### Instruction: Evaluate $2911_{11}-1392_{11}$. Express your answer in base 11, using A as the digit representing 10 in base 11.### Response: To subtract two numbers in base 11, I need to align them according to their place values and subtract each pair of digits from right to left, just like in base 10.
However, I also need to remember that each digit in base 11 can represent a value from 0 to 10, and that when I subtract a larger digit from a smaller one, I need to borrow from the next place value, which is worth 11 times as much as the current one.
So, starting from the rightmost digit, I have 1 - 2.
This is negative, so I need to borrow from the next place value.
I can think of this as adding 11 to the 1 and subtracting 1 from the next digit.
So I get 12 - 2 = A, and the next digit becomes 0 instead of 1.
Moving to the next pair of digits, I have 0 - 9.
This is also negative, so I need to borrow again.
I add 11 to the 0 and subtract 1 from the next digit.
I get 11 - 9 = 2, and the next digit becomes 8 instead of 9.
Next, I have 8 - 3.
This is positive, so I don't need to borrow.
I just subtract normally and get 8 - 3 = 5.
Finally, I have 2 - 1.
This is also positive, so I don't need to borrow.
I just subtract normally and get 2 - 1 = 1.
So, the final answer is 152A in base 11.