Regrouping — Definition, Formula & Examples
Regrouping is the process of exchanging values between place-value columns when adding or subtracting. For example, when a column's sum exceeds 9 in addition, you "carry" the extra ten to the next column, and in subtraction, you "borrow" from a higher place value.
Regrouping is the procedure of decomposing or composing groups of ten (or powers of ten) across adjacent place-value positions so that standard column-by-column addition or subtraction can be completed when a digit operation produces a result outside the range 0–9.
How It Works
When you add two digits in the same column and get 10 or more, write the ones digit below the line and carry the 1 to the next column to the left. When you subtract and the top digit is smaller than the bottom digit, borrow 1 from the next column to the left, which adds 10 to the current column. Each "1" you carry or borrow represents one group of ten in that place value.
Worked Example
Problem: Subtract 368 from 523 using regrouping.
Step 1: Start in the ones column: 3 minus 8. Since 3 is less than 8, borrow 1 ten from the tens column. The ones digit becomes 13, and the tens digit drops from 2 to 1.
Step 2: Move to the tens column: 1 minus 6. Since 1 is less than 6, borrow 1 hundred from the hundreds column. The tens digit becomes 11, and the hundreds digit drops from 5 to 4.
Step 3: Subtract in the hundreds column.
Answer: 523 − 368 = 155
Why It Matters
Regrouping is the foundation of multi-digit arithmetic you will use throughout school and daily life—calculating prices, measuring distances, and handling money all depend on it. Mastering regrouping also prepares you for long multiplication and long division, where the same place-value exchanges appear repeatedly.
Common Mistakes
Mistake: Forgetting to reduce the digit you borrowed from by 1.
Correction: Every time you borrow, the digit in the next column to the left decreases by 1. Write the new smaller digit above the original to keep track.