What is “Regrouping” in Math?
Regrouping in math can be defined as the process of grouping numbers in tens while performing mathematical operations, such as addition and subtraction.
What is Addition with Regrouping?
The process of addition with regrouping involves adding each place value individually and eventually reaching the highest place. Regrouping is ideal for adding large numbers. For example, while adding 16 and 78, we will use the regrouping of places method.
First, write the equation in column form.
Now, if we try to add the ones first, that will be 6 + 8, which will give us 14. But we cannot write 14 in the ones place because only one digit can be placed in the ones place. This is where regrouping comes into action. In regrouping, we take 10 ones and convert them to 1 ten.
So, 6 + 8 will give us 14, which we can write as “one group of tens” and “four ones.”
We will write 4 in the ones column and 1 ten in the tens column. Now, it’s time to add the tens.
So, the sum is 94.
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Solved Examples on Addition Regrouping
Example 1: Find the sum of 29 and 35.
Solution: First, we will arrange the numbers in columns as per their place value.
Now, by adding the ones, 9 + 5, we will get 14. According to the regrouping of places, we have one group of tens and four ones. So, we carry over the “one” to the tens column.
Now, adding the tens, we will get 1 + 2 + 3 = 6
This gives us 64 as the sum.
Example 2: Jacob received 27 gifts for his birthday. His elder brother surprised him with 15 more gifts. How many gifts does Jacob have now?
Solution: The addition equation will look like, 27 + 15 = ?
Now, let us arrange the numbers in their columns.
Tens | Ones |
|---|---|
2 | 7 |
+ 1 | 5 |
When we add the ones, 7 + 5, we will get 12, which means 1 group of tens and 2 ones. So, we carry over the “one” to the tens.
Tens | Ones |
|---|---|
| \(^1~2\) | 7 |
1 | 5 |
2 |
Now, we will add the tens, 1 + 2 + 1 = 4
So, the sum will be,
Tens | Ones |
|---|---|
2 | 7 |
1 | 5 |
4 | 2 |
The sum is 42.
Jacob has 42 gifts in total.
Example 3: Find the sum of 48 and 35
Solution: Let us first arrange the numbers in columns as per their place value.
Tens | Ones |
|---|---|
4 | 8 |
+ 3 | 5 |
Now, we will add the ones, 8 + 5, which will give us 13. According to the regrouping of places, we have one group of tens and three ones. So, we will carry over the “one” to the tens column.
Now, it’s time to add the tens. 1 + 4 + 3 = 8
The sum will be 83.
Example 4: Jessica wrote 14 pages on Thursday. She wrote 37 pages on Friday and Saturday. How many pages did Jessica write in total?
Solution: According to the problem, the addition equation will be, 14 + 37 = ?
First, we will arrange the numbers in columns as per their place values.
Tens | Ones |
|---|---|
1 | 4 |
+ 3 | 7 |
Let us add the ones first. From the place value columns, 4 + 7 will give us 11. According to the regrouping of places, we have one group of tens and one group of ones. Now, we carry over the “one” to the tens.
After this, we will add the tens. 1 + 1 + 3 = 5
Jessica wrote 51 pages in total.
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Regrouping in addition is possible if a single digit is being added to a double digit and for double-digit additions. When the answer is greater than 10, regrouping in addition can be used.
Regrouping in math involves the method of creating groups of tens when adding two-digit numbers. It is another form of “carrying over.”