What is Regrouping in Math? – Definition, Subtraction & Addition
Starting in second grade, students begin to learn how to add and subtract numbers that are greater than one digit. To do this, they need to be taught how to regroup. This lesson will define regrouping and show examples for both addition and subtraction.
What is Regrouping?
For some people, the thought of doing or teaching math is a traumatic experience. Hopefully, through this simple lesson, we will be able to help with that anxiety, at least when it comes to teaching regrouping.
In math, regrouping is the process of making groups of tens when adding or subtracting two digit numbers (or more) and is another name for carrying and borrowing. If that sounds like nonsense to you, fear not, because we will spell out the process clearly for you.
Regrouping in Addition
Look at the following addition problem:
1 7
+ 1 3
3 0
If you are at least in fourth grade (you are probably much older), this problem should be a no-brainer. Of course, 17 plus 13 equals 30. However, this problem contains an important example of regrouping that you will have to teach your students.
In the above problem, you would start adding the numbers in the ones column first (7 + 3). When you add those two numbers, the answer you get is 10. However, you cannot place the 10 underneath the ones column, because you can only place one digit per column. So, what should you do?
The answer to that is simple; you regroup! By regroup, we mean you change your 10 ones into 1 ten. To do this, you place the zero from the number 10 in the ones column and place the 1 above the tens column. Doing this indicates that there are 0 ones and 1 additional ten. After you have regrouped, you can then add the tens column (1 + 1 + 1), which equals 3. Using regrouping, the problem will look like this:
1
1 7
+ 1 3
3 0
The 1 on top of the tens column is the indicator that there are regrouped numbers from the ones column.
Let’s look at one more example to help clarify things even further.
2 6
+ 1 7
4 3
In this example, the answer might not have been as obvious as the previous example. When completing this problem, you should first add the ones column (6 + 7), which equals 13. Again, you can’t place a two digit number under the ones column, so you must regroup. First, place the 3 under the ones column and the 1 above the tens column. Then, add the tens column (1 + 2 + 1), which equals 4. The problem should look like this:
1
2 6
+ 1 7
4 3
Note, you should regroup whenever a column in an addition problem adds up to more than 10. The process is the same when adding numbers that are more than two digits. You simply regroup the number above the next column to the left. For example:
1 1
1 7 5
+ 2 3 6
4 1 1
As before, you start with the ones column (5 + 6) which equals 11. You place the 1 in the ones column and regroup to the tens column. You then add the tens column (1 + 7 + 3), which equals 11. Again, place the 1 underneath the tens column and regroup to the hundreds column. Finally, add the hundreds column (1 + 1 + 2), which equals 4, giving you the total 411.
Regrouping in Subtraction
Regrouping in subtraction is slightly different from regrouping in addition. First, look at the following example:
3 2
– 1 7
1 5
In subtraction, you only regroup when the number on the bottom is greater than the number on top. A common expression to use when teaching this kind of regrouping to young kids is, ‘If there’s more on the floor, go next door!’ This means that if the number being subtracted is greater than the number it’s being subtracted from, you must regroup.
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