What Is Regrouping in Math?
Regrouping is one of the most important concepts in elementary arithmetic. It is the process of trading between place values — converting 10 ones into 1 ten (in addition) or converting 1 ten into 10 ones (in subtraction).
You might know it by its older names: carrying (in addition) and borrowing (in subtraction). Modern math education prefers "regrouping" because it describes what actually happens — rearranging the same value into different place-value groups.
How regrouping works in addition
When adding 27 + 15:
- Ones column: 7 + 5 = 12 ones
- 12 ones is too many for the ones column (which can only hold 0-9)
- Regroup: trade 10 of those ones for 1 ten
- Write 2 in the ones column, carry 1 to the tens column
- Tens column: 2 + 1 + 1 (carried) = 4 tens
- Answer: 42
The regrouping trade: 10 ones = 1 ten. The total value does not change — you are just reorganizing.
How regrouping works in subtraction
When subtracting 42 - 17:
- Ones column: 2 - 7. You cannot take 7 from 2.
- Regroup: trade 1 ten for 10 ones
- Now the ones column has 12, and the tens column has 3
- 12 - 7 = 5 ones, 3 - 1 = 2 tens
- Answer: 25
The regrouping trade: 1 ten = 10 ones. Same trade, opposite direction.
Key Insight: Regrouping is not a trick or a shortcut. It is a direct consequence of our base-10 number system, where each place is worth 10 times the place to its right. Every time you accumulate 10 in one place, you trade for 1 in the next place. Every time you need more in one place, you trade from the next place.
Why it matters
Regrouping is essential for:
- Multi-digit addition and subtraction
- Multi-digit multiplication (partial products generate regrouping)
- Long division (the subtract step often requires regrouping)
- Decimal arithmetic (same concept, extended to tenths and hundredths)
A child who understands regrouping — who can explain why they "carry the 1" — has the foundation for all multi-digit arithmetic. A child who memorizes the procedure without understanding will struggle when the problems get larger or more complex.
How to teach it
The best approach is physical trading with base-ten blocks or bundled objects. See our full teaching guide: How to Teach Regrouping in Addition and How to Teach Regrouping in Subtraction.
Regrouping is trading between place values. That is the entire concept. Once your child understands the trade — and can explain why it preserves the total value — every multi-digit operation becomes a variation on the same idea.