Addition with Regrouping

What Is Regrouping?#

When we add numbers, sometimes we get more than 9 in one place value column. When that happens, we need to regroup — we bundle up 10 ones into 1 ten, or 10 tens into 1 hundred, and carry it over to the next column. Regrouping is sometimes called carrying in addition.

Why Do We Regroup?#

Remember: each place value column can only hold digits 0 through 9. If you get 10 or more in a column, it spills over into the next column!

Think of it like this: Imagine you have 10 single blocks. If you stack them all together, you now have 1 tall rod of 10. You have regrouped 10 ones into 1 ten!

A Simple Example: Regrouping Ones to Tens#

Let us add 37 + 45.

  37
+ 45
----

Step 1: Add the ones column. 7 + 5 = 12. That is more than 9!

• Write the 2 in the ones column.
• Regroup (carry) the 1 ten to the tens column.

Step 2: Add the tens column. 3 + 4 = 7, plus the 1 we carried = 8.

• Write the 8 in the tens column.

Answer: 82

Checking Your Work#

A great way to check is to go back and add in a different order (start from the larger number, then add the smaller one). If you get the same answer, you are correct!

You can also use base-ten blocks to model regrouping. Put out 37 blocks (3 tens rods and 7 unit cubes) and add 45 blocks (4 tens rods and 5 unit cubes). Count the ones — you get 12 unit cubes. Bundle 10 of them into a ten rod. Now count everything: 8 tens rods + 2 unit cubes = 82. You regrouped!

Practicing regrouping with physical materials first helps make the written method easier to understand.