Additon for Base 12 ...?

Question

Perform the following addition for base 12 (show the process- The answer should be in BASE 12 form - NO decimal):

..AB198
+99A51

Answer 1

Hi,

AB198 is 10(*12^4) + 11(12^3) + 1(12^2) + 9(12^1) + 8 = 226628

99A51 is 9(*12^4) + 9(12^3) + 10(12^2) + 5(12^1) + 1 = 203677

226628 + 203677 = 430305 in base 10

If you divide 430305 by 12^5, it goes in once with a remainder of 181473.
Then if you divide 181473 by 12^4, it goes in 8 times with a remainder of 15585.
Then if you divide 15585 by 12^3, it goes in 9 times with a remainder of 33. 12^2 can not divide into this number.
Then if you divide 33 by 12^1, it goes in 2 times with a remainder of 9.
The base 12 solution is 189029.


Adding in base 12 gives the same answer:
....AB198
..+99A51 Adding from the right side, 8 + 1 = 9
....----------
..............9 Then 9 + 5 = 14, but that makes 1 group of 12 to carry into the next column, leaving 14 - 12 or 2 behind in the second column.
.........1
....AB198
..+99A51
....----------
.............29

Now 1 + 1 + 10 for A add to 12. That makes 1 group of 12 to carry into the next column, leaving 12 - 12 or 0 behind in the third column.

......1.1
....AB198
..+99A51
....----------
..........029

Now 1 + B + 9 = 1 + 11 + 9 = 21. That makes 1 group of 12 to carry into the next column, leaving 21 - 12 or 9 behind in the fourth column.

....11.1
....AB198
..+99A51
....----------
.......9029

1 + A + 9 = 1 + 10 + 9 = 20. That makes 1 group of 12 to carry into the next sixth column, leaving 20 - 12 or 8 behind in the fifth column.

..111.1
....AB198
..+99A51
....----------
..189029

I hope that helps!! :-)

Answer 2

8+1=9
9+5=fourteen, since we are base 12 then write a 2 and carry 12 as a 1 to the next column.
1+A+1=0 like above carry a 1.
B+9+1=9and carry a 1.
A+9+1=8 and carry a 1
add a 1 at the end.
final answer:
189029

Answer 3

Remember that using different bases is just like using 10 base system, you just have to remember the extra (or missing) digits. Notice, that on columns 2, 3, & 4 there we carries of 1 on each column.

AB198
+99A51
-------------
199029