What is regrouping in math?

Regrouping is trading equal amounts between place values, such as 10 ones for 1 ten or 1 ten for 10 ones, so that addition or subtraction is easier to do. The total amount does not change, only how it is written in each place.

Why does my child need to learn regrouping?

Regrouping is needed for many multi-digit addition and subtraction problems, including with money and decimals. It builds a strong understanding of place value, which supports later work with larger numbers and more complex operations.

What is regrouping in subtraction, and how is it different from addition?

In subtraction, regrouping means breaking a larger place into smaller units when there are not enough ones, tens, or hundreds to subtract. For example, 1 ten can be regrouped as 10 ones to help subtract. In addition, regrouping usually means combining 10 smaller units into 1 larger unit when a place has 10 or more.

How can I explain what is regrouping to my child at home?

You can use real objects like coins, blocks, or small snacks. Show that 10 single pieces can be traded for a group of 10, and that the total amount stays the same. Then connect that idea to the digits in a written problem, showing how tens and ones are traded when adding or subtracting.

What Is Regrouping? Definition and Examples

Regrouping explained for kids

Regrouping is like trading in math. If you have 10 ones, you can trade them for 1 ten, or trade 1 ten for 10 ones. The total amount of stuff does not change, it just looks different. Regrouping helps when you add or subtract bigger numbers.

Worked examples with regrouping

Example 1 (early grades, 2-digit addition with regrouping)

Problem: 47 + 38 = ?

First, add the ones: 7 ones + 8 ones = 15 ones. That is 1 ten and 5 ones. Regroup the 15 ones as 1 ten and 5 ones, so write down 5 ones and keep 1 ten to add with the tens.

Next, add the tens: 4 tens (40) + 3 tens (30) + 1 regrouped ten (10) = 8 tens (80). So 47 + 38 = 85.

Example 2 (upper grades, 3-digit subtraction with two regroupings)

Problem: 402 − 187 = ?

Start with the ones: 2 ones − 7 ones cannot be done with only 2 ones. Regroup 1 ten from the tens place, but the tens digit is 0, so first regroup 1 hundred from the hundreds place. The 4 hundreds (400) become 3 hundreds (300), and you trade 1 hundred for 10 tens, so there are now 10 tens (100) and still 2 ones.

Now regroup 1 ten from the 10 tens. The 10 tens (100) become 9 tens (90), and you trade 1 ten for 10 ones, so there are now 12 ones.

Subtract the ones: 12 ones − 7 ones = 5 ones.

Subtract the tens: 9 tens (90) − 8 tens (80) = 1 ten (10).

Subtract the hundreds: 3 hundreds (300) − 1 hundred (100) = 2 hundreds (200).

So 402 − 187 = 215.

How regrouping fits into later math

Regrouping starts with 2-digit addition and subtraction within 100, then extends to 3-digit problems and beyond. Children learn to regroup in both directions: combining 10 ones into 1 ten, and breaking 1 ten into 10 ones when needed.

As your child moves into upper elementary grades, regrouping shows up in multi-digit problems and with decimals, such as adding money amounts like 12.75 + 8.90. The same place-value idea applies: 10 hundredths make 1 tenth, and 10 tenths make 1 one.

Understanding regrouping clearly helps with the standard algorithms for addition and subtraction, and prepares your child for more advanced operations that also rely on place value.

Common mistakes with regrouping

Only changing the digit, not the value. A child might turn 7 ones + 8 ones into "15" and write 15 in the ones place, giving 715 instead of 85 for 47 + 38. Correction: 15 ones is 1 ten and 5 ones, so only 5 stays in the ones place and the 1 ten is regrouped.
Forgetting to add the regrouped ten or hundred. In 58 + 27, a child might get 5 tens + 2 tens = 7 tens and ignore the regrouped ten from 8 + 7, writing 75 instead of 85. Correction: after regrouping 15 ones as 1 ten and 5 ones, that extra ten must be added to the tens place.
Regrouping when it is not needed. In 64 − 21, a child might still try to regroup because they are used to the pattern, and change 6 tens to 5 tens and 14 ones, then subtract incorrectly to get 53. Correction: since 4 ones − 1 one can be done without regrouping, keep the place values as they are and subtract directly.

Where regrouping shows up in everyday life

Regrouping happens any time amounts are traded between units. When counting coins, 10 pennies can be traded for 1 dime, and 10 dimes can be traded for 1 dollar. When telling time, 60 minutes regroup into 1 hour. These trades keep the total amount the same, just like regrouping in math problems.

Related math terms to explore

Regrouping is closely connected to basic operations and how number sentences are written. You may also want to read about:

What is regrouping?