Solve Vertical Subtraction: 12001 minus 1542

$\begin{aligned} &12001 \\ -& \\ &~~1542 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

To solve the problem of subtracting 1542 from 12001, we will perform vertical subtraction, borrowing where necessary:

• Step 1: Align the numbers by place value:

• $\begin{array}{c} ~~~12001 \\ - \phantom{0} 1542 \\ \hline \end{array}$

• Step 2: Start subtracting from the rightmost digit (ones place):

• The ones column requires borrowing since $1 < 2$. Borrow from the tens.

• The tens column is 0, so we need to borrow from the hundreds. The hundreds column is also 0, so we move to the thousands. The thousands column has 2, which becomes 1, and the hundreds column becomes 10, and then the tens column becomes 9. The ones column becomes 11.

• Now subtract: Ones column: $11 - 2 = 9$

• Step 3: Move to the tens place: Subtract $9 - 4 = 5$

• Step 4: Move to the hundreds place: Subtract $9 - 5 = 4$ after borrowing.

• Step 5: Move to the thousands place: Subtract $1 - 1 = 0$

• Step 6: Finally, in the ten-thousands: Note that $1$ merely moves down as there’s no digit to deduct.

Putting it all together:

$\begin{array}{c} ~~~ 12001 \\ - \phantom{0}1542 \\ \hline ~~~10459 \\ \end{array}$

Therefore, the final solution to the problem is $10459$.