Addition: How does addition table work?

The addition table is a mathematical tool used to show the result of adding two numbers together for all possible combinations of those numbers within a given range. The table typically consists of rows and columns representing the two addends, with the sum of the two numbers appearing in each cell.
For example, if we have an addition table that shows the results of adding two single-digit numbers together (0-9), the table would look like this:
| | 0| 1| 2| 3| 4| 5| 6| 7| 8| 9|
|—|—|—|—|—|—|—|—|—|—|—|
|0| 0| 1| 2| 3| 4| 5| 6| 7| 8| 9|
|1| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|
|2| 2| 3| 4| 5| 6| 7| 8| 9|10|11|
|3| 3| 4| 5| 6| 7| 8| 9|10|11|12|
|4| 4| 5| 6| 7| 8| 9|10|11|12|13|
|5| 5| 6| 7| 8| 9|10|11|12|13|14|
|6| 6| 7| 8| 9|10|11|12|13|14|15|
|7| 7| 8| 9|10|11|12|13|14|15|16|
|8| 8| 9|10|11|12|13|14|15|16|17|
|9| 9|10|11|12|13|14|15|16|17|18|
This table can be used to quickly find the sum of any two single-digit numbers by looking up their corresponding cells in the table.
In general, addition tables can be created for any combination of numbers, such as two-, three-, or four-digit numbers, decimal numbers, or even complex numbers. The basic principle remains the same: to add two numbers together, simply look up their values in the appropriate cells of the table and read off the resulting sum.

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