Addition Algorithms
Learn how to add 3-digit numbers using the written algorithm, including how to carry when a column adds up to 10 or more.
What Is a Written Algorithm?
A written algorithm is a step-by-step method we write down to solve a maths problem. For addition, we line up numbers in columns — ones under ones, tens under tens, hundreds under hundreds — and add from right to left.
How to Set Out Your Addition
No carrying needed
Step 1 — Ones: 3 + 5 = 8. Write 8 in the ones column.
Step 2 — Tens: 4 + 3 = 7. Write 7 in the tens column.
Step 3 — Hundreds: 2 + 1 = 3. Write 3 in the hundreds column.
Answer: 378
Carrying (Regrouping)
When a column adds up to 10 or more, we write the ones digit in that column and carry the tens digit to the next column on the left. This is called regrouping.
Remember the Rule
If any column gives you 10 or more, write the last digit in that column and carry the first digit to the top of the next column.
Example: If ones column = 14, write 4 in the ones column and carry 1 to the tens column.
Addition with Carrying
Carrying from ones and tens
Ones: 7 + 8 = 15. Write 5, carry 1 to tens.
Tens: 5 + 6 + 1 (carried) = 12. Write 2, carry 1 to hundreds.
Hundreds: 2 + 1 + 1 (carried) = 4. Write 4.
Answer: 425
Checking Your Answer
Always check your addition by estimating first. Round each number to the nearest hundred and add them in your head. If your answer is close to your estimate, you are likely correct!
Estimate First
257 + 168 → about 300 + 200 = 500
Our answer was 425, which is close to 500. ✓
Add in a Different Order
Try adding the numbers the other way around. If 257 + 168 = 425, then 168 + 257 should also equal 425.
Key Vocabulary
Algorithm
A step-by-step method for solving a maths problem.
Carry (Regroup)
When a column adds to 10 or more, move the tens digit to the next column on the left.
Place Value
The value of a digit based on its position — ones, tens, or hundreds.
Estimate
A rough calculation to check if your answer makes sense.
Worked Examples
Calculate 312 + 245
Ones: 2 + 5 = 7. Write 7.
Tens: 1 + 4 = 5. Write 5.
Hundreds: 3 + 2 = 5. Write 5.
Answer: 557
Calculate 364 + 178
Ones: 4 + 8 = 12. Write 2, carry 1.
Tens: 6 + 7 + 1 = 14. Write 4, carry 1.
Hundreds: 3 + 1 + 1 = 5. Write 5.
Answer: 542
Sam has 246 stickers. He gets 385 more. How many does he have altogether?
Ones: 6 + 5 = 11. Write 1, carry 1.
Tens: 4 + 8 + 1 = 13. Write 3, carry 1.
Hundreds: 2 + 3 + 1 = 6. Write 6.
Answer: Sam has 631 stickers altogether.
Knowledge Check
Select the correct answer for each question.
Question 1: What is 134 + 253?
Question 2: What is 275 + 348?
Question 3: In 456 + 379, what do you carry from the ones column?
Question 4: Mia has 318 beads and buys 264 more. How many beads does she have now?
Question 5: What is 547 + 263?
Key Concepts Summary
- ●Line up digits in columns: ones, tens, hundreds.
- ●Always start adding from the ones column (right side).
- ●If a column adds to 10 or more, write the ones digit and carry the tens digit.
- ●Always add the carried digit at the top of the next column.
- ●Estimate first by rounding to check your answer makes sense.