To subtract two numbers in base 5, you perform the subtraction column by column, just like in base 10, but carrying and borrowing are done in base 5. Let's subtract 431 (base 5) - 144 (base 5):
431
- 144
- 1. Subtract the rightmost column (1 - 4). Since 1 is smaller than 4, we need to borrow from the next column. In base 5, borrowing means subtracting 1 from the next column and adding 5 to the current column. So we borrow from the 3 and it becomes 2, and add 5 to the 1, making it 6. Now, subtract 4 from 6, which is 2.
42(1+5)
- 1 4
-------
2
- 2. Subtract the middle column (2 - 1). This is straightforward: 2 - 1 = 1.
42
- 1
-------
1
- 3. Subtract the leftmost column (4 - 0). Since there's nothing to subtract, this remains 4.
4
-
-------
4
So, 431 (base 5) - 144 (base 5) = **412 (base 5)**.
431
- 144
-----
412