Vertical Subtraction: Finding the Difference Between 1000 and 872

$$$\begin{aligned} &1000 \\ -& \\ &~~872 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

To solve this problem, we will use vertical subtraction with borrowing:

• Step 1: Understand the given numbers
  We need to perform the subtraction $1000 - 872$. Let's write them vertically:

1000
-872
_____

• Step 2: Begin with the units digit
  The units digit for the minuend $1000$ is 0, and the subtrahend $872$ is 2. Because you cannot subtract $2$ from $0$, we need to borrow from the next digit over.

  • The tens digit is also $0$, so we need to borrow from the hundreds digit, $0$.

  • Continue borrowing to the thousands place:

  • The thousands digit $1$ will become $0$, the hundreds digit becomes $10$, then $9$ (after lending $1$ to adjust tens place), tens digit becomes $10$, then $9$ (after lending $1$ to adjust units place), and finally, units digit becomes $10$.

  • Result during subtraction step:

  • The number adjusted pre-subtraction is $09910$.

• Step 3: Perform the subtraction
  

  • Now perform each column subtraction:

  • Units: $10 - 2 = 8$

  • Tens: $9 - 7 = 2$

  • Hundreds: $9 - 8 = 1$

  • There is no digit left to subtract in the thousands place, following the adjustment.

• Conclusion
  Bringing the results together from the adjustments and borrowing:

  • The result of the subtraction is $128$.

Therefore, the solution to the problem is $128$.