show how to do 14+231 in a base 12 system

Solution:
1. Express the numbers in their base 10 equivalent:
- 14_{12} = 1 \cdot 12^1 + 4 \cdot 12^0 = 12 + 4 = 16
- 231_{12} = 2 \cdot 12^2 + 3 \cdot 12^1 + 1 \cdot 12^0 = 288 + 36 + 1 = 325

2. Add the numbers in base 10:
- 16 + 325 = 341

3. Convert the sum back to base 12:
- To convert 341 to base 12, divide by 12 and keep track of the remainders.
- 341 \div 12 = 28 with remainder 5 (the rightmost digit)
- 28 \div 12 = 2 with remainder 4
- 2 \div 12 = 0 with remainder 2

4. Read the remainders from last to first to get 245_{12}.

Thus, 14_{12} + 231_{12} = 245_{12}.