Addition With Regrouping (3-Digit)
Addition with regrouping (also called addition with carrying) is needed when the sum of digits in any column is 10 or more. The extra value is carried to the next column on the left.
For example, in 358 + 274, the ones column gives 8 + 4 = 12. We write 2 in the ones place and carry 1 to the tens column.
What is Addition With Regrouping (3-Digit) - Class 3 Maths (Addition and Subtraction (Grade 3))?
Regrouping means reorganizing values from one place to the next. In addition, when a column sum is 10 or more:
- Write the ones digit of the sum in that column.
- Carry the tens digit to the next column on the left.
10 ones = 1 ten | 10 tens = 1 hundred
Solved Examples
Example 1: Regrouping in Ones Only
Question: Add 246 + 318.
Think:
- Ones: 6 + 8 = 14 → write 4, carry 1
- Tens: 4 + 1 + 1(carry) = 6
- Hundreds: 2 + 3 = 5
Answer: 246 + 318 = 564
Example 2: Regrouping in Tens Only
Question: Add 471 + 283.
Think:
- Ones: 1 + 3 = 4
- Tens: 7 + 8 = 15 → write 5, carry 1
- Hundreds: 4 + 2 + 1(carry) = 7
Answer: 471 + 283 = 754
Example 3: Regrouping in Both Ones and Tens
Question: Add 567 + 385.
Think:
- Ones: 7 + 5 = 12 → write 2, carry 1
- Tens: 6 + 8 + 1 = 15 → write 5, carry 1
- Hundreds: 5 + 3 + 1 = 9
Answer: 567 + 385 = 952
Example 4: Sum Crosses 1000
Question: Add 759 + 486.
Think:
- Ones: 9 + 6 = 15 → write 5, carry 1
- Tens: 5 + 8 + 1 = 14 → write 4, carry 1
- Hundreds: 7 + 4 + 1 = 12 → write 2, carry 1 (to thousands)
Answer: 759 + 486 = 1245
Example 5: Word Problem — Chapatis for a Function
Question: For a school function, 475 chapatis were made in the morning and 368 in the evening. How many chapatis were made in total?
Think:
- Ones: 5 + 8 = 13 → write 3, carry 1
- Tens: 7 + 6 + 1 = 14 → write 4, carry 1
- Hundreds: 4 + 3 + 1 = 8
Answer: 843 chapatis were made in total.
Example 6: Adding Numbers Ending in 9
Question: Add 199 + 356.
Think:
- Ones: 9 + 6 = 15 → write 5, carry 1
- Tens: 9 + 5 + 1 = 15 → write 5, carry 1
- Hundreds: 1 + 3 + 1 = 5
Answer: 199 + 356 = 555
Example 7: Word Problem — Saving Coins
Question: Priya saved ₹287 and her brother Dev saved ₹465. How much did they save together?
Think:
- Ones: 7 + 5 = 12 → write 2, carry 1
- Tens: 8 + 6 + 1 = 15 → write 5, carry 1
- Hundreds: 2 + 4 + 1 = 7
Answer: They saved ₹752 together.
Example 8: Adding to 999
Question: Add 999 + 1.
Think:
- Ones: 9 + 1 = 10 → write 0, carry 1
- Tens: 9 + 0 + 1 = 10 → write 0, carry 1
- Hundreds: 9 + 0 + 1 = 10 → write 0, carry 1
Answer: 999 + 1 = 1000
Example 9: Checking with Estimation
Question: Add 376 + 458 and check using estimation.
Think:
- Ones: 6 + 8 = 14 → write 4, carry 1
- Tens: 7 + 5 + 1 = 13 → write 3, carry 1
- Hundreds: 3 + 4 + 1 = 8
- Sum = 834
- Estimate: 400 + 500 = 900. 834 is close to 900 ✓
Answer: 376 + 458 = 834 (reasonable, since estimate is 900).
Real-World Applications
Where is addition with regrouping used?
- Shopping bills: Total cost of items: ₹487 + ₹356 = ₹843. The ones column (7+6=13) and tens column (8+5+1=14) both need regrouping.
- Sports totals: Combining runs from two innings: 278 + 345 = 623.
- School events: Total items collected for charity: 389 books + 476 notebooks = 865 items.
- Distance calculations: Trip segments: 167 km + 285 km = 452 km.
- Weight combinations: A sack of rice (475 g) plus a sack of dal (358 g) = 833 g total.
Most real-world addition problems involve regrouping because everyday numbers rarely have digits that all add up to less than 10. Mastering regrouping is essential for practical arithmetic.
Key Points to Remember
- Regrouping is needed when a column sum is 10 or more.
- Write the ones digit in the column and carry the tens digit to the next column.
- 10 ones = 1 ten; 10 tens = 1 hundred; 10 hundreds = 1 thousand.
- The sum of two 3-digit numbers can be a 4-digit number.
- Use estimation to check if your answer is reasonable.
- Regrouping can happen in one, two, or all three columns.
Practice Problems
- Add 459 + 276.
- Add 387 + 548.
- Add 694 + 307 (check: does ones column need regrouping?).
- Meera has ₹578 and earns ₹367 more. How much does she have?
- Add 888 + 112.
- Add 999 + 999.
- A school has 486 boys and 529 girls. Find the total students.
Frequently Asked Questions
Q1. What is regrouping in addition?
Regrouping means carrying a value to the next place when a column sum reaches 10 or more. For example, 8 + 7 = 15, so we write 5 and carry 1 to the next place.
Q2. Is carrying and regrouping the same thing?
Yes. Carrying is the older term for regrouping. Both mean the same thing — transferring extra value to the next column.
Q3. How many times can you regroup in one problem?
You can regroup in every column. In 3-digit addition, you might regroup in the ones, tens, and hundreds columns — up to three times.
Q4. What if I forget to carry?
Your answer will be smaller than the correct answer. Always write the carry digit above the next column so you do not forget to add it.
Q5. Can the sum of two 3-digit numbers be more than 1000?
Yes. The largest possible sum is 999 + 999 = 1998. Any sum above 999 becomes a 4-digit number.
Q6. How do I check my addition?
Use estimation (round and add), add in reverse order, or subtract one addend from the sum. If the result matches the other addend, your addition is correct.
Q7. Why is regrouping important?
Without regrouping, you could only add numbers whose column sums are less than 10. Regrouping allows you to add any numbers, no matter how large the column sums are.
Q8. What happens when you carry from the hundreds column?
The carry goes into the thousands place, making the answer a 4-digit number. For example, 700 + 500 = 1200.
Related Topics
- Addition Without Regrouping (3-Digit)
- Addition of 3-Digit Numbers
- Addition Word Problems (Grade 3)
- Subtraction of 3-Digit Numbers
- Subtraction With Regrouping (3-Digit)
- Subtraction Without Regrouping (3-Digit)
- 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)
