What is Regrouping in Addition?
Regrouping in math is the process of creating groups of tens while carrying out operations like addition for two-digit numbers, or while adding bigger numbers. The regrouping is done as per the place value of the digits in the numbers being added.
For example, while adding two two-digit numbers, such as 16 and 15, you will need to regroup. When you add 6 and 5, you get 11, or “one” ten and “one” one. This is where regrouping steps in. You regroup the tens into the tens column (carrying over in simple terms) and leave the ones in the ones column.
How do we use Partial Sums to Add?
In the partial sums method, the numbers are added in parts according to their place value. Then the partial sums are added together to get the resultant sum.
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Solved Examples
Example 1: Find: 28 + 34.
Solution: Let us use both the regrouping method and the partial sums method to find the total of 28 + 34.
Regrouping:
We will arrange the numbers in columns as per their place value.
2 8
+ 3 4
———
First, by adding the ones, 8 and 4, we will get 12. According to the regrouping of places, we have one group of tens and two ones. So, we “carry over” the one to the tens column.
| \(^1~2\) | 8 |
|---|---|
3 | 4 |
2 |
Now, adding the tens, we will get: 1 + 2 + 3 = 6
| \(^1~2\) | 8 |
|---|---|
3 | 4 |
6 | 2 |
The sum is 62.
Partial Sums:
Let us first arrange the numbers as per their place value.
Tens | Ones |
|---|---|
2 | 8 |
3 | 4 |
Now, we will find the partial sums.
After adding the partial sums, the total comes to 62.
As you can see, both methods give the same answer.
Example 2: 74 + 16 = ?
Solution: Let us find the solution by applying the regrouping and partial sums methods.
First, arrange the numbers as per their place value.
Tens | Ones |
|---|---|
7 | 4 |
1 | 6 |
Now, we can use regrouping of places or partial sums to find the total.
With the regrouping method, we will add the ones, 4 and 6, and that will give us 10. Now we have one group of tens and zero ones. So, we carry over the “one” to the tens column.
\(^1~7\) | 4 |
|---|---|
1 | 6 |
0 |
Let us now add the tens: 1 + 7 + 1 = 9.
\(^1~7\) | 4 |
|---|---|
1 | 6 |
9 | 0 |
The sum is 90.
In the partial sums method, we will arrange the numbers as per their place value.
Tens | Ones |
|---|---|
7 | 4 |
1 | 6 |
Let us now find the partial sums.
The sum is 90.
Example 3: Find: 43 + 17 + 37
Solution: While adding three two-digit numbers, we can take up the addition in any of the following ways.
So, let us arrange the numbers into columns.
Tens | Ones |
|---|---|
| \(^1~4\) | 3 |
1 | 7 |
+3 | 7 |
9 | 7 |
Thus, the answer is 97.
Example 4: Add: 15 + 34 + 11
Solution: Let us use the regrouping of places method to find the sum.
1 | 5 |
|---|---|
3 | 4 |
+ 1 | 1 |
Here, we can add the first two digits in the ones place or the latter two digits in the ones place.
| \(^1~1\) | 5 |
|---|---|
3 | 4 |
+ 1 | 1 |
6 | 0 |
The answer is 60.
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Regrouping of places is highly essential for younger kids as they are taught to add two or more numbers in the classroom. In the column method of addition, the numbers are arranged vertically, which is visually engaging and quick to learn.
In both methods, children are taught to add numbers of two or more digits that are placed in columns as per their place values. This enables flexibility among the students as they learn both methods.