Subtraction With Regrouping (3-Digit)
Subtraction with regrouping (also called borrowing) is needed when a digit in the top number is smaller than the corresponding digit in the bottom number. We borrow 1 from the next place to the left.
For example, in 432 − 258, the ones column has 2 − 8. Since 2 is less than 8, we borrow from the tens place.
What is Subtraction With Regrouping (3-Digit) - Class 3 Maths (Addition and Subtraction (Grade 3))?
Regrouping in subtraction means borrowing from a higher place value to make the subtraction possible in the current column.
1 hundred = 10 tens | 1 ten = 10 ones
When do you regroup? Whenever the top digit in a column is smaller than the bottom digit.
Solved Examples
Example 1: Borrowing in the Ones Place
Question: Subtract 453 − 276.
Think:
- Ones: 3 − 6 → cannot, borrow 1 ten → 13 − 6 = 7
- Tens: 4 (was 5, gave 1) − 7 → cannot, borrow 1 hundred → 14 − 7 = 7
- Hundreds: 3 (was 4, gave 1) − 2 = 1
Answer: 453 − 276 = 177
Example 2: Borrowing in the Tens Place Only
Question: Subtract 836 − 471.
Think:
- Ones: 6 − 1 = 5 (no borrowing)
- Tens: 3 − 7 → cannot, borrow 1 hundred → 13 − 7 = 6
- Hundreds: 7 (was 8, gave 1) − 4 = 3
Answer: 836 − 471 = 365
Example 3: Borrowing Across a Zero
Question: Subtract 405 − 178.
Think:
- Ones: 5 − 8 → cannot, borrow from tens, but tens is 0
- Borrow from hundreds: 4 hundreds → 3 hundreds + 10 tens
- Now borrow from tens: 10 tens → 9 tens, ones become 15
- Ones: 15 − 8 = 7
- Tens: 9 − 7 = 2
- Hundreds: 3 − 1 = 2
Answer: 405 − 178 = 227
Example 4: Subtracting from 1000
Question: Subtract 1000 − 456.
Think:
- Ones: 0 − 6 → borrow chain through tens and hundreds
- 1000 → 0 thousands, 9 hundreds, 9 tens, 10 ones
- Ones: 10 − 6 = 4
- Tens: 9 − 5 = 4
- Hundreds: 9 − 4 = 5
Answer: 1000 − 456 = 544
Example 5: Word Problem — Stickers Left
Question: Dev had 612 stickers. He gave 385 stickers to his friends. How many stickers are left?
Think:
- Ones: 2 − 5 → borrow → 12 − 5 = 7
- Tens: 0 (was 1, gave 1) − 8 → borrow → 10 − 8 = 2
- Hundreds: 5 (was 6, gave 1) − 3 = 2
Answer: Dev has 227 stickers left.
Example 6: Word Problem — Auto-Rickshaw Distance
Question: An auto-rickshaw's meter shows 742 km total. It showed 589 km yesterday. How many km did it travel today?
Think:
- 742 − 589
- Ones: 2 − 9 → borrow → 12 − 9 = 3
- Tens: 3 (was 4, gave 1) − 8 → borrow → 13 − 8 = 5
- Hundreds: 6 (was 7, gave 1) − 5 = 1
Answer: It travelled 153 km today.
Example 7: Checking by Addition
Question: Find 930 − 574 and check your answer.
Think:
- Ones: 0 − 4 → borrow → 10 − 4 = 6
- Tens: 2 (was 3, gave 1) − 7 → borrow → 12 − 7 = 5
- Hundreds: 8 (was 9, gave 1) − 5 = 3
- Answer: 356
- Check: 356 + 574 = 930 ✓
Answer: 930 − 574 = 356
Example 8: Word Problem — Train Seats
Question: A train has 800 seats. 537 seats are booked. How many seats are empty?
Think:
- 800 − 537
- Ones: 0 − 7 → borrow from tens, but tens is 0
- 800 → 7 hundreds, 10 tens, 0 ones → 7 hundreds, 9 tens, 10 ones
- Ones: 10 − 7 = 3
- Tens: 9 − 3 = 6
- Hundreds: 7 − 5 = 2
Answer: 263 seats are empty.
Example 9: Multiple Borrowing
Question: Subtract 701 − 465.
Think:
- Ones: 1 − 5 → borrow from tens: tens is 0, borrow from hundreds
- 7 hundreds → 6 hundreds, 10 tens → 9 tens + 11 ones
- Ones: 11 − 5 = 6
- Tens: 9 − 6 = 3
- Hundreds: 6 − 4 = 2
Answer: 701 − 465 = 236
Real-World Applications
Real-life situations requiring subtraction with regrouping:
- Giving change: A shopkeeper receives ₹500 for an item costing ₹347. Change = 500 − 347 = 153. This requires borrowing.
- Remaining stock: A shop had 612 items and sold 385. Remaining = 612 − 385 = 227.
- Time remaining: If a movie is 120 minutes long and 75 minutes have passed, remaining = 120 − 75 = 45 minutes.
- Weight difference: A watermelon weighs 804 g and a mango weighs 367 g. Difference = 804 − 367 = 437 g.
Most real-world subtraction problems require regrouping because the digit in the top number is often smaller than the corresponding digit in the bottom number. Practising with regrouping builds accuracy and confidence.
Key Points to Remember
- Regroup when the top digit is smaller than the bottom digit in any column.
- Borrow 1 from the next place: 1 hundred = 10 tens, 1 ten = 10 ones.
- When the tens digit is 0, borrow from the hundreds first, then from the tens.
- Always check your answer by adding: Difference + Subtrahend = Minuend.
- Write the borrowing marks clearly to avoid mistakes.
Practice Problems
- Subtract 623 − 357.
- Subtract 804 − 569.
- Subtract 700 − 283.
- Meera had ₹543. She spent ₹278. How much is left?
- Subtract 910 − 648.
- A school had 856 pencils. 479 were distributed. How many remain?
- Find 1000 − 375.
Frequently Asked Questions
Q1. What does borrowing mean in subtraction?
Borrowing means taking 1 from the next higher place. For example, if you cannot subtract 8 from 3 in the ones column, borrow 1 ten (which becomes 10 ones), making it 13 − 8 = 5.
Q2. How do you borrow when there is a zero in the tens place?
Go to the hundreds place. Reduce the hundreds digit by 1 and make the tens digit 10. Then borrow from the tens for the ones. For example, 503 → 4 hundreds, 9 tens, 13 ones.
Q3. What if there are zeros in both tens and hundreds?
Borrow from the thousands place (like in 1000 − 456). Convert 1000 to 0 thousands, 9 hundreds, 9 tens, 10 ones, then subtract normally.
Q4. Is borrowing the same as regrouping?
Yes. Borrowing is the traditional term, regrouping is the modern term. Both mean the same process of exchanging 1 unit of a higher place for 10 units of a lower place.
Q5. How do I avoid mistakes when borrowing?
Write the borrowed values clearly. Cross out the digit you borrow from and write the reduced number. Write the new larger number next to the digit you are subtracting from.
Q6. Can the answer be 0 after borrowing?
Yes. For example, 300 − 300 = 0. Also, a particular column can have a result of 0 (e.g., in 420 − 120, the ones and tens columns both give 0).
Q7. Why do we start subtracting from the ones place?
Starting from the ones lets us know if we need to borrow from the tens. If we started from the left, we would not know whether borrowing is needed from the right.
Q8. Can borrowing happen in every column?
Yes. In problems like 432 − 276, borrowing happens in both the ones and tens columns. You may need to borrow in every column.
Related Topics
- Subtraction of 3-Digit Numbers
- Subtraction Without Regrouping (3-Digit)
- Addition of 3-Digit Numbers
- Addition Without Regrouping (3-Digit)
- Addition With Regrouping (3-Digit)
- Addition Word Problems (Grade 3)
- Subtraction Word Problems (Grade 3)
- Mental Math (Grade 3)
- Adding 4 or More Numbers
- Checking Addition and Subtraction
- Mixed Operations (Grade 3)
- Mixed Word Problems (Grade 3)
