Beginner math lesson
Addition with carrying and regrouping
Carrying is really regrouping. When a column makes 10 or more, you trade 10 ones for 1 ten, 10 tens for 1 hundred, or 10 hundreds for 1 thousand.
Who this helps
This lesson is for students learning column addition, adults relearning paper-and-pencil arithmetic, and parents who want a clear way to explain why carrying works instead of treating it as a trick.
Step-by-step explanation
- Line up place values. Ones go under ones, tens go under tens, hundreds go under hundreds.
- Start with the ones column. Add the digits on the far right first.
- Regroup if the sum is 10 or more. Write the ones digit below the line and carry the tens digit to the next column.
- Add the carried number in the next column. The carried 1 is not extra. It represents one group of the next place value.
- Continue left. Regroup again if another column makes 10 or more.
- Check by estimating. Round the addends to see whether your exact answer is reasonable.
Worked examples
Example 1: Add with one carry
Add 48 + 27.
1 48 + 27 ---- 75
Ones: 8 + 7 = 15. Write 5 ones and carry 1 ten. Tens: 1 + 4 + 2 = 7 tens.
Answer: 75.
Example 2: Add three-digit numbers
Add 356 + 287.
11 356 + 287 ----- 643
Ones: 6 + 7 = 13, so write 3 and carry 1. Tens: 1 + 5 + 8 = 14, so write 4 and carry 1. Hundreds: 1 + 3 + 2 = 6.
Answer: 643.
Example 3: Add numbers with different lengths
Add 2,406 + 785.
1 2,406 + 785 ------- 3,191
Line up the ones digits before adding. Ones: 6 + 5 = 11. Tens: 1 + 0 + 8 = 9. Hundreds: 4 + 7 = 11, so write 1 and carry 1 thousand. Thousands: 1 + 2 = 3.
Answer: 3,191.
Common mistakes
- Not lining up the ones digits. In 2,406 + 785, the 5 belongs under the 6, not under the 0.
- Forgetting the carried 1. A carried number must be added into the next column.
- Writing 15 under one column. If the ones sum is 15, write 5 in the ones place and carry 1 ten.
- Carrying to the wrong column. A carry from the ones column goes to the tens column, not the hundreds column.
- Skipping the estimate check. If 356 + 287 gives 5,143, an estimate near 600 shows something went wrong.
Practice questions
- 36 + 28
- 57 + 16
- 84 + 49
- 238 + 157
- 406 + 295
- 728 + 186
- 1,245 + 689
- 3,508 + 2,764
Answer key
- 64
- 73
- 133
- 395
- 701
- 914
- 1,934
- 6,272