Long addition feels easier when every digit has a clear job. Let’s add 727 + 729, the example from this guide, one place at a time.
Line up the place values
Write hundreds under hundreds, tens under tens, and ones under ones. The two numbers each have 7 hundreds, 2 tens, and a final ones digit. Keeping the columns aligned prevents a common mistake: adding a ten to a one.
| Place | First number | Second number |
|---|---|---|
| Hundreds | 7 | 7 |
| Tens | 2 | 2 |
| Ones | 7 | 9 |
This table is the same information as a vertical written sum. It simply makes each place-value column explicit before regrouping begins.
Add from right to left
- Ones: 7 + 9 = 16. Write 6 in the ones place and carry 1 ten.
- Tens: 2 + 2 + 1 carried ten = 5 tens. Write 5.
- Hundreds: 7 + 7 = 14 hundreds. Write 14 in the remaining places.
The result is 1,456.
The carried 1 is a ten, not an extra one. That is why it is added in the tens column. The 14 hundreds in the last step are 1 thousand and 4 hundreds, which is how the written answer begins with 14.
Check with place value
Break the numbers apart: 727 = 700 + 20 + 7 and 729 = 700 + 20 + 9. Combine the parts: 1,400 + 40 + 16 = 1,456. Reaching the same result in two ways is a useful confidence check.
Why regrouping matters
“Carrying” is not a mysterious mark above the next digit. It records an exchange: 10 ones become 1 ten, and 10 tens become 1 hundred. A place-value chart or base-ten blocks can make that exchange visible. For this problem, combine 7 ones and 9 ones to make 16 ones; trade 10 of them for one ten and leave 6 ones in the answer.
Estimate before calculating, too. Both numbers are a little over 700, so the total should be a little over 1,400. An answer such as 456 or 14,560 would fail that quick sense check.
Practise at home
Invite a learner to explain each column aloud. Then try 456 + 378 = 834 and 619 + 524 = 1,143. The first problem involves regrouping in the ones and tens columns; the second crosses one thousand. Let the child use blocks or draw hundreds, tens and ones before moving to a compact written layout. Checking with subtraction or an estimate can be more valuable than racing to the next example.
If a child is still learning regrouping, practise smaller sums first. The addition practice hub and addition worksheets offer a place to build fluency before extending to three-digit calculations. A place-value explanation can help clarify why carrying one ten changes the next column.