### Instruction: Add $175_{9} + 714_{9} + 61_9$.  Express your answer in base $9$.### Response: To add numbers in base $9$, I need to align the digits by place value and add them column by column, starting from the rightmost one.
If the sum of a column exceeds $8$, I need to carry over the remainder to the next column and write down the quotient.
For example, $8 + 3 = 11$, which is $12_9$ in base $9$, so I write $2$ and carry $1$.
Let me apply this method to the given problem.
I write the numbers in a vertical column, aligning the digits by place value.
I notice that the first number has only three digits, so I add a leading zero to make the alignment easier.
I get:
0175
0714
0061
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I start by adding the rightmost column: $5 + 4 + 1 = 10$.
This is $11_9$ in base $9$, so I write $1$ and carry $1$.
I move to the next column: $7 + 1 + 6 + 1 = 15$.
This is $16_9$ in base $9$, so I write $6$ and carry $1$.
I move to the next column: $1 + 7 + 0 + 1 = 9$.
This is $10_9$ in base $9$, so I write $0$ and carry $1$.
I move to the leftmost column: $0 + 0 + 0 + 1 = 1$.
This is just $1_9$ in base $9$, so I write $1$ and I'm done.
The final answer is $1061_9$.