## Thinking Mathematically (6th Edition)

The difference in the indicated base is ${{5}_{\text{six}}}$.
Start by subtracting the numbers in the right-hand column:${{4}_{\text{six}}}-{{5}_{\text{six}}}$. ${{5}_{\text{six}}}$is greater than ${{4}_{\text{six}}}$. So, we need to borrow from the preceding column. Now, borrow one group of 6 because in the provided question we are working in base six. This gives a sum of $4+6$ or 10 in base ten. Now, subtract 5 from 10: \begin{align} & \text{ 2} \\ & \begin{matrix} \text{ 3}{{\text{4}}_{\text{six}}} \\ -{{25}_{\text{six}}} \\ 5 \\ \end{matrix} \\ \end{align} Now, perform the subtraction in the second column from the right. That is, subtract 2 from 2: \begin{align} & \text{ 2} \\ & \begin{matrix} \text{ 3}{{\text{4}}_{\text{six}}} \\ -{{25}_{\text{six}}} \\ {{05}_{\text{six}}} \\ \end{matrix} \\ \end{align} The difference in the indicated base is ${{5}_{\text{six}}}$.