show how to do 349-231 in a base 12 system

Solution:
1. Convert the numbers 349 and 231 from base 12 to decimal:
- 349 base 12: (3 \times 12^2) + (4 \times 12^1) + (9 \times 12^0) = (3 \times 144) + (4 \times 12) + (9 \times 1) = 432 + 48 + 9 = 489
- 231 base 12: (2 \times 12^2) + (3 \times 12^1) + (1 \times 12^0) = (2 \times 144) + (3 \times 12) + (1 \times 1) = 288 + 36 + 1 = 325

2. Subtract the converted numbers in decimal:
- Subtraction: 489 - 325 = 164

3. Convert the result back to base 12:
- The highest power of 12 in 164 is 12^1 (since 12^2 = 144 is too large).
- Divide 164 by 12: 164 \div 12 = 13 \text{ remainder } 8
- 13 in base 12 is represented as 1 \times 12 + 1 remainder is 1.
- Therefore, 164 in base 12 is 118.

4. Therefore, 349 base 12 minus 231 base 12 equals:
118 base 12.