Subtraction with Regrouping — Definition, Formula & Examples
Subtraction with regrouping is a method used when a digit in the top number is smaller than the digit below it, so you borrow 1 from the next higher place value to complete the subtraction.
Regrouping in subtraction is the process of decomposing a unit from a higher place value into 10 units of the adjacent lower place value, enabling column-by-column subtraction when the minuend's digit in a given place is less than the corresponding digit of the subtrahend.
How It Works
Work from right to left, one column at a time. If the top digit in a column is smaller than the bottom digit, borrow 1 from the column to its left. That borrowed 1 equals 10 in the current column, so you add 10 to the top digit before subtracting. Remember to reduce the digit you borrowed from by 1. Continue this process for each column until the subtraction is complete.
Worked Example
Problem: Subtract 427 − 258.
Ones column: 7 minus 8: since 7 is less than 8, borrow 1 from the tens column. The 7 becomes 17, and the tens digit (2) drops to 1.
Tens column: The tens digit is now 1 (after borrowing). 1 minus 5: since 1 is less than 5, borrow 1 from the hundreds column. The 1 becomes 11, and the hundreds digit (4) drops to 3.
Hundreds column: The hundreds digit is now 3. Subtract normally.
Answer: 427 − 258 = 169
Why It Matters
Regrouping is the foundation for subtracting any multi-digit numbers by hand. It also builds the place-value understanding you need for long division, decimal arithmetic, and mental math strategies used throughout school and everyday life.
Common Mistakes
Mistake: Forgetting to reduce the digit you borrowed from by 1.
Correction: Every time you borrow, cross out the digit in the next column and write it as one less. For example, if you borrow from a 4, it becomes 3.