Addition of 3-Digit Numbers
Addition of 3-digit numbers means finding the total (sum) of two or more numbers that have three digits each. The process involves adding the ones first, then the tens, then the hundreds.
Sometimes the sum of digits in a column is 10 or more. In that case, we regroup (carry over) to the next place. Addition can be done with or without regrouping.
What is Addition of 3-Digit Numbers - Class 3 Maths (Addition and Subtraction (Grade 3))?
Addition is the process of combining two or more numbers to get a total called the sum.
Addend + Addend = Sum
Steps for column addition of 3-digit numbers:
- Write the numbers one below the other, aligning ones, tens, and hundreds.
- Add the ones column. If the sum is 10 or more, write the ones digit and carry the tens digit.
- Add the tens column (include any carry). Regroup if needed.
- Add the hundreds column (include any carry).
Solved Examples
Example 1: Addition Without Regrouping
Question: Add 234 + 512.
Think:
- Ones: 4 + 2 = 6
- Tens: 3 + 1 = 4
- Hundreds: 2 + 5 = 7
Answer: 234 + 512 = 746
Example 2: Addition With Regrouping in Ones
Question: Add 357 + 428.
Think:
- Ones: 7 + 8 = 15 → write 5, carry 1
- Tens: 5 + 2 + 1 (carry) = 8
- Hundreds: 3 + 4 = 7
Answer: 357 + 428 = 785
Example 3: Addition With Regrouping in Tens
Question: Add 463 + 291.
Think:
- Ones: 3 + 1 = 4
- Tens: 6 + 9 = 15 → write 5, carry 1
- Hundreds: 4 + 2 + 1 (carry) = 7
Answer: 463 + 291 = 754
Example 4: Addition With Regrouping in Both Ones and Tens
Question: Add 586 + 347.
Think:
- Ones: 6 + 7 = 13 → write 3, carry 1
- Tens: 8 + 4 + 1 = 13 → write 3, carry 1
- Hundreds: 5 + 3 + 1 = 9
Answer: 586 + 347 = 933
Example 5: Sum Exceeding 999
Question: Add 678 + 456.
Think:
- Ones: 8 + 6 = 14 → write 4, carry 1
- Tens: 7 + 5 + 1 = 13 → write 3, carry 1
- Hundreds: 6 + 4 + 1 = 11 → write 1 in hundreds, 1 in thousands
Answer: 678 + 456 = 1134 (a 4-digit number)
Example 6: Word Problem — School Supplies
Question: A school bought 325 notebooks and 248 pencils. How many items were bought in total?
Think:
- Ones: 5 + 8 = 13 → write 3, carry 1
- Tens: 2 + 4 + 1 = 7
- Hundreds: 3 + 2 = 5
Answer: The school bought 573 items in total.
Example 7: Adding Three 3-Digit Numbers
Question: Add 142 + 235 + 311.
Think:
- Ones: 2 + 5 + 1 = 8
- Tens: 4 + 3 + 1 = 8
- Hundreds: 1 + 2 + 3 = 6
Answer: 142 + 235 + 311 = 688
Example 8: Word Problem — Mango Trees
Question: A farm has 467 mango trees in one section and 385 in another. How many mango trees are there altogether?
Think:
- Ones: 7 + 5 = 12 → write 2, carry 1
- Tens: 6 + 8 + 1 = 15 → write 5, carry 1
- Hundreds: 4 + 3 + 1 = 8
Answer: The farm has 852 mango trees.
Example 9: Word Problem — Distance
Question: Kavi's family drove 256 km on day one and 178 km on day two. What was the total distance?
Think:
- Ones: 6 + 8 = 14 → write 4, carry 1
- Tens: 5 + 7 + 1 = 13 → write 3, carry 1
- Hundreds: 2 + 1 + 1 = 4
Answer: Total distance = 434 km.
Example 10: Adding with Zeros
Question: Add 500 + 307.
Think:
- Ones: 0 + 7 = 7
- Tens: 0 + 0 = 0
- Hundreds: 5 + 3 = 8
Answer: 500 + 307 = 807
Real-World Applications
Where is 3-digit addition used?
- Shopping: Buying two or more items and finding the total cost. A shirt costs ₹350 and trousers cost ₹475 — total = ₹825.
- School: Adding marks in different subjects: Maths (85) + Science (92) + English (78) + Hindi (88) = 343.
- Travel: Finding total distance by adding distances of different legs of a journey: 256 km + 178 km = 434 km.
- Attendance: Total students present = boys (267) + girls (298) = 565.
- Savings: Meera saved ₹425 in January and ₹387 in February. Total savings = ₹812.
Addition of 3-digit numbers is one of the most frequently used mathematical operations in daily life. From calculating bills to tracking scores, it appears everywhere.
Key Points to Remember
- Always write numbers column-wise, aligning ones under ones, tens under tens, hundreds under hundreds.
- Add from right to left: ones first, then tens, then hundreds.
- If a column sum is 10 or more, write the ones digit and carry the tens digit to the next column.
- The sum of two 3-digit numbers can be a 4-digit number (e.g., 678 + 456 = 1134).
- To check your answer, you can use estimation or add in a different order (addition is commutative).
Practice Problems
- Add 321 + 456.
- Add 487 + 365.
- Add 259 + 741.
- Ria has ₹435 and gets ₹289 more. How much does she have now?
- Add 600 + 399.
- Add 156 + 237 + 408.
- A library has 573 Hindi books and 468 English books. Find the total.
Frequently Asked Questions
Q1. What is regrouping in addition?
Regrouping (also called carrying) happens when the sum of a column is 10 or more. The ones digit stays in that column, and the tens digit is carried to the next column on the left.
Q2. Can the sum of two 3-digit numbers be a 4-digit number?
Yes. The largest sum is 999 + 999 = 1998, which is a 4-digit number. Any sum greater than 999 will be a 4-digit number.
Q3. Why do we add from right to left?
We start from the ones column because any carry from that column affects the tens column. If we started from the left, we would not know if there is a carry from the right.
Q4. What is the order property of addition?
Addition is commutative: changing the order of addends does not change the sum. 234 + 512 = 512 + 234 = 746.
Q5. How do I check if my addition is correct?
You can check by: (1) adding again in reverse order, (2) using estimation to see if the answer is reasonable, or (3) subtracting one addend from the sum to get the other.
Q6. What happens when we add 0 to a number?
Adding 0 to any number gives the same number. For example, 456 + 0 = 456. Zero is called the additive identity.
Q7. How is 3-digit addition different from 2-digit addition?
The process is the same — add column by column from right to left. The only difference is that 3-digit addition has an extra column (hundreds) to add.
Q8. Can I add more than two 3-digit numbers at once?
Yes. Write all numbers in columns and add each column. You may need to carry larger numbers (e.g., if three ones digits add to 25, write 5 and carry 2).
Related Topics
- Subtraction of 3-Digit Numbers
- Addition Word Problems (Grade 3)
- Addition Without Regrouping (3-Digit)
- Addition With Regrouping (3-Digit)
- Subtraction With Regrouping (3-Digit)
- Subtraction Without Regrouping (3-Digit)
- Subtraction Word Problems (Grade 3)
- Mental Math (Grade 3)
- Adding 4 or More Numbers
- Checking Addition and Subtraction
- Mixed Operations (Grade 3)
- Mixed Word Problems (Grade 3)
