What Is Addition with Regrouping?
Addition with regrouping (also called "carrying") is a method used when adding numbers where the sum of digits in any place value column is 10 or more. When this happens, we need to "carry over" the extra value to the next column.
Core Addition Concepts:
Regrouping: The process of carrying over values when the sum in a column reaches 10 or more
Place Value: The value of a digit based on its position (ones, tens, hundreds)
Carrying: Moving excess value from one column to the next
Ones Place: The rightmost column representing single units
Tens Place: The column representing groups of ten
- Add Ones Column: Add the digits in the ones place
- Check for Regrouping: If sum is 10 or more, carry to tens
- Add Tens Column: Add the digits in the tens place including carry
- Write Answer: Record the final sum in correct positions
1. Add the ones column: 7 + 5 = 12
2. Since 12 ≥ 10, write 2 in ones place and carry 1 to tens
3. Add the tens column: 2 + 1 + 1 (carried) = 4
4. Write 4 in tens place: 42
When the sum in any column is 10 or more, we must regroup by carrying to the next column.
Always carry the tens digit from the sum to the next column when regrouping.
1. Add the ones column: 8 + 6 = 14
2. Since 14 ≥ 10, write 4 in ones place and carry 1 to tens
3. Add the tens column: 3 + 2 + 1 (carried) = 6
4. Write 6 in tens place: 64
The carried digit represents the tens in the sum of the previous column.
Remember to add the carried number to the next column's sum.
1. Add the ones column: 9 + 7 = 16
2. Since 16 ≥ 10, write 6 in ones place and carry 1 to tens
3. Add the tens column: 4 + 1 + 1 (carried) = 6
4. Write 6 in tens place: 66
Even when starting with a 9 in the ones place, the regrouping process remains the same.
The regrouping process is consistent regardless of the starting digits.
| 28 + 14 = ___ | 36 + 27 = ___ | 45 + 18 = ___ |
| 19 + 23 = ___ | 34 + 29 = ___ | 27 + 35 = ___ |
| 46 + 17 = ___ | 38 + 24 = ___ | 53 + 19 = ___ |
1. Add the ones column first
2. Check if the sum is 10 or more
3. If yes, write the ones digit and carry the tens
4. Add the tens column including any carried number
5. Write the final answer
Work through each problem step by step. Don't rush the regrouping process!
Always verify your answer by checking that the regrouping was done correctly.
| 57 + 28 = ___ | 64 + 19 = ___ | 38 + 47 = ___ |
| 46 + 37 = ___ | 29 + 58 = ___ | 53 + 29 = ___ |
| 48 + 36 = ___ | 67 + 18 = ___ | 59 + 27 = ___ |
1. Focus on accuracy with larger numbers
2. Double-check your carrying
3. Use estimation to verify reasonableness
4. Practice mental math shortcuts
These problems require more careful attention to carrying. Take your time!
Larger numbers require the same regrouping process - just more careful attention.