What is Addition With Regrouping?

Instructor: T.J. Hoogsteen

T.J. is currently a grade 5 teacher and Vice-Principal. He has a master's degree in Educational Administration and is working toward an Ed.D. in Educational Leadership.

In this lesson, you will learn about how to use regrouping in addition. You will learn what regrouping is, how to regroup, and why it is important. Then, practice what you've learned with a quiz!

What is Regrouping?

Imagine that you and some friends are entering a baseball tournament. You can have a maximum of 9 players per team. Every time a team gets to 9 players the next person to enter gets placed on a new team. You could say that this new entrant has been regrouped.

This is a little bit like regrouping in addition. You can have a maximum of 9 in any place value, but as soon as that number gets to ten, you need to regroup.

You use regrouping in addition when you do vertical addition equations like this:

Vertical Addition

How to Regroup

In this lesson, you will see two ways to regroup: with base ten blocks and standard written form.

This is what 36 + 45 would look like with base ten blocks.

Base Ten 1

When adding, always start working in the ones column. To do this, move the ones from the 45 (on the bottom) to the top.

Base 10 2

I have more than 9 ones. I have 11 so I trade 10 ones for a 10-rod.

Base 10 3

Then, I move the 10-rod to the correct place value column.

Base 10 3

When finished adding the digits in the ones column, move over to the tens column and add those digits. With base ten blocks, do this by moving the 10-rods from the bottom to the top.

Now, I have 8 tens and 1 one or 81. So, 36 + 45=81.

Standard Regrouping

Now, I'll show you the standard written form of 36 + 45.

Standard 1

When I add the digit from the bottom of the ones column to the one on top, I get 6 + 5, which equals 11. Remember though, I can have a maximum of 9 in the ones column so I can't put the whole eleven there. I can put the digit representing the ones (1) in the ones column, and the other digit (1) gets regrouped to the tens column, like this:

Standard 2

Then, I can finish by adding the numbers in the tens column--3 + 4. Remember to add the regrouped ten as well-- 3 + 4 + 1.

Standard 3

This equals 8 so I put it in the tens column, for a total of 81.

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