3 Digit Addition

3-digit addition is the addition of numbers where either one or all the addends are of 3 digits. We know that addition is an operation used in Math to get the sum of numbers. While the addition of one-digit numbers can be done mentally, the addition of 3 digit numbers needs to follow some rules. 3 digit addition can be done with regrouping or without regrouping using the basic rules of addition. Let us learn more about 3-digit addition in this article.

In 3-digit addition, we need to place the given numbers into columns according to their respective place values, like ones, tens, hundreds, thousands, and so on. The addition of 3-digit numbers is similar to 2-digit numbers where numbers can be added without regrouping (carrying) or with regrouping. It should be noted that the numbers that are being added are called addends and the answer that is obtained after adding these numbers is called their sum. Let us see the basic steps that are followed in 3-digit addition.

• Step 1: Place the given numbers (addends) one below the other in such a way that they fall correctly under the columns of ones, tens, and hundreds.
• Step 2: Start adding the numbers from right to left beginning from the ones column, followed by the tens column and then the hundreds column.
• Step 3: After all the columns are added, we get the sum of the given numbers.

While adding 3-digit numbers, if the sum of any 2 digits is less than or equal to 9, we write the sum below the respective column and after all the columns are added, the answer is obtained. This is called addition without regrouping. For example, let us add the numbers 148 and 431 to see 3-digit addition without regrouping.

Let us understand 3-digit addition with the help of the following steps:

• Step 1: Add the numbers under the ones column. 8 + 1 = 9. Write the sum (9) in ones column.
• Step 2: Add the numbers under the tens column. 4 + 3 = 7. Write the sum (7) in the tens column.
• Step 3: Add the numbers under the hundreds column. 1 + 4 = 5. Write the sum (5) in the hundreds column.

Thus, the sum of the numbers 148 and 431 is 579.

Regrouping is another name for carrying over. In the operation of addition, when the sum of the addends is greater than 9 in any of the columns, we regroup the numbers and carry over the extra digit to the preceding column. Let us understand this with the help of the following example, let us add 582 and 173.

Let us understand 3-digit addition with regrouping using the following steps:

• Step 1: Add the numbers under the ones column. 2 + 3 = 5. Write 5 in ones column.
• Step 2: Add the numbers under the tens column. 8 + 7 = 15. Write 5 in the tens column and carry 1 to the hundreds column. We did this step because after adding 8 and 7 we get 15, but we cannot place 15 in the tens column because we can write just one digit below each column. So, we regroup the number 15. For this, we place the 5 in the tens column (corresponding column) and place the 1 on top of the hundreds column (the preceding column). In other words, when we get two-digit numbers as the sum, we place the ones digit in the corresponding column and we carry over the tens digit to the next column to the left. This carry-over is added in that column where it is placed and the addition continues.
• Step 3: Add the numbers in the hundreds column. This means, 5 + 1 + 1 (carry-over ) = 7. Here, after the carry-over is placed in the hundreds column, it is added along with the other addends.

Thus, the sum of the numbers 582 and 173 is 755.

☛ Related Articles

• 2-Digit Addition
• 2-Digit Subtraction
• 2-Digit Multiplication
• 3-Digit Subtraction
• 3-Digit Multiplication
• 4-Digit Addition
• 4-Digit Subtraction
• Addition With Regrouping
• Addition and Subtraction of Decimals

What is 3-Digit Addition in Math?

3-digit addition is the addition of numbers where either one or all the addends are of 3 digits. 3 digit addition can be done with regrouping or without regrouping using the basic rules of addition. We usually use the column addition method to add 3 digit numbers, where we place the given addends one below the other according to their place values and start adding them, beginning from the ones column, then, moving on to the tens column and then the hundreds column.

What is 3-Digit Addition With Regrouping?

Regrouping is another name for carrying over. In the addition operation, when the sum of the addends is greater than 9 in any of the columns, it is called regrouping or addition with carrying over. For example, let us add 487 and 143 and understand 3-digit addition with regrouping using the following steps.

• Step 1: Place the given numbers one below the other according to their place values.
• Step 2: Add the numbers under the ones column. 7 + 3 = 10. Now, we cannot place '10' in ones column since we can write only one digit below each column, so we regroup the number 10. For this, we write 0 in ones column and carry 1 to the tens column. This 1 (carry-over) will be added along with the numbers in the tens column.
• Step 3: Add the numbers in the tens column. This means, 8 + 4 + 1 (carry-over) = 13. We will again regroup 13 and write 3 in the tens column and carry 1 to the hundreds column.
• Step 3: Add the numbers in the hundreds column. This means, 4 + 1 + 1 (carry-over) = 6. Thus, the sum of the numbers 487 and 143 is 630.

How to do 3-Digit Addition?

3-digit addition is the addition of numbers in which any one addend or all the addends have 3 digits. We can add 3-digit numbers by writing them into columns according to their place values. Then, we begin adding the numbers from the ones columns, moving on to the tens column, and then the hundreds column. For example, to add 342 + 123, we add the digits under the ones column (2 + 3 = 5). Then, we add the digits under the tens column (4 + 2 = 6). Then, we add the digits in the hundreds column, (3 + 1 = 4). So, the sum of the given numbers 342 and 123 is 465.

What is 3-Digit Addition Without Carrying?

While adding 3-digit numbers, if the sum of any 2 digits is less than or equal to 9, we write the sum below the respective column and after all the columns are added, the final answer is obtained. This is called addition without carrying or regrouping. For example, let us add the numbers 412 and 243 and see 3-digit addition without regrouping.

• Step 1: Add the numbers under the ones column. 2 + 3 = 5. Write the sum (5) in ones column.
• Step 2: Add the numbers under the tens column. 1 + 4 = 5. Write the sum (5) in the tens column.
• Step 3: Add the numbers under the hundreds column. 4 + 2 = 6. Write the sum (6) in the hundreds column.

Thus, the sum of the 3-digit numbers 412 and 243 without carrying, is 655.

What is 3-Digit Addition and Subtraction with Regrouping?

In the operation of addition, regrouping is also known as carrying, while in subtraction, regrouping is known as borrowing. For example, in 3-digit addition, sometimes the sum of two numbers is more than 9. In this case, we regroup the sum by carrying over the extra digit to the preceding column. For example, let us add 148 and 124.

• Step 1: Add the numbers under the ones column. 8 + 4 = 12. Now, we cannot place '12' in ones column because we can write only one digit below each column, so we regroup the number 12. For this, we write 2 in ones column and carry 1 to the tens column. This 1 (carry-over) will be added along with the numbers in the tens column.
• Step 3: Add the numbers in the tens column. This means, 4 + 2 + 1 (carry-over) = 7.
• Step 3: Add the numbers in the hundreds column. This means, 1 + 1 = 2. Thus, the sum of the numbers 148 and 124 is 272.

In case of 3-digit subtraction, sometimes, a digit in the upper row is smaller than the digit in the lower row. In this case, we borrow a number from the preceding column so that the smaller minuend becomes bigger than the subtrahend. This is called regrouping or borrowing, For example, let us subtract 478 from 792.

• Step 1: Arrange the numbers according to their place value. Start subtracting the digits from ones place. We can see that 2 is smaller than 8. So, we will borrow 1 from the tens column which will make it 12. So, 12 - 8 = 4. This is known as regrouping or borrowing in subtraction. Now, we will write 4 under the ones column.
• Step 2: After giving 1 to the ones column in the previous step, the '9' in the tens column changes to 8. Now, let us subtract the digits at the tens place and write 1 under the tens column (8 - 7 = 1).
• Step 3: In the hundreds column, we will subtract 4 from 7 and write 3 in the column. (7 - 4 = 3). Thus, after subtracting the given numbers by regrouping, we get the difference as 314.