By Pamela Martin | Updated Aug 30, 2022
TongRo Images / Getty Images
Regrouping—also known as carrying in addition and borrowing in subtraction—is a foundational skill that helps students manage the base‑10 structure of numbers. The place value system tells us that a digit’s position determines whether it represents ones, tens, hundreds, thousands, and so on. For example, the number 8,364 contains eight groups of 1,000, three groups of 100, six groups of 10, and four groups of 1.
When a column of digits exceeds nine, we regroup the excess into the next higher place value. For instance, if the ones column totals 13, we write 3 in the ones place and carry 10 to the tens column. Similarly, a tens column total of 38 becomes 8 in the tens place and 3 carried to the hundreds column. A practical example: adding 734 + 69. The ones column sums to 13, so we write 3 and carry 1 to the tens. Adding the carried 1 to the tens column’s 3 gives 4, then we add the 6 in the hundreds column, arriving at 803.
Regrouping in subtraction is necessary when a digit in the minuend is smaller than the corresponding digit in the subtrahend. Consider 41 – 17. Because 1 (ones) is less than 7, we borrow 10 from the tens place. The minuend becomes (30 + 10) – (10 + 7). Subtracting the ones gives 10 – 7 = 3, and the tens column yields 3 – 1 = 2, resulting in a final answer of 24.
Mastering regrouping not only improves speed but also builds a deeper understanding of how numbers are constructed—a critical skill for all levels of math education.
