Borrowing and Regrouping in Subtraction
Borrowing is needed when a digit in the minuend is smaller than the corresponding digit in the subtrahend. You borrow 10 from the column on the left.
Why Borrow?
In base 10, each place is worth 10 times the one to its right. Borrowing 1 from the tens column gives you 10 extra ones.
Step-by-Step
- If top digit < bottom digit in a column, borrow from the next column left.
- Reduce that column's top digit by 1.
- Add 10 to the current column's top digit.
- Now subtract normally.
Try It Yourself: 54 − 28
Press each step below (or use Auto Play) to watch the four-step borrowing method — check, borrow, add 10, subtract — play out on 54 − 28.
Check: 26 + 28 = 54 ✓ Borrowing just moves a ten from one column to its neighbour — nothing is gained or lost.
Example 1 – One Borrow
Ones: 4−8 impossible. Borrow: tens 5→4, ones 4→14. 14−8=6. Tens: 4−2=2. Answer: 26. Check: 26+28=54 ✓
Example 2 – Two Borrows
Ones: 2−7 → borrow; tens 3→2, ones →12. 12−7=5. Tens: 2−8 → borrow; hundreds 4→3, tens →12. 12−8=4. Hundreds: 3−1=2. Answer: 245
Example 3 – Borrowing Across Zero
Ones: 3−8 → borrow, but tens is 0. Go to hundreds: 4→3, tens 0→10, then borrow tens: 10→9, ones 3→13. 13−8=5. Tens: 9−6=3. Hundreds: 3−1=2. Answer: 235
Key Takeaways
- Borrow when the minuend digit is smaller than the subtrahend digit.
- Reduce the next column by 1; add 10 to the current column.
- When borrowing across a zero, trace back through each zero in turn.
- Always check: difference + subtrahend = minuend.
Practice: Borrow and Subtract
Every question below needs at least one borrow — that's guaranteed. If you get it wrong (or leave it blank), we'll regroup column by column together.