2<\/sub><span style=\"font-size: 1rem; text-align: initial;\">\u00a0+ 101111<\/span><sub style=\"text-align: initial;\">2<\/sub><span style=\"font-size: 1rem; text-align: initial;\">.<\/span><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q290695\">Show Solution<\/span><\/p>\n<div id=\"q290695\" class=\"hidden-answer\" style=\"display: none\">\n<p>10010010<sub>2<\/sub><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p><strong>Creating an Addition Table for a Base Higher Than 10<\/strong><\/p>\n<p>Create the addition table for base 12.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q290697\">Show Solution<\/span><\/p>\n<div id=\"q290697\" class=\"hidden-answer\" style=\"display: none\">\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\n<div class=\"os-solution-container\">\n<p id=\"para-00034\"><strong>Step 1:<\/strong>\u00a0Recall, in base 12, the symbol set is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, and B. So, the addition table begins as shown below.<\/p>\n<div id=\"table-00019\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00019\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>+<\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>2<\/strong><\/td>\n<td><strong>3<\/strong><\/td>\n<td><strong>4<\/strong><\/td>\n<td><strong>5<\/strong><\/td>\n<td><strong>6<\/strong><\/td>\n<td><strong>7<\/strong><\/td>\n<td><strong>8<\/strong><\/td>\n<td><strong>9<\/strong><\/td>\n<td><strong>A<\/strong><\/td>\n<td><strong>B<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>2<\/strong><\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>3<\/strong><\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>4<\/strong><\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>5<\/strong><\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>6<\/strong><\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>7<\/strong><\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>8<\/strong><\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>9<\/strong><\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>A<\/strong><\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>B<\/strong><\/td>\n<td>B<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00035\"><strong>Step 2:<\/strong>\u00a0The diagonal immediately to the right of the filled in boxes is where the 10 goes for this base.<\/p>\n<div id=\"table-00020\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00020\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td>+<\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>2<\/strong><\/td>\n<td><strong>3<\/strong><\/td>\n<td><strong>4<\/strong><\/td>\n<td><strong>5<\/strong><\/td>\n<td><strong>6<\/strong><\/td>\n<td><strong>7<\/strong><\/td>\n<td><strong>8<\/strong><\/td>\n<td><strong>9<\/strong><\/td>\n<td><strong>A<\/strong><\/td>\n<td><strong>B<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td><strong>2<\/strong><\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>3<\/strong><\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>4<\/strong><\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>5<\/strong><\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>6<\/strong><\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>7<\/strong><\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>8<\/strong><\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>9<\/strong><\/td>\n<td>9<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>A<\/strong><\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>B<\/strong><\/td>\n<td>B<\/td>\n<td>10<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00036\"><strong>Step 3:<\/strong>\u00a0Using the pattern we\u2019re familiar with, and counting in base 12, we can fill in the other cells.<\/p>\n<div id=\"table-00021\" class=\"os-table\">\n<table data-id=\"table-00021\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td style=\"width: 31px;\">+<\/td>\n<td style=\"width: 27px;\"><strong>0<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>1<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>2<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>3<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>4<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>5<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>6<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>7<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>8<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>9<\/strong><\/td>\n<td style=\"width: 37px;\"><strong>A<\/strong><\/td>\n<td style=\"width: 39px;\"><strong>B<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>0<\/strong><\/td>\n<td style=\"width: 27px;\">0<\/td>\n<td style=\"width: 37px;\">1<\/td>\n<td style=\"width: 37px;\">2<\/td>\n<td style=\"width: 37px;\">3<\/td>\n<td style=\"width: 37px;\">4<\/td>\n<td style=\"width: 37px;\">5<\/td>\n<td style=\"width: 37px;\">6<\/td>\n<td style=\"width: 37px;\">7<\/td>\n<td style=\"width: 37px;\">8<\/td>\n<td style=\"width: 37px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 39px;\">B<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>1<\/strong><\/td>\n<td style=\"width: 27px;\">1<\/td>\n<td style=\"width: 37px;\">2<\/td>\n<td style=\"width: 37px;\">3<\/td>\n<td style=\"width: 37px;\">4<\/td>\n<td style=\"width: 37px;\">5<\/td>\n<td style=\"width: 37px;\">6<\/td>\n<td style=\"width: 37px;\">7<\/td>\n<td style=\"width: 37px;\">8<\/td>\n<td style=\"width: 37px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 39px;\">10<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>2<\/strong><\/td>\n<td style=\"width: 27px;\">2<\/td>\n<td style=\"width: 37px;\">3<\/td>\n<td style=\"width: 37px;\">4<\/td>\n<td style=\"width: 37px;\">5<\/td>\n<td style=\"width: 37px;\">6<\/td>\n<td style=\"width: 37px;\">7<\/td>\n<td style=\"width: 37px;\">8<\/td>\n<td style=\"width: 37px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 39px;\">11<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>3<\/strong><\/td>\n<td style=\"width: 27px;\">3<\/td>\n<td style=\"width: 37px;\">4<\/td>\n<td style=\"width: 37px;\">5<\/td>\n<td style=\"width: 37px;\">6<\/td>\n<td style=\"width: 37px;\">7<\/td>\n<td style=\"width: 37px;\">8<\/td>\n<td style=\"width: 37px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 37px;\">11<\/td>\n<td style=\"width: 39px;\">12<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>4<\/strong><\/td>\n<td style=\"width: 27px;\">4<\/td>\n<td style=\"width: 37px;\">5<\/td>\n<td style=\"width: 37px;\">6<\/td>\n<td style=\"width: 37px;\">7<\/td>\n<td style=\"width: 37px;\">8<\/td>\n<td style=\"width: 37px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 37px;\">11<\/td>\n<td style=\"width: 37px;\">12<\/td>\n<td style=\"width: 39px;\">13<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>5<\/strong><\/td>\n<td style=\"width: 27px;\">5<\/td>\n<td style=\"width: 37px;\">6<\/td>\n<td style=\"width: 37px;\">7<\/td>\n<td style=\"width: 37px;\">8<\/td>\n<td style=\"width: 37px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 37px;\">11<\/td>\n<td style=\"width: 37px;\">12<\/td>\n<td style=\"width: 37px;\">13<\/td>\n<td style=\"width: 39px;\">14<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>6<\/strong><\/td>\n<td style=\"width: 27px;\">6<\/td>\n<td style=\"width: 37px;\">7<\/td>\n<td style=\"width: 37px;\">8<\/td>\n<td style=\"width: 37px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 37px;\">11<\/td>\n<td style=\"width: 37px;\">12<\/td>\n<td style=\"width: 37px;\">13<\/td>\n<td style=\"width: 37px;\">14<\/td>\n<td style=\"width: 39px;\">15<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>7<\/strong><\/td>\n<td style=\"width: 27px;\">7<\/td>\n<td style=\"width: 37px;\">8<\/td>\n<td style=\"width: 37px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 37px;\">11<\/td>\n<td style=\"width: 37px;\">12<\/td>\n<td style=\"width: 37px;\">13<\/td>\n<td style=\"width: 37px;\">14<\/td>\n<td style=\"width: 37px;\">15<\/td>\n<td style=\"width: 39px;\">16<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>8<\/strong><\/td>\n<td style=\"width: 27px;\">8<\/td>\n<td style=\"width: 37px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 37px;\">11<\/td>\n<td style=\"width: 37px;\">12<\/td>\n<td style=\"width: 37px;\">13<\/td>\n<td style=\"width: 37px;\">14<\/td>\n<td style=\"width: 37px;\">15<\/td>\n<td style=\"width: 37px;\">16<\/td>\n<td style=\"width: 39px;\">17<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>9<\/strong><\/td>\n<td style=\"width: 27px;\">9<\/td>\n<td style=\"width: 37px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 37px;\">11<\/td>\n<td style=\"width: 37px;\">12<\/td>\n<td style=\"width: 37px;\">13<\/td>\n<td style=\"width: 37px;\">14<\/td>\n<td style=\"width: 37px;\">15<\/td>\n<td style=\"width: 37px;\">16<\/td>\n<td style=\"width: 37px;\">17<\/td>\n<td style=\"width: 39px;\">18<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>A<\/strong><\/td>\n<td style=\"width: 27px;\">A<\/td>\n<td style=\"width: 37px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 37px;\">11<\/td>\n<td style=\"width: 37px;\">12<\/td>\n<td style=\"width: 37px;\">13<\/td>\n<td style=\"width: 37px;\">14<\/td>\n<td style=\"width: 37px;\">15<\/td>\n<td style=\"width: 37px;\">16<\/td>\n<td style=\"width: 37px;\">17<\/td>\n<td style=\"width: 37px;\">18<\/td>\n<td style=\"width: 39px;\">19<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 31px;\"><strong>B<\/strong><\/td>\n<td style=\"width: 27px;\">B<\/td>\n<td style=\"width: 37px;\">10<\/td>\n<td style=\"width: 37px;\">11<\/td>\n<td style=\"width: 37px;\">12<\/td>\n<td style=\"width: 37px;\">13<\/td>\n<td style=\"width: 37px;\">14<\/td>\n<td style=\"width: 37px;\">15<\/td>\n<td style=\"width: 37px;\">16<\/td>\n<td style=\"width: 37px;\">17<\/td>\n<td style=\"width: 37px;\">18<\/td>\n<td style=\"width: 37px;\">19<\/td>\n<td style=\"width: 39px;\">1A<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><span class=\"os-caption\">Base 12 addition table<\/span><\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p id=\"para-00037\">Notice that the lower-right entry is 1A<sub>12<\/sub>, as this is the number one past 19<sub>12<\/sub>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p><strong>Adding in Base 12<\/strong><\/p>\n<p>Calculate\u00a03A7<sub>12<\/sub>\u00a0+ 9BA<sub>12<\/sub>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q290698\">Show Solution<\/span><\/p>\n<div id=\"q290698\" class=\"hidden-answer\" style=\"display: none\">\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\n<div class=\"os-solution-container\">\n<p id=\"para-00040\"><strong>Step 1:<\/strong>\u00a0Using the process established in the earlier addition problem, set up the columns.<\/p>\n<div id=\"table-00022\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00022\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td>3<\/td>\n<td>A<\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td>+<\/td>\n<td>9<\/td>\n<td>B<\/td>\n<td>A<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00041\"><strong>Step 2:<\/strong>\u00a0Using the rules from the base 12 addition table, and being careful to carry the 1 when necessary, we get the following:<\/p>\n<div id=\"table-00023\" class=\"os-table\">\n<table class=\"unnumbered\" style=\"height: 48px;\" data-id=\"table-00023\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr style=\"height: 12px;\">\n<td style=\"height: 12px; width: 102.963px;\"><\/td>\n<td style=\"height: 12px; width: 100.887px;\">1<\/td>\n<td style=\"height: 12px; width: 109.025px;\">1<\/td>\n<td style=\"height: 12px; width: 109.05px;\"><\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"height: 12px; width: 102.963px;\"><\/td>\n<td style=\"height: 12px; width: 100.887px;\">3<\/td>\n<td style=\"height: 12px; width: 109.025px;\">A<\/td>\n<td style=\"height: 12px; width: 109.05px;\">7<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"height: 12px; width: 102.963px;\">+<\/td>\n<td style=\"height: 12px; width: 100.887px;\">9<\/td>\n<td style=\"height: 12px; width: 109.025px;\">B<\/td>\n<td style=\"height: 12px; width: 109.05px;\">A<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"height: 12px; width: 102.963px;\"><strong>1<\/strong><\/td>\n<td style=\"height: 12px; width: 100.887px;\"><strong>1<\/strong><\/td>\n<td style=\"height: 12px; width: 109.025px;\">A<\/td>\n<td style=\"height: 12px; width: 109.05px;\">5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00042\">The ones that were carried are located over the columns.<\/p>\n<p id=\"para-00043\">So, 3A7<sub>12<\/sub>\u00a0+ 9BA<sub>12<\/sub>= 11A5<sub>12<\/sub>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Calculate 4B3<sub>12<\/sub>\u00a0+ B06<sub>12<\/sub>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q290699\">Show Solution<\/span><\/p>\n<div id=\"q290699\" class=\"hidden-answer\" style=\"display: none\">\n<p>13B9<sub>12<\/sub><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"How to Add hexadecimal numbers the easy way.  Step-by-step.\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/rF8eKBQNXDc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Subtracting in Other Bases<\/h3>\n<p>Sometimes carrying is necessary when adding numbers. Likewise, sometimes borrowing is necessary when subtracting numbers.\u00a0 As you view these two videos, pay close attention to the steps and understanding what it means to borrow.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-6\" title=\"Subtracting: three digit numbers and basic regrouping | Arithmetic | Khan Academy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/9T3AAn-Cw3g?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-7\" title=\"Subtracting: Regrouping from zero | Addition and subtraction | Arithmetic | Khan Academy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/3lHBgFvr3yE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><span id=\"term-00001\" data-type=\"term\">Subtraction in bases<\/span>\u00a0other than base 10 follow the same processes as base 10 subtraction, but, as with addition, using the addition table for the base.<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p><strong>Subtracting in Base 6<\/strong><\/p>\n<p>Calculate\u00a052<sub>6<\/sub>\u00a0\u2212 34<sub>6<\/sub>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q290700\">Show Solution<\/span><\/p>\n<div id=\"q290700\" class=\"hidden-answer\" style=\"display: none\">\n<h4 data-type=\"solution-title\"><span class=\"os-title-label\">Solution<\/span><\/h4>\n<div class=\"os-solution-container\">\n<p id=\"para-00052\"><strong>Step 1:<\/strong>\u00a0Let\u2019s set up the subtraction using columns.<\/p>\n<div id=\"table-00026\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00026\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td>5<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>\u2212<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00053\"><strong>Step 2:<\/strong>\u00a0Just as we might do in base 10, we borrow a 1 from the 5 for the ones digit. The 1 borrowed represents a group of 6.<\/p>\n<div id=\"table-00027\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00027\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"MathJax-Element-161-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;inline&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/mrow&gt;&lt;annotation-xml encoding=&quot;MathML-Content&quot;&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/annotation-xml&gt;&lt;\/semantics&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-3240\" class=\"math\"><span id=\"MathJax-Span-3241\" class=\"mrow\"><span id=\"MathJax-Span-3242\" class=\"semantics\"><span id=\"MathJax-Span-3243\" class=\"mrow\"><span id=\"MathJax-Span-3244\" class=\"mrow\"><span id=\"MathJax-Span-3245\" class=\"menclose\"><del><span id=\"MathJax-Span-3246\" class=\"mrow\"><span id=\"MathJax-Span-3247\" class=\"mn\">5\u00a0<\/span><\/span><\/del><\/span><span id=\"MathJax-Span-3248\" class=\"mn\">\u00a04<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td><strong>12<\/strong><\/td>\n<\/tr>\n<tr>\n<td>\u2212<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00054\"><strong>Step 3:<\/strong>\u00a0Referring to the base 6 addition table, we see that 4 + 4 = 12, so 12<sub>6<\/sub>\u00a0\u2212 4<sub>6<\/sub>\u00a0is 4<sub>6<\/sub>.<\/p>\n<div id=\"table-00028\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00028\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"MathJax-Element-161-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;inline&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/mrow&gt;&lt;annotation-xml encoding=&quot;MathML-Content&quot;&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/annotation-xml&gt;&lt;\/semantics&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-3240\" class=\"math\"><span id=\"MathJax-Span-3241\" class=\"mrow\"><span id=\"MathJax-Span-3242\" class=\"semantics\"><span id=\"MathJax-Span-3243\" class=\"mrow\"><span id=\"MathJax-Span-3244\" class=\"mrow\"><span id=\"MathJax-Span-3245\" class=\"menclose\"><del><span id=\"MathJax-Span-3246\" class=\"mrow\"><span id=\"MathJax-Span-3247\" class=\"mn\">5\u00a0<\/span><\/span><\/del><\/span><span id=\"MathJax-Span-3248\" class=\"mn\">\u00a04<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td><strong>1<\/strong>2<\/td>\n<\/tr>\n<tr>\n<td>\u2212<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><strong>4<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00055\"><strong>Step 4:<\/strong>\u00a0Now we deal with the \u201ctens\u201d (really, sixes) digit, 4<sub>6<\/sub>\u00a0\u2212 3<sub>6<\/sub>, which equals 1<sub>6<\/sub>\u00a0according to the base 6 addition table.<\/p>\n<div id=\"table-00029\" class=\"os-table\">\n<table class=\"unnumbered\" data-id=\"table-00029\">\n<colgroup>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/>\n<col data-width=\"1pt\" \/><\/colgroup>\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"MathJax-Element-161-Frame\" class=\"MathJax\" style=\"box-sizing: border-box; overflow: initial; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;inline&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/mrow&gt;&lt;annotation-xml encoding=&quot;MathML-Content&quot;&gt;&lt;mrow&gt;&lt;menclose notation=&quot;horizontalstrike&quot;&gt;&lt;mn&gt;5&lt;\/mn&gt;&lt;\/menclose&gt;&lt;mn&gt;4&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/annotation-xml&gt;&lt;\/semantics&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-3240\" class=\"math\"><span id=\"MathJax-Span-3241\" class=\"mrow\"><span id=\"MathJax-Span-3242\" class=\"semantics\"><span id=\"MathJax-Span-3243\" class=\"mrow\"><span id=\"MathJax-Span-3244\" class=\"mrow\"><span id=\"MathJax-Span-3245\" class=\"menclose\"><del><span id=\"MathJax-Span-3246\" class=\"mrow\"><span id=\"MathJax-Span-3247\" class=\"mn\">5\u00a0<\/span><\/span><\/del><\/span><span id=\"MathJax-Span-3248\" class=\"mn\">\u00a04<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/td>\n<td><strong>1<\/strong>2<\/td>\n<\/tr>\n<tr>\n<td>\u2212<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><strong>1<\/strong><\/td>\n<td>4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"para-00056\">So, 52<sub>6<\/sub>\u00a0\u2212 34<sub>6<\/sub>\u00a0= 14<sub>6<\/sub>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Calculate 115<sub>6<\/sub>\u00a0\u2212 43<sub>6<\/sub>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q290701\">Show Solution<\/span><\/p>\n<div id=\"q290701\" class=\"hidden-answer\" style=\"display: none\">\n<p>32<sub>6<\/sub><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>You will see two different approaches to representing the value borrowed:<br \/>\n1. Writing the borrowed amount by adding the digit 1 (like above example) keeping all values in the problem in the given base.<br \/>\n2. Writing the borrowed amount in base 10 since it&#8217;s &#8220;scratch paper&#8221; as in the videos below.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-8\" title=\"Subtracting in other bases\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/1O3DG2UShGI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-57\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Math in Society. <strong>Authored by<\/strong>: Lippman, David. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID 8681. <strong>Authored by<\/strong>: Lippman, David. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li> Convert Numbers in Base Ten to Different Bases:  Calculator Method. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/YNPTYelCeIs\">https:\/\/youtu.be\/YNPTYelCeIs<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":503070,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Math in Society\",\"author\":\"Lippman, David\",\"organization\":\"\",\"url\":\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID 8681\",\"author\":\"Lippman, David\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"cc\",\"description\":\" Convert Numbers in Base Ten to Different Bases:  Calculator Method\",\"author\":\"James Sousa (Mathispower4u.com) \",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/YNPTYelCeIs\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"32a7386d-3a04-43e5-951a-684c16d617ab","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-57","chapter","type-chapter","status-publish","hentry"],"part":33,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/pressbooks\/v2\/chapters\/57","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/wp\/v2\/users\/503070"}],"version-history":[{"count":26,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/pressbooks\/v2\/chapters\/57\/revisions"}],"predecessor-version":[{"id":1178,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/pressbooks\/v2\/chapters\/57\/revisions\/1178"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/pressbooks\/v2\/parts\/33"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/pressbooks\/v2\/chapters\/57\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/wp\/v2\/media?parent=57"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/pressbooks\/v2\/chapter-type?post=57"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/wp\/v2\/contributor?post=57"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/wp-json\/wp\/v2\/license?post=57"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}