Addition with Regrouping (Carrying)
Regrouping (also called carrying) is what you do when the digits in a single column add up to ten or more. You cannot write a two-digit number in a single column — you write the ones digit and carry the tens digit to the column on the left.
Why Regrouping Is Necessary
Our number system is base-10. Once a column reaches 10, we must move a group of ten into the next column. For example, 10 ones = 1 ten; 10 tens = 1 hundred. This is what "carrying" physically means.
Step-by-Step Method
- Add the ones column.
- If the result is 10 or more, write the ones digit below and carry the tens digit to the top of the tens column.
- Add the tens column, including the carried digit.
- Repeat as needed for higher columns.
Worked Examples
¹
4 7
+ 3 5
-----
8 2
Ones: 7 + 5 = 12. Write 2, carry 1. Tens: 4 + 3 + 1 = 8. Answer: 82
¹ ¹
3 7 8
+ 4 6 4
-------
8 4 2
Ones: 8 + 4 = 12 → write 2, carry 1. Tens: 7 + 6 + 1 = 14 → write 4, carry 1. Hundreds: 3 + 4 + 1 = 8. Answer: 842
¹ ¹ ¹
9 8 7
+ 1 2 3 4 (actually: 0987 + 1234)
Wait — let us use a cleaner example:
5 6 8
+ 4 7 5
-------
1 0 4 3
Ones: 8 + 5 = 13 → write 3, carry 1. Tens: 6 + 7 + 1 = 14 → write 4, carry 1. Hundreds: 5 + 4 + 1 = 10 → write 0, carry 1. Thousands: 0 + 0 + 1 = 1. Answer: 1043
Common Mistakes
- Writing the full two-digit column total below the line (e.g., writing 12 instead of 2 with a carry).
- Forgetting to add the carried digit in the next column.
- Carrying when the column totals less than 10 (not needed).
- Adding the carry to the wrong column.
Key Takeaways
- Carry when a column total is 10 or more.
- Write the ones digit below; write the tens digit small above the next column.
- The carried digit is always 1 when adding two numbers; it can be higher when adding three or more.
Practice Questions
- Calculate 38 + 45 using column addition with carrying.
- Calculate 276 + 358.
- Add 689 + 471.
- Calculate 987 + 546.
- A shop sells 367 items on Saturday and 485 on Sunday. What is the total?