Subtract 257 from 1000: Vertical Format Solution

Video Solution

Solution Steps

00:00 Solve

00:03 Each time it's considered a borrowing of 2 digits, and then we'll place

00:06 0 is less than 7

00:09 The tens digit is also equal to 0 so we can't borrow from it

00:12 The hundreds digit is also equal to 0 so we can't borrow from it

00:16 We'll borrow a thousand from the thousands place for the hundreds

00:20 So now instead of 0 we'll have 10, in hundreds!

00:24 And now we'll borrow ten from the hundreds for the tens

00:27 Which will turn the hundreds from 10 to 9

00:31 So now instead of 0 we'll have 10, in tens!

00:35 And now we'll borrow ten from the tens for the ones

00:38 Which will turn the tens from 10 to 9

00:42 So now instead of 0 we'll have 10, in ones!

00:48 Now we'll subtract ones from ones, and place in ones

00:54 Subtract tens from tens, and place in tens

00:58 Subtract hundreds from hundreds, and place in hundreds

01:02 Place 0 in the missing digits

01:06 Subtract thousands from thousands, and place in thousands

01:10 And that's the solution to the problem

Step-by-Step Solution

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

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

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 $743$ .