2 Digit Addition - With Regrouping

What is 2 Digit Addition?

2 digit addition is the process of adding numbers between 10 and 99. These numbers consist of a tens place and a ones place.

For example:

• 47 has 4 tens and 7 ones

• 32 has 3 tens and 2 ones

In double digit addition, we always align the numbers by their place value, placing ones under ones and tens under tens. Addition starts from the right (ones column) and moves to the left (tens column).

There are two main methods used in 2 digit addition:

• 2 digit addition without regrouping, where no carrying is needed

• 2 digit addition with regrouping, where carrying over to the next place value is required

Both methods follow the same basic structure but differ in whether or not you need to carry a digit to the next column.

Read More: 2 Digit Subtraction

When Do We Use 2 Digit Additions With Regrouping?

We use 2 digit addition with regrouping when the sum of the digits in the ones place is greater than 9. In such cases, the total cannot be written in a single digit, so we need to carry the extra value into the tens column. This process is known as regrouping.

For example:

If you add 7 and 5 in one place, the result is 12. You write 2 in the ones column and carry over 1 to the tens column.

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Steps to Solve 2 Digit Additions With Regrouping

Let’s understand the steps to solve 2-digit addition with regrouping with an example.

Example: Add 46 and 38

Step 1: Arrange the numbers or addends according to their place value, i.e., ones and tens column-wise. So, 7 and 6 will be placed under the ones column and 4 and 3 will come under the tens column.

Step 2: Start adding the numbers from the right, i.e., the ones column, and then move towards the left, i.e., the tens column. Here, 7 + 6 = 13

Step 3: If the sum in the ones column is more than 9, we obtain a double-digit number. te 3 in the ones column.

Step 4: While adding the tens column, we include the number that was carried over from the ones column.  So we add 4 + 3 + 1 (carry-over) = 8

Step 5: Once both columns are added, we write the final sum. After completing the addition, we get 47 + 36 = 83.

Read More: Multiplying Decimals

Steps to Solve 2-Digit Addition of Decimals With Regrouping

For decimals, we use the same steps as in whole-number addition. Regrouping is required when the sum of digits in the tenths column is greater than 9 (i.e., 0.9 or more). Let's understand the steps to solve 2-digit decimal addition with regrouping using an example.

Step 1: Arrange the numbers according to their place value, making sure to align the decimal points. The digits 7 and 6 are in the tenths column, and 4 and 2 are in the ones column.

Step 2: Start with the tenths column on the right. Add 7 and 6, which gives 13.

Step 3: Since 13 is a two-digit number, write 3 in the tenths column and carry over 1 to the ones column.

Step 4:  Move to the ones column and add the digits along with the carried-over 1.
4 + 2 = 6
6 + 1 = 7

Step 5: Write 7 in the ones column. The decimal point remains in its original position between the ones and tenths places. The result of adding 4.7 and 2.6 is 7.3.

2-Digit Decimal Addition Without Regrouping

Adding 2-digit decimal numbers without regrouping follows the same process as whole numbers. Let’s understand this with an example.

Example: Add 4.5 and 2.3

Step 1:  Arrange the numbers according to their place value, aligning the decimal points. Place the tenths digits (5 and 3) in the tenths column and the ones digits (4 and 2) in the ones column.

Step 2: Start with the rightmost column (tenths): 5 + 3 = 8. Move to the ones column and add 4 + 2 = 6.

Step 3: Combine the results of both columns to get the sum.

The sum of 4.5 and 2.3 is 6.8.

Note: The decimal point remains in its original position throughout the addition.

Read More: Rounding Numbers: Concept, Rules, and Examples

Steps to Solve 2-Digit Addition Without Regrouping 

2-digit addition without regrouping is used when the sum of digits in each column is 9 or less. In this case, there is no need to carry over, and the addition is completed directly column by column. Let’s understand the process with an example.

Example: Add 52 and 14

Step 1: Arrange the numbers according to their place values. Place the digits 2 and 4 in the ones column, and 5 and 1 in the tens column.

Step 2: Begin with the ones column. 

2 + 4 = 6

Step 3: Move to the tens column.
5 + 1 = 6

Step 4: Write the sum of each column in its respective place. The result of adding 52 and 14 is 66.

Also Read: Before Number Concept

2 Digit Additions With Regrouping Examples

1. Add the numbers 57 and 68 with regrouping.

Solution:

Place the numbers column-wise according to place value. Add the ones column: 7 + 8 = 15. Write 5 in the ones column and carry 1 to the tens column. Add the tens column: 5 + 6 + 1 (carry) = 12. Write 2 in the tens column and carry 1 to hundreds. The sum of 57 and 68 is 125.

2. Add the numbers 4.7 and 2.6 with regrouping.

Solution:

Align the decimal points and place the numbers column-wise. Add the tenths column: 7 + 6 = 13. Write 3 in the tenths place and carry 1 to the ones column. Add the ones column: 4 + 2 + 1 (carry) = 7. The sum of 4.7 and 2.6 is 7.3.

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