### Instruction: Find $4321_{5}-1234_{5}$. Express your answer in base $5$.### Response: To subtract two numbers in base $5$, I need to align the digits and subtract them from right to left, borrowing from the next column if needed.
I start with the ones column: $1_{5}-4_{5}$.
Since $1_{5}$ is smaller than $4_{5}$, I need to borrow $1$ from the fives column.
This means I add $5$ to $1_{5}$, which gives $6_{5}$, and subtract $1$ from the fives column, which gives $1_{5}$.
Now I can subtract $6_{5}-4_{5}$, which gives $2_{5}$.
I write $2_{5}$ in the ones column of the answer.
I move to the fives column: $1_{5}-3_{5}$.
Again, $1_{5}$ is smaller than $3_{5}$, so I need to borrow $1$ from the twenty-fives column.
This means I add $5$ to $1_{5}$, which gives $6_{5}$, and subtract $1$ from the twenty-fives column, which gives $2_{5}$.
Now I can subtract $6_{5}-3_{5}$, which gives $3_{5}$.
I write $3_{5}$ in the fives column of the answer.
I move to the twenty-fives column: $2_{5}-2_{5}$.
This is easy: $2_{5}-2_{5}$ is $0_{5}$.
I write $0_{5}$ in the twenty-fives column of the answer.
I move to the last column: $4_{5}-1_{5}$.
This is also easy: $4_{5}-1_{5}$ is $3_{5}$.
I write $3_{5}$ in the last column of the answer.
I have subtracted all the digits, and I have no more columns to borrow from, so I am done.
The final answer is $3032_{5}$.