Introduction
Subtraction with borrowing is used when a digit in the minuend is smaller than the digit in the subtrahend at the same place value.
Visualizing the Borrow (Carry)
When you borrow 1 from a neighbor, you are actually taking 10 units of the current place value. Notice how the values change in the table below.
| Place | TTh | Th | H | T | U |
|---|---|---|---|---|---|
| Changes | 3 (4-1) | 15 (5+10) | 1 (2-1) | 13 (3+10) | |
| Top Num | 7 | 4 | 5 | 2 | 3 |
| Bottom Num | - 1 | 2 | 8 | 0 | 9 |
| Difference | 6 | 1 | 7 | 1 | 4 |
Borrowing Process
1. Start from Units.
2. If borrowing from a zero, move further left until you find a non-zero digit.
Examples
Example 1: 30005 - 12345
Tricks and Shortcuts
For numbers ending in many zeros (like 50000), subtract 1 from both numbers to eliminate borrowing (e.g., 49999 - 12344 instead of 50000 - 12345).
Common Mistakes
Forgetting to update the neighbor's value after borrowing. Incorrectly borrowing from a zero without moving to the next place value.
Practice Questions
Easy Questions
- 87654 - 32143 = ?
- 55555 - 11111 = ?
- 90000 - 40000 = ?
Medium Questions
- 72341 - 45672 (Use borrowing).
- A library has 45000 books. 12850 were lent out. How many are left?
- Difference between 63200 and 15400.
Hard Questions
- Subtract the smallest 5-digit number from the largest 5-digit number.
- A project costs 65000. You have 48750. How much more is needed?
- Calculate: (45600 + 12000) - 34500.
Revision Summary
Borrowing is simply redistributing values between place holders to make subtraction possible. Always double-check by addition.