Subtract 257 from 1000: Vertical Format Solution

To solve this subtraction problem of 1000 minus 257, we will use a systematic vertical subtraction method that involves borrowing:

• Step 1: Start with the numbers aligned vertically:

$\begin{aligned} &1000 \\ -& \\ &~~257 \\ \end{aligned}$

• Step 2: Subtract the rightmost digits (in the units place):

• Since 0 is less than 7, we need to borrow. The next column (tens place) also is 0, so we move to the hundreds place to borrow. Reducing the 1 to 0, we turn the 0 into a 10 in the tens column and then subtract 1 to borrow into the units column, turning it into 9. The soon-to-be 10 in the units column becomes 10.

• Step 3: The positions now look like:

$\begin{aligned} &\phantom{10\ \ }~9~10 \\ &~1~0~0~0 \\ - &~~~~2~5~7 \\ \underline{\phantom{70}} \\ \end{aligned}$

• Step 4: Now, 10 minus 7 is 3. Write 3 down.

• Step 5: Move to the tens column: 9 minus 5 equals 4. Write 4 under the line.

• Step 6: Lastly, subtract the hundreds column: 0 minus 2 requires borrowing again, leaving that position as 7.

• The final calculated result is:

  $\begin{aligned} &1000 \\ -&~~257 \\ &~\overline{~743} \\ \end{aligned}$

  Therefore, the solution to the subtraction problem is $743$.