Subtraction of 4-Digit Numbers
Subtraction of 4-digit numbers uses the column method with borrowing (regrouping) when a digit in the top number is smaller than the digit below it. You subtract from the ones place moving leftward.
This skill is used for finding differences in distances, calculating change in money, comparing populations, and solving word problems.
What is Subtraction of 4-Digit Numbers - Class 4 Maths (Operations)?
Column subtraction is the standard method:
- Write the larger number on top and the smaller number below, aligning place values.
- Subtract from right to left (ones first).
- If the top digit is smaller than the bottom digit, borrow 1 from the next place to the left (this adds 10 to the current place).
Always subtract from right to left: Ones → Tens → Hundreds → Thousands
Types and Properties
Subtraction without borrowing:
| Th | H | T | O | |
|---|---|---|---|---|
| 8 | 7 | 6 | 5 | |
| - | 3 | 4 | 2 | 1 |
| 5 | 3 | 4 | 4 |
8,765 - 3,421 = 5,344
| Th | H | T | O | |
|---|---|---|---|---|
| 5 | 2 | 3 | 4 | |
| - | 1 | 8 | 5 | 7 |
| 3 | 3 | 7 | 7 |
5,234 - 1,857 = 3,377
Solved Examples
Example 1: Example 1: Subtraction without borrowing
Problem: Subtract 6,897 - 2,354.
Solution:
Step 1: Ones: 7 - 4 = 3
Step 2: Tens: 9 - 5 = 4
Step 3: Hundreds: 8 - 3 = 5
Step 4: Thousands: 6 - 2 = 4
Answer: 6,897 - 2,354 = 4,543
Example 2: Example 2: Subtraction with one borrow
Problem: Subtract 7,423 - 3,568.
Solution:
Step 1: Ones: 3 - 8. Cannot do. Borrow 1 from tens: 13 - 8 = 5. Tens digit becomes 1.
Step 2: Tens: 1 - 6. Cannot do. Borrow 1 from hundreds: 11 - 6 = 5. Hundreds digit becomes 3.
Step 3: Hundreds: 3 - 5. Cannot do. Borrow 1 from thousands: 13 - 5 = 8. Thousands digit becomes 6.
Step 4: Thousands: 6 - 3 = 3.
Answer: 7,423 - 3,568 = 3,855
Example 3: Example 3: Borrowing across zeros
Problem: Subtract 5,003 - 2,467.
Solution:
Step 1: Ones: 3 - 7. Cannot do. Need to borrow from tens, but tens = 0.
Step 2: Borrow from hundreds, but hundreds = 0 too. Go to thousands.
Step 3: Borrow 1 from 5 (thousands): 5 becomes 4. Hundreds gets 10, but gives 1 to tens: becomes 9. Tens gets 10 but gives 1 to ones: becomes 9. Ones gets 10: becomes 13.
Step 4: Ones: 13 - 7 = 6. Tens: 9 - 6 = 3. Hundreds: 9 - 4 = 5. Thousands: 4 - 2 = 2.
Answer: 5,003 - 2,467 = 2,536
Example 4: Example 4: Subtraction from a round number
Problem: Subtract 8,000 - 3,456.
Solution:
Step 1: 8,000 has three zeros. Borrow from thousands: 8 becomes 7, hundreds gets 10, then 9 (gives 1 to tens), tens becomes 10, then 9 (gives 1 to ones), ones becomes 10.
Step 2: Ones: 10 - 6 = 4. Tens: 9 - 5 = 4. Hundreds: 9 - 4 = 5. Thousands: 7 - 3 = 4.
Answer: 8,000 - 3,456 = 4,544
Example 5: Example 5: Word problem - money
Problem: Aditi had ₹5,750. She bought a dress for ₹2,890. How much money is left?
Solution:
Step 1: Ones: 0 - 0 = 0
Step 2: Tens: 5 - 9. Borrow: 15 - 9 = 6. Hundreds becomes 6.
Step 3: Hundreds: 6 - 8. Borrow: 16 - 8 = 8. Thousands becomes 4.
Step 4: Thousands: 4 - 2 = 2.
Answer: Aditi has ₹2,860 left.
Example 6: Example 6: Word problem - difference in heights
Problem: Mount Everest is 8,849 m tall. Mount Kilimanjaro is 5,895 m tall. What is the difference in height?
Solution:
Step 1: Ones: 9 - 5 = 4
Step 2: Tens: 4 - 9. Borrow: 14 - 9 = 5. Hundreds becomes 7.
Step 3: Hundreds: 7 - 8. Borrow: 17 - 8 = 9. Thousands becomes 7.
Step 4: Thousands: 7 - 5 = 2.
Answer: Difference = 2,954 m
Example 7: Example 7: Checking subtraction with addition
Problem: Subtract 4,826 - 1,937. Verify using addition.
Solution:
Subtraction: 4,826 - 1,937 = 2,889
Verification: 2,889 + 1,937 = 4,826. This matches the original number.
Answer: 2,889 (verified)
Example 8: Example 8: Word problem - population
Problem: A town had 7,350 people last year. This year it has 6,825 people. How many people left?
Solution:
Step 1: Ones: 0 - 5. Borrow: 10 - 5 = 5. Tens becomes 4.
Step 2: Tens: 4 - 2 = 2
Step 3: Hundreds: 3 - 8. Borrow: 13 - 8 = 5. Thousands becomes 6.
Step 4: Thousands: 6 - 6 = 0.
Answer: 525 people left the town.
Example 9: Example 9: Subtracting a 3-digit from a 4-digit number
Problem: Subtract 3,204 - 567.
Solution:
Step 1: Treat 567 as 0,567. Align: 3,204 - 0,567.
Step 2: Ones: 4 - 7. Borrow: 14 - 7 = 7. Tens becomes 9 (after borrowing from hundreds, which becomes 1).
Step 3: Tens: 9 - 6 = 3.
Step 4: Hundreds: 1 - 5. Borrow from thousands: 11 - 5 = 6. Thousands becomes 2.
Step 5: Thousands: 2 - 0 = 2.
Answer: 3,204 - 567 = 2,637
Example 10: Example 10: Word problem - cricket runs
Problem: India scored 6,543 runs in a series. Australia scored 5,678 runs. By how many runs did India win?
Solution:
Step 1: Ones: 3 - 8. Borrow: 13 - 8 = 5.
Step 2: Tens: 3 - 7. Borrow: 13 - 7 = 6.
Step 3: Hundreds: 4 - 6. Borrow: 14 - 6 = 8.
Step 4: Thousands: 5 - 5 = 0.
Answer: India won by 865 runs.
Key Points to Remember
- Align numbers by place value with the larger number on top.
- Subtract from right to left.
- When the top digit is smaller, borrow 1 from the next left place (adds 10 to the current place).
- Borrowing across zeros requires chain borrowing (go to the nearest non-zero digit).
- Check subtraction by adding the answer to the smaller number — it should give the larger number.
- Subtracting a smaller-digit number from a larger-digit number: fill with leading zeros for alignment.
Practice Problems
- Subtract 9,876 - 4,321.
- Subtract 5,200 - 3,674.
- Subtract 7,001 - 2,856.
- Subtract 4,000 - 1,999.
- Dev had ₹8,500. He spent ₹3,745 on books. How much is left?
- A library has 6,230 books. 2,485 are issued out. How many remain?
- Subtract 3,050 - 1,876 and verify using addition.
- A school trip costs ₹4,200. Neha has ₹2,875. How much more does she need?
Frequently Asked Questions
Q1. What is borrowing in subtraction?
Borrowing (regrouping) happens when the top digit is smaller than the bottom digit. You take 1 from the next left place, which adds 10 to the current place. For example, to do 3 - 8 in the ones place, borrow from tens: 13 - 8 = 5.
Q2. How do you subtract across zeros?
When you need to borrow but the next place is 0, go to the nearest non-zero digit. For example, in 5,003 - 2,467: borrow from 5 (thousands). It cascades through the zeros, turning each 0 into 9 (after lending).
Q3. How do you check a subtraction answer?
Add the answer (difference) to the number you subtracted. The result should equal the original top number. Example: 7,000 - 2,345 = 4,655. Check: 4,655 + 2,345 = 7,000.
Q4. Can the answer be a 3-digit number?
Yes. If the two 4-digit numbers are close in value, the difference can be 3 digits or fewer. For example, 5,100 - 4,800 = 300.
Q5. Does the order matter in subtraction?
Yes. Unlike addition, subtraction is not commutative. 5,000 - 3,000 = 2,000, but 3,000 - 5,000 would give a negative number (not covered in Class 4). Always subtract the smaller from the larger.
Q6. What is the shortcut for subtracting from a round number?
For 1,000 - any number, subtract each digit from 9 (except the last non-zero digit, subtract from 10). Example: 1,000 - 357 = 643 (9-3=6, 9-5=4, 10-7=3).
Q7. Can I use estimation to check subtraction?
Yes. Round both numbers and estimate the difference. If your exact answer is far from the estimate, recheck. Example: 8,756 - 3,214: estimate = 9,000 - 3,000 = 6,000. Exact = 5,542 (reasonably close).
Q8. Is subtraction of 4-digit numbers in NCERT Class 4?
Yes. NCERT Class 4 Maths covers subtraction of 4-digit numbers with and without borrowing, including word problems.
