# 4 Digit 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'll learn about 4-digit addition, as well as about how and when to regroup. After working through a real-life example, you'll also have the chance to solve some 4-digit addition problems.

## Understanding Regrouping

Jason was rummaging around in his attic when he found an old pinball game and decided to play a few rounds. In his first game, he scored 3965 points. In his second game, he beat that score with a total of 4387 points. Jason wanted to know how many points he scored in both games. However, since he was in the attic, he didn't have a cell phone or calculator. He did find a piece of paper and pencil though, so he wrote his scores down like this:

As each of Jason's scores involves four numbers, he'll be solving a 4-digit addition problem. To do this, he'll use regrouping, which just means exchanging groups of ones for tens, or groups of tens for hundreds, and groups of hundreds for thousands.

In Jason's equation, you'll notice that the two numbers are placed one on top of the other (vertically), instead of like this: 3965 + 4387 (horizontally). This makes adding the numbers easier and helps to organize the answer. You'll find this is especially true when you're doing 2-digit, 3-digit, or 4-digit addition. When completing a problem like this, always start by adding the numbers in the ones place value, as shown below.

Here, 7 + 5 = 12. Place the 2 in the ones column, and then carry the 1 to the tens column. Anytime an answer in a column is 10 or more you regroup this way. The next step is to move to the tens column, and add the top and bottom digits.

When adding 8 + 6, remember to add 1, or the ten that you just regrouped: 8 + 6 + 1 = 15.

Place the 5 in the tens column, and regroup the ten to the next column. After adding the tens column and regrouping, move to the hundreds column, and add the top and bottom digits.

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