Subtraction is a fundamental arithmetic operation where we find the difference between two numbers. When subtracting larger digits from smaller ones within a number, we use a technique called borrowing (also known as regrouping). This method ensures accurate calculations when the top digit is smaller than the bottom digit in any column.

What is Borrowing?

Borrowing occurs when the digit being subtracted is larger than the digit it is being subtracted from. In such cases, we “borrow” 10 from the next higher place value (left column) to make the subtraction possible.

Examples 

To further understand subtraction with borrowing, let’s go through additional examples, including both two-digit and three-digit numbers.

Two-Digit Subtraction with Borrowing

Problem: 72 – 47

Step-by-Step Solution:

1. Set up the problem vertically: 72 –47
2. Subtract the ones place (2 – 7):
   • Since 2 is smaller than 7, we need to borrow from the tens place.
   • Borrow 1 from the tens place (7 becomes 6), and add 10 to the ones place (2 becomes 12).
   • Now, subtract: 12 – 7 = 5
3. Subtract the tens place (6 – 4):
   • After borrowing, the tens digit is 6.
   • Subtract: 6 – 4 = 2
4. Final Answer: 25

Three-Digit Subtraction with Borrowing

Problem: 503 – 278

1. Set up the problem vertically: 503 –278
2. Subtract the ones place (3 – 8):
   • 3 is smaller than 8, so we must borrow from the tens place.
   • However, the tens digit is 0, meaning we cannot borrow directly from it.
   • First, borrow from the hundreds place:
     • 5 (hundreds) becomes 4.
     • 0 (tens) becomes 10 (since we add 10).
   • Now, borrow from the tens place to the ones place:
     • 10 (tens) becomes 9.
     • 3 (ones) becomes 13.
   • Subtract the ones place: 13 – 8 = 5
3. Subtract the tens place (9 – 7):
   • After borrowing, the tens digit is 9.
   • Subtract: 9 – 7 = 2
4. Subtract the hundreds place (4 – 2):
   • Subtract: 4 – 2 = 2
5. Final Answer: 225

More Practice

1. a) 36-19

6-9 cannot be calculated, so we borrow from 3 of the first number; borrowing 1, 3 becomes 2

We calculate 16-9=7

As 3 became 2, we calculate 2-1=1

So, the result of the calculation 36-19=17

b) 57-38

7-8 cannot be calculated, so we borrow from 5 of the first number, borrowing 1, 5 becomes 4

We calculate 17-8=9

As 5 became 4, we calculate 4-3=1

So, the result of the calculation 57-38=19

c) 73-65

3-5 cannot be calculated, so we borrow from 7 of the first number, borrowing 1, 7 becomes 6

We calculate 13-5=8

As 7 became 6, we calculate 6-6=0

So, the result of the calculation 36-19=8

2. a) 357-129

7-9 cannot be calculated, so we borrow from the next digit of the first number, i.e. from 5; so 5 becomes 4

We calculate 17-9=8

Next we calculate 4-2=2 (as we borrowed from 5 it became 4)

And in the end 3-1=2

The result is 228.

b) 455-287

5-7 cannot be calculated, so we borrow from the next digit of the first number, i.e. from 5; so 5 becomes 4

We calculate 15-7=8

Next we calculate 4-8 cannot be calculated, so we borrow from the next digit, i.e. from 4 (the first digit of the first number), and 4 becomes 3

We calculate 14-8=6

And in the end 3-2=1

The result is 168.

c) 672-498

2-8 cannot be calculated, so we borrow from the next digit of the first number, i.e. from 7; so 7 becomes 6

We calculate 12-8=4

Next we calculate 6-9 cannot be calculated, so we borrow from the next digit, i.e. from 6 (the first digit of the first number), and 6 becomes 5

We calculate 16-9=7

And in the end 5-4=1

The result is 174.

Subtraction of Two and Three-Digit Numbers with Borrowing is important because it builds a strong foundation for advanced math, develops critical problem-solving skills and avoids misconceptions in higher math.