Subtracting three-digit numbers with borrowing (also known as regrouping) occurs when a digit in the minuend (the number from which you are subtracting) is smaller than the corresponding digit in the subtrahend (the number you are subtracting). Here’s how to handle this:

Steps to Subtract Three-Digit Numbers with Borrowing:

1. Write the Numbers in Columns:
– Write the minuend above the subtrahend, aligning the digits by place value (hundreds, tens, and units).

2. Subtract the Units (Ones) Column:
– Compare the digit in the units column of the minuend with the corresponding digit in the subtrahend.
– If the digit in the minuend is smaller, you need to borrow from the tens column.
– Decrease the digit in the tens column by 1, and add 10 to the digit in the units column of the minuend.
– Subtract the digit in the subtrahend from the new digit in the minuend.

3. Subtract the Tens Column:
– If you borrowed from the tens column in the previous step, remember that the digit in the minuend’s tens column is now one less.
– If this digit is smaller than the corresponding digit in the subtrahend, borrow from the hundreds column.
– Decrease the digit in the hundreds column by 1, and add 10 to the digit in the tens column of the minuend.
– Subtract the digit in the subtrahend from the new digit in the minuend.

4. Subtract the Hundreds Column:
– If you borrowed from the hundreds column, subtract the subtrahend’s digit from the new (decreased) digit in the minuend.

5. Write Down the Result:
– Combine the results from each column to get the final answer.

Example:

Let’s subtract  654 – 278 :

          654
       – 278
        ——-
   

1. Units (Ones) column:
– 4 – 8 requires borrowing because 4 is smaller than 8.
– Borrow 1 from the tens column (which has a 5). The tens column becomes 4, and the units column becomes \14.
– Now, 14 – 8 = 6.

2. Tens column:
– After borrowing, the tens column is 4.
– Subtract 7 from 4, but 4 – 7 requires borrowing from the hundreds column.
– Borrow 1 from the hundreds column (which has a 6). The hundreds column becomes 5, and the tens column becomes 14.
– Now, 14 – 7 = 7.

3. Hundreds column:
– After borrowing, the hundreds column is 5.
– Subtract 2 from 5: 5 – 2 = 3.

So, 654 – 278 = 376.

Final Answer:

            654
         – 278
          ——-
           376

Borrowing is essential when the digit in the minuend is smaller than the corresponding digit in the subtrahend. It allows you to regroup the numbers, making the subtraction possible without negative results.