{"id":4342,"date":"2023-06-08T03:36:44","date_gmt":"2023-06-08T03:36:44","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=4342"},"modified":"2024-10-18T20:52:28","modified_gmt":"2024-10-18T20:52:28","slug":"early-counting-systems-apply-it-2","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/early-counting-systems-apply-it-2\/","title":{"raw":"Early Counting Systems: Apply It 2","rendered":"Early Counting Systems: Apply It 2"},"content":{"raw":"

Unlocking the Mayan Code: Understanding the Vigesimal System Cont.<\/h2>\r\n

Reading Mayan numbers can be an interesting and engaging way to explore ancient numerical systems. Here's a step-by-step guide on how to read Mayan numbers:<\/p>\r\n

How to: Read Mayan numbers<\/strong>
\r\n
    \r\n\t
  1. Understand the Basics<\/strong>: Mayan numbers are based on a vigesimal (base-20) system, meaning they count in intervals of [latex]20[\/latex].<\/li>\r\n\t
  2. Familiarize Yourself with the Symbols<\/strong>: The Mayan number system uses three main symbols: a shell-like symbol representing zero, a dot for one, and a horizontal bar for five. These symbols are combined to represent higher numbers.<\/li>\r\n\t
  3. Start from the Bottom<\/strong>: Mayan numbers are read from the bottom up, opposite to the way we typically read numbers. The lowest value is represented by the bottom row, and the highest value is at the top.<\/li>\r\n\t
  4. Recognize Place Value<\/strong>: Each position in a Mayan number represents a different place value, similar to our decimal system. The rightmost position represents ones, the next position to the left represents twenties, the next represents four hundred, and so on.<\/li>\r\n\t
  5. Count the Dots and Bars<\/strong>: To read a Mayan number, count the number of dots and bars in each position and multiply it by the corresponding place value. Add up the values of all the positions to determine the total number.<\/li>\r\n<\/ol>\r\n<\/section>\r\n
    What is the value of the following Mayan number?
    \"A<\/center>
    \r\n[reveal-answer q=\"760307\"]Show Solution[\/reveal-answer]
    \r\n[hidden-answer a=\"760307\"]This number has [latex]11[\/latex] in the ones place, zero in the [latex]20[\/latex]s place, and [latex]18[\/latex] in the [latex]20^2 = 400s[\/latex] place. Hence, the value of this number in base-ten is:[latex]18 \u00d7 400 + 0 \u00d7 20 + 11 \u00d7 1 = 7211[\/latex].
    \r\n[\/hidden-answer]<\/section>\r\n
    [ohm2_question hide_question_numbers=1]9038[\/ohm2_question]<\/section>\r\n

    Just like in the decimal system, you can perform addition in the Mayan numerical system. When adding Mayan numbers together, we\u2019ll adopt a scheme that the Mayans probably did not use but which will make life a little easier for us.<\/p>\r\n

    Add, in Mayan, the numbers [latex]37[\/latex] and [latex]29[\/latex]:[footnote]\"https:\/\/web.archive.org\/web\/20060116045138\/http:\/\/mathforum.org\/k12\/mayan.math\/mayan2.html\"[\/footnote]
    \"Fig5_1_30\"<\/center>[reveal-answer q=\"193127\"]Show Solution[\/reveal-answer]
    \r\n[hidden-answer a=\"193127\"]First draw a box around each of the vertical places. This will help keep the place values from being mixed up.
    \"Fig5_1_31\"<\/center>\r\n

     <\/p>\r\n\r\nNext, put all of the symbols from both numbers into a single set of places (boxes), and to the right of this new number draw a set of empty boxes where you will place the final sum:

    \"Fig5_1_32\"<\/center>\r\n

     <\/p>\r\n

    You are now ready to start carrying. Begin with the place that has the lowest value, just as you do with Arabic numbers. Start at the bottom place, where each dot is worth [latex]1[\/latex]. There are six dots, but a maximum of four are allowed in any one place; once you get to five dots, you must convert to a bar. Since five dots make one bar, we draw a bar through five of the dots, leaving us with one dot which is under the four-dot limit. Put this dot into the bottom place of the empty set of boxes you just drew:<\/p>\r\n

    \"Fig5_1_33\"<\/center>\r\n

     <\/p>\r\n

    Now look at the bars in the bottom place. There are five, and the maximum number the place can hold is three. Four bars are equal to one dot in the next highest place<\/em>.<\/p>\r\n

    Whenever we have four bars in a single place we will automatically convert that to a dot <\/em>in the next place up. We draw a circle around four of the bars and an arrow up to the dots' section of the higher place. At the end of that arrow, draw a new dot. That dot represents [latex]20[\/latex] just the same as the other dots in that place. Not counting the circled bars in the bottom place, there is one bar left. One bar is under the three-bar limit; put it under the dot in the set of empty places to the right.<\/p>\r\n

    \"Fig5_1_34\"<\/center>\r\n

     <\/p>\r\n

    Now there are only three dots in the next highest place, so draw them in the corresponding empty box.<\/p>\r\n

    \"Fig5_1_35\"<\/center>\r\n

     <\/p>\r\n

    We can see here that we have [latex]3[\/latex] twenties ([latex]60[\/latex]), and [latex]6[\/latex] ones, for a total of [latex]66[\/latex]. We check and note that [latex]37 + 29 = 66[\/latex], so we have done this addition correctly. Is it easier to just do it in base-ten? Probably, but that\u2019s only because it\u2019s more familiar to you. Your task here is to try to learn a new base system and how addition can be done in slightly different ways than what you have seen in the past. Note, however, that the concept of carrying is still used, just as it is in our own addition algorithm.<\/p>\r\n

    [\/hidden-answer]<\/p>\r\n<\/section>\r\n

    [ohm2_question hide_question_numbers=1]9039[\/ohm2_question]<\/section>\r\n

    Congratulations on completing the Mayan Code activity! You've delved into the world of ancient Mayans, grasped their unique base-20 system, and practiced calculations in their manner. This experience underscores the universality of mathematics across cultures and time, highlighting the sophistication of Mayan mathematical knowledge. Remember the key elements of their numerical system: its vertical layout, use of three symbols, and the concept of place value.<\/p>","rendered":"

    Unlocking the Mayan Code: Understanding the Vigesimal System Cont.<\/h2>\n

    Reading Mayan numbers can be an interesting and engaging way to explore ancient numerical systems. Here’s a step-by-step guide on how to read Mayan numbers:<\/p>\n

    How to: Read Mayan numbers<\/strong><\/p>\n
      \n
    1. Understand the Basics<\/strong>: Mayan numbers are based on a vigesimal (base-20) system, meaning they count in intervals of [latex]20[\/latex].<\/li>\n
    2. Familiarize Yourself with the Symbols<\/strong>: The Mayan number system uses three main symbols: a shell-like symbol representing zero, a dot for one, and a horizontal bar for five. These symbols are combined to represent higher numbers.<\/li>\n
    3. Start from the Bottom<\/strong>: Mayan numbers are read from the bottom up, opposite to the way we typically read numbers. The lowest value is represented by the bottom row, and the highest value is at the top.<\/li>\n
    4. Recognize Place Value<\/strong>: Each position in a Mayan number represents a different place value, similar to our decimal system. The rightmost position represents ones, the next position to the left represents twenties, the next represents four hundred, and so on.<\/li>\n
    5. Count the Dots and Bars<\/strong>: To read a Mayan number, count the number of dots and bars in each position and multiply it by the corresponding place value. Add up the values of all the positions to determine the total number.<\/li>\n<\/ol>\n<\/section>\n
      What is the value of the following Mayan number?<\/p>\n
      \"A<\/div>\n
      <\/div>\n