Addition With Regrouping

Addition with regrouping is done when the sum of the addends exceeds 9 in any of the columns. The columns refer to the place value columns of ones, tens, hundreds, and so on, under which the addends are placed appropriately. We regroup this two-digit sum into tens and ones and then carry over the tens digit of the sum to the preceding column and write the ones digit in that particular column. Regrouping is a method that can be done while adding and subtracting any two or more numbers.

Addition with regrouping is a process of arranging numbers in columns of tens and ones for addition. Addition with regrouping is also known as addition with carrying. In addition with regrouping, we place two or more large numbers column-wise according to their place value, and when the sum of any of these columns is more than 9, we regroup that sum into tens and ones. Let us understand this with the help of the following example.

Example: Add 18 + 5

Solution: Let us add these numbers by regrouping.

• Step 1: Place 18 and 5 in proper columns according to their place values one below the other as shown above.
• Step 2: Add 8 and 5 which comes to 13. Since 13 has exceeded 9 we will regroup it. In other words, 13 is a two-digit number so we will regroup this sum into tens and ones. This means we will carry over the tens digit of the sum to the preceding column and write the ones digit in that particular column. Here, we will write 3 in ones column, and carry over 1 to the tens column.
• Step 3: This 1 which is a carryover in the tens column will be added to the existing number which is 1. So the sum of this column will be 2. Therefore, the sum of 18 + 5 = 23.

Addition with regrouping is also known as addition with carrying because we carry over a digit to the preceding column. This can be done with both 2-digit numbers, 3-digit numbers, or any other larger number. The most important part in addition with regrouping is arranging the numbers according to their place value, i.e., ones, tens, hundreds, and so on. The following steps explain the way in which we do addition with regrouping.

• Step 1: Arrange the numbers in columns according to their place values.
• Step 2: Just like normal addition, start adding from ones place, moving on to tens place, the hundreds place, and so on.
• Step 3: If the sum in any of the columns is more than 9, we regroup this sum into tens and ones. We write the ones digit of this sum under that particular column and we carry over the tens digit of the sum to the next column. This carried-over digit is added along with the addends of that specific column.
• Step 4: Once all the columns are added, we get the total sum.

Now, let us learn about 2-digit addition with regrouping and 3-digit addition with regrouping in the following sections.

In 2-digit addition with regrouping, we use the same steps as discussed above. Let us understand this with the help of an example.

Example: Add 38 + 26

Solution: Let us add these numbers using the following steps.

• Step 1: Arrange 38 and 26 column-wise according to their place value. So, 8 and 6 will come in ones column and 3 and 2 will come in the tens column.
• Step 2: Start adding the numbers in ones column, and we get 8 + 6 = 14. Since 14 exceeds 9, we need to regroup it. So, we write 4 in this column and carry over 1 to the next column.
• Step 3: Now we move on to the tens column and add the numbers along with the carried over number. This means it is 3 + 2 + 1 = 6. So, we write 6 as the sum of this column. Therefore, 38 + 26 = 64.

Now, let us understand 2-digit addition with regrouping.

3-digit addition with regrouping is similar to 2-digit addition with regrouping. Let us understand this with the help of the following example.

Example: Add 295 + 143

Solution: Let us add 295 +143 using the following steps.

• Step 1: Arrange 295 and 143 column-wise according to their place value. So, 5 and 3 will come in ones column, 9 and 4 will come in the tens column, and 2 and 1 will come under hundreds column.
• Step 2: Start adding the numbers in ones column, and we get 5 + 3 = 8.
• Step 3: Now we move on to the tens column and add the numbers, 9 + 4 = 13. Since 13 exceeds 9, we need to regroup it. So, we write 3 in this column and carry over 1 to the next column.
• Step 4: Now, we move on to the hundreds column and add the numbers along with the carried-over number. This means it will be 2 + 1 + 1 = 4. So, we write 4 as the sum of this column. Therefore, 295 + 143 = 438

Adding Decimals With Regrouping

For adding decimals with regrouping, we use the same steps as discussed above. However, we need to keep in mind that the decimal points should be aligned one below the other and we also need to take care of the decimal part that has different place values like tenths, hundredths and so on. Let us understand with the help of the following example.

Example: Add 15.5 + 3.9

Solution: Let us add these numbers using the following steps.

• Step 1: Arrange the numbers according to their place value, such that the decimals points are aligned one below the other as shown above.
• Step 2: Write zeros in the places wherever the length of decimal numbers is not the same.
• Step 3: Now add the decimal numbers in the same way as we add whole numbers. We start adding the numbers in the tenths column. This will be 5 + 9 = 14. Since 14 exceeds 9, we need to regroup it. So, we write 4 in this column and carry over 1 to the next column.
• Step 4: Now, we move on to the ones column and add the numbers along with the carried-over number. This means it will be 5 + 3 + 1 = 9. So, we write 9 as the sum of this column.
• Step 5: Now, we move on to the tens column and add the numbers, This is 1 + 0 = 1. Once all the columns are added, we get the total sum. Therefore, 15.5 + 3.9 = 19.4

☛ Related Topics

• Addition and Subtraction of decimals
• Properties of Addition
• Additions of Fractions

What is Addition With Regrouping?

Addition with regrouping is also known as addition with carrying. In addition with regrouping, we place two or more large numbers (addends) column-wise according to their place value, and when the sum of any of these columns is more than 9, we regroup that sum into tens and ones and carry over the tens digit to the next column. Addition with regrouping can be performed with 2-digit numbers, 3-digit numbers, and so on.

What is Addition with Carrying?

Addition with regrouping is also known as addition with carrying because we carry over a digit to the preceding column. This happens when we add large numbers. After arranging the addends into columns as per their place values, we start adding the numbers in each column and write their respective sums below them. If the sum of any of these columns exceeds 9, we regroup the sum into tens and ones such that we carry over the tens digit of the sum to the next column and write the ones digit in the same column. This carried-over number is added along with the addends of that particular column.

How to do Addition With Regrouping?

Addition with regrouping can be done using the following steps.

• Step 1: Arrange the numbers in columns according to their place values.
• Step 2: Just like normal addition, start adding the numbers under ones column, move on to the tens column, the hundreds column, and so on.
• Step 3: If the sum in any of the columns is more than 9, we regroup this sum into tens and ones. We write the ones digit of this sum under that particular column and we carry over the tens digit of the sum to the next column. This carried-over digit is added along with the addends of that specific column.
• Step 4: Once all the columns are added, we get the total sum.

How to do 2-Digit Addition With Regrouping?

2-digit addition with regrouping is done by placing the addends into appropriate columns according to their place value. For example, let us add 24 + 18.

• We start adding the numbers in ones column and then move on to the tens column. Here, 4 and 8 are in the ones column and 2 and 1 are in the tens column. We begin with adding 4 + 8 = 12.
• If the sum of the ones column exceeds 9 we regroup the sum into tens and ones. Then, we carry over the tens digit of the sum to the next column and write the ones digit in the same column. Here, 12 exceeds 9 so we regroup 12 in such a way that 2 is written in ones column and 1 is carried over to the next column.
• This carried-over number is added along with the addends of the tens column. In this case, when we add the numbers in the tens column, we get, 2 + 1 + 1 (carry-over) = 4. Hence, 24 + 18 = 42.

How to do 3-Digit Addition With Regrouping?

3-digit numbers are also added in the same manner as we add 2-digit numbers. The numbers are placed in columns according to their place value, i.e., ones, tens, and hundreds. For example, let us add 128 + 95.

• We start adding the numbers in ones column. Here, 8 + 5 = 13
• If the sum of any of the columns is more than 9, we regroup the sum into tens and ones. Then, we carry over the tens digit to the next column and write the ones digit in that particular column. So here 13 will be regrouped due to which 3 will be written under the ones column and 1 will be carried over to the tens column.
• The carried-over number is added along with the addends of that column. So when we move on to the tens column we add 2 + 9 + 1 = 12. This sum exceeds 9 so this too will be regrouped due to which 2 will be written in this column while 1 will be carried over to the hundreds column.
• Now, when we add the numbers in the hundreds column along with the carry-over, we get, 1 + 1 = 2.
• Therefore, 128 + 95 = 223.

What is the Difference Between Addition with and without Regrouping?

Addition with regrouping is done when the sum of any of the place value columns exceeds 9. We regroup the sum into tens and ones such that we carry over the tens digit of the sum to the next column and write the ones digit in the same column. This carried-over number is added along with the addends of that particular column. In addition without regrouping, the sum of any of the columns does not exceed 9 so we do not need to carry over any digit.