Summarize this article:
295 LearnersLast updated on December 12, 2025
3-Digit Addition
3-digit addition is a basic arithmetic operation where each addend has three digits. One-digit addition can be performed easily, often using mental math. In 3-digit addition, we add two or more numbers together with or without regrouping. In this article, we will learn how to perform 3-digit addition and its key steps in detail.
What is Addition?
There are four basic arithmetic operations in math:
- Addition
- Subtraction
- Multiplication
- Division.
Addition is a mathematical operation where we add two or more numbers together to find the result. The result of adding numbers is known as the sum. The symbol used to represent addition is ‘+’.
In our daily life, we use addition to calculate quantities and measure values. For example, to calculate the daily income, scores on exams, or to calculate the score in games.
What is 3-Digit Addition?
3-digit addition is the process of adding numbers that have three digits. Every addition has two parts: addends and sum. The numbers you are adding are called addends, and the result is called the sum.
To add 3-digit numbers, we arrange the numbers according to place value and add the digits in the same place (ones, tens, hundreds). 3-digit numbers range from 100 to 999. Addition can be done with or without carrying (regrouping).
Steps to Add 3-Digit Numbers
Step 1: Arrange the numbers one below the other according to their place values (ones, tens, hundreds).
Step 2: Start adding from right to left: first the ones, then the tens, then the hundreds.
Step 3: Write the final result as the sum.
Examples (without regrouping):
\( \begin{array}{r} 234 \\ + 123 \\ \hline 357 \end{array} \)
Ones: 4 + 3 = 7
Tens: 3 + 2 = 5
Hundreds: 2 + 1 = 3
What is 3-Digit Addition Without Regrouping?
3-digit addition without regrouping is when the sum of the digits in each place (ones, tens, hundreds) is nine or less, so we do not need to carry. We add the numbers in the same place and write the result below.
Steps to Add 3-Digit Numbers Without Regrouping
Write the numbers in columns according to ones, tens, and hundreds.
Add the ones column and write the result in the ones place.
Add the tens column and write the result in the tens place.
Add the hundreds column and write the result in the hundreds place.
The final answer is the sum.
Example:
Add 257 + 432
\( \begin{array}{r} 257 \\ + 432 \\ \hline 689 \end{array} \)
Ones: 7 + 2 = 9
Tens: 5 + 3 = 8
Hundreds: 2 + 4 = 6
Explore Our Programs
What is 3-Digit Addition With Regrouping?
3-digit addition with regrouping is used when the sum of the digits in any place (ones, tens, hundreds) is more than 9. In this case, we carry over the extra value to the next column on the left.
Steps to Add 3-Digit Numbers With Regrouping
Write the numbers in columns according to ones, tens, and hundreds.
Add the ones column. If the sum is more than 9, write the ones digit and carry over the tens digit to the tens column.
Add the tens column, including any carry over. If the sum is more than 9, write the ones digit and carry over the tens digit to the hundreds column.
Add the hundreds column, including any carry over.
The final answer is the sum.
Example:
Add 671 + 154
\(\begin{array}{r} 671 \\ + 154 \\ \hline 825 \end{array} \)
Ones: 1 + 4 = 5 → write 5
Tens: 7 + 5 = 12 → write 2, carry 1 to hundreds
Hundreds: 6 + 1 + 1 (carry) = 8 → write 8.
Tips and Tricks to Master 3-Digit Addition
3-digit addition means adding numbers from 100 to 999 by lining up ones, tens, and hundreds and adding from right to left. Parents and teachers can help children learn carrying over and place values.
- Line up the digits in columns (ones, tens, hundreds). Parents and teachers can help children do this carefully.
- Start adding from right to left: ones first, then tens, then hundreds.
- Add each place separately.
Example:
Add 722 + 536
Hundreds: 700 + 500 = 1200
Tens: 20 + 30 = 50
Ones: 2 + 6 = 8
Sum: 722 + 536
= 1258
- Carry over if a column adds to more than 9. Parents and teachers can remind children to carry over to the next column on the left.
- Use a place-value chart to make it easier to read the numbers correctly.
Common Mistakes and How to Avoid Them on 3-Digit Addition
3-digit addition is a simple arithmetic operation that enhances our basic mathematical skills and problem-solving abilities. However, students often make some mistakes when they work with this type of addition and derive incorrect sums. Here are some common errors and helpful solutions to avoid these mistakes.
Mistake 1
Incorrect Alignment of 3-Digits Number
Students sometimes misalign the digits, which can lead to errors. So always place the 3-digit number based on their place values, to avoid confusions and errors.
For example, add 176 + 171.
Writing it as:
176 +
171
-------
247
-------
This is incorrect.
It should be correctly aligned as:
176
+ 171
-------
247
-------
Mistake 2
Forgetting to Carry Over the Value
If the sum of digits in any column is greater than 9, then carry over the extra value to the next place value column on the left. Otherwise, the final answer will be incorrect if the extra value is not carried over to the next column.
For example, add 329 and 126.
329
+ 126
-------
455
-------
The sum of 329 and 126 is 455.
Mistake 3
Starting the Addition from the Left Side
When adding 3-digit numbers, students sometimes start from left to right, which is incorrect. So, always remember that the addition should start from the right, that is from the one's place, then tens, hundreds.
Mistake 4
Doing Mental Calculations When Adding 3-digit Numbers
Performing mental calculations with 3-digit numbers may lead to incorrect answers. If the given numbers are large, then perform the addition on paper to make it easier to get the correct answer.
For instance, add 987 and 938, 987 + 938 = 1925
It is difficult to calculate mentally, so it is better to do the addition with the help of a pen and paper.
Mistake 5
Forgetting to Check the Final Result
Once the addition is completed, check whether the answer is right or wrong. Some students ignore the double-check step and end up with incorrect sums. So, check the answer for better accuracy.
Real-life Applications of 3-Digit Addition
In our daily lives, we use 3-digit addition in various situations, from counting to planning events for a large group. Here are some real-world applications of this type of addition.
- Shopping: While shopping, we need to calculate the total cost of multiple items to know the total expenditure. If the prices are larger than 100 and less than 999, we can use the 3-digit addition.
For example, if we buy 3 pieces of furniture for $321, $542, and $873, then the total price will be:
$321 + $542 + $873 = $1736
- Travelling: When we go on a tour or travel long distances, we can use 3-digit addition to calculate the distance we cover.
For example, if we drive 130 km to Georgia, then 432 to Washington, the total distance we cover is: 130 + 432 = 562 km
- Planning events: If we plan a function, events or conferences, we must calculate the number of guests who will attend the event to provide essential items.
For instance, if we are planning an event and need to invite 200 relatives, 100 friends, and 200 others, then the total number of guests will be:
200 + 100 + 200 = 500 guests.
- Banking and Finance: When we invest in banks, we must calculate our savings to know the balance.
For instance, if we invest $100 in January and $650 in April, then the total balance is:
100 + 650 = $750
- Counting population: 3-digit additions are used to count the total number of individuals for making records.
For example, if a hospital has 102 patients in ICU and 210 patients in general ward, then the total number of patients are 102 + 210 = 312
Solved Examples of 3 Digit Addition
Problem 1
Perform 3-digit addition on the given numbers: 349 + 276
625
Explanation
To perform 3-digit addition, first, we need to arrange the given numbers according to their place values.
Then, the problem becomes:
349
+ 276
- To begin with, add the numbers under the ones place column.
9 + 6 = 15
Write 5 in the ones place and carry over 1 to the tens place.
- Next, add the numbers in the tens place.
4 + 7 + 1 (carry over) = 12
Write 2 in the tens place and carry over 1 to the hundreds place.
- Finally, add the numbers in the hundreds place.
3 + 2 + 1 (carry over) = 6
Write 6 in the hundreds place.
- 349 + 276 = 625
Hence, the sum of the 3-digit numbers 349 and 276 is 625.
Problem 2
Find the sum of 285 and 198.
483
Explanation
We need to arrange the numbers based on their place values.
285
+ 198
We will start the addition from right to left.
- First, add the numbers in the ones place.
5 + 8 = 13
Write 3 in the ones place and carry over 1 to the tens place.
- Next, add the numbers in the tens place.
8 + 9 + 1 (carry over) = 18
Write 8 in the tens place and carry over 1 to the hundreds place.
- Finally, add the numbers in the hundreds place.
2 + 1 + 1 (carry over) = 4
Write 4 in the hundreds place.
- 285 + 198 = 483.
Therefore, the sum of 285 and 198 is 483.
Problem 3
Add the 3-digit numbers: 611 + 477.
1088
Explanation
Here, we have to add the 3-digit numbers:
611
+ 477
- Let us start by adding 1 and 7 in the ones place:
1 + 7 = 8
- Next, add the numbers in the tens place.
1 + 7 = 8
- Finally, add the numbers in the hundreds place.
6 + 4 = 10
As, the sum is 10, so we write the 0 in hundreds places and carry 1 to the thousands place.
- So, 611 + 477 = 1088
Hence, the total when 611 and 477 are added together is 1088.
Problem 4
Find the sum of 976 and 832.
1808
Explanation
To begin with, arrange the numbers according to their place value.
976
+ 832
- First, add the numbers in the ones place.
6 + 2 = 8
Write 8 in the ones place.
- Secondly, add the numbers in the tens place.
7 + 3 = 10
Write 0 in the tens place and carry over 1 to the hundreds place.
- Finally, add the numbers in the hundreds place.
9 + 8 + 1 (carry over) = 18
As the sum is 18, we write 8 in hundreds place and carried over 1 to thousand place
- Write the final result as the sum.
976 + 832 = 1808
Hence, adding the 3-digit numbers 976 and 832 gives a sum of 1808.
Problem 5
Perform 3-digit addition on the given numbers: 543 + 281.
824
Explanation
We need to perform 3-digit addition on the given numbers:
543
+ 281
- First, add the numbers in the ones place.
3 + 1 = 4
Write 4 in the ones place.
- Next, add the numbers in the tens place.
4 + 8 = 12
Write 2 in the tens place and carry over 1 to the hundreds place.
- Finally, add the numbers in the hundreds place.
5 + 2 + 1 (carry over) = 8
Write 8 in the hundreds place.
- 543 + 281 = 824
Therefore, when you add 543 and 281, the result is 824.
FAQs on 3-Digit Addition
1.How to explain 3-digit addition to my child?
2.How to teach my child to do 3-digit addition with regrouping?
3.How to teach my child 3-digit addition without regrouping?
4.How do I check whether the sum done by my child is correct or not?
5.State whether the following additions done by my child are true or false for 3-digit addition. a) 199 + 421 = 620 b) 650 + 262 =922
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
