Addition with regrouping is a method used when the sum of digits in a column is 10 or greater. We "regroup" the extra value by carrying it over to the next column on the left.
Process: Start with the ones place: 8 + 2 = 10. Write 0 in the ones place and carry the 1 to the tens place. Then add the tens place: 1 (carried) + 3 + 2 = 6. The final answer is 60.
Regrouping is sometimes called "carrying." It helps us correctly add numbers that create sums of 10 or more in any column.
Follow these steps to add two-digit numbers when regrouping is needed.
Process: First, ones place: 7 + 8 = 15. Write 5 in the ones place and carry the 1 to the tens place. Then tens place: 1 (carried) + 5 + 3 = 9. The final answer is 95.
Always start adding from the rightmost column (ones place) and move left. The carried number is always added to the next left column.
When adding three-digit numbers, you may need to regroup in the ones, tens, or both columns using the same process.
Process: Ones place: 8 + 6 = 14. Write 4 and carry 1 to tens place. Tens place: 1 (carried) + 2 + 9 = 12. Write 2 and carry 1 to hundreds place. Hundreds place: 1 (carried) + 4 + 1 = 6. Final answer: 624.
Process: Ones place: 6 + 7 = 13. Write 3 and carry 1. Tens place: 1 (carried) + 8 + 5 = 14. Write 4 and carry 1. Hundreds place: 1 (carried) + 3 + 4 = 8. Final answer: 843.
With three-digit numbers, you might regroup once, twice, or not at all. Always check each column carefully before moving to the next.
Some addition problems require regrouping across multiple columns or consecutive regrouping.
Process: Ones place: 9 + 5 = 14. Write 4 and carry 1. Tens place: 1 (carried) + 9 + 3 = 13. Write 3 and carry 1. Hundreds place: 1 (carried) + 2 + 1 = 4. Final answer: 434.
Process: Ones place: 0 + 0 = 0. Tens place: 5 + 5 = 10. Write 0 and carry 1. Hundreds place: 1 (carried) + 8 + 3 = 12. Write 12, creating a thousands place. Final answer: 1,200.
When the sum of the leftmost column is 10 or greater, you'll create a new place value (from hundreds to thousands in three-digit addition).
Always verify your addition by using inverse operations or re-calculating to ensure accuracy.
Process: To verify 148 + 119 = 267, subtract 148 from 267. Ones place: 7 - 8 (can't do), so regroup from tens: 17 - 8 = 9. Tens place: 5 (after regrouping) - 4 = 1. Hundreds place: 2 - 1 = 1. Result is 119, which matches our other addend.
Good mathematicians always check their work. This helps catch regrouping errors and builds confidence in your answers.