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.
Example 1 – One Borrow
54 − 28
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
432 − 187
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
403 − 168
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 Questions
- Calculate 62 − 38.
- Calculate 354 − 178.
- Calculate 600 − 247.
- Calculate 5,003 − 2,468.
- A train has 302 passengers; 145 get off. How many remain?