When adding three-digit numbers, you may need to trade ten ones for one ten, or ten tens for one hundred. This regrouping (carrying) allows you to solve additions like 187 + 125 correctly.
Start with base-ten blocks to physically show when ten ones must be traded for a ten. Gradually move to drawings, then to the abstract algorithm.
You already know how to add three-digit numbers when no place value overflows — you just line up hundreds, tens, and ones and add each column. You also know how to trade 10 ones for 1 ten. Now those two skills combine. When a column's sum reaches 10 or more, you can't fit it in one digit, so you regroup: carry 1 into the next column to the left and write only the leftover ones.
Take 187 + 125. Start with the ones: 7 + 5 = 12. You can't write "12" in the ones place, so you write the 2 and carry the 1 ten to the tens column. Now the tens: 1 (carried) + 8 + 2 = 11 tens. Again, too big for one digit — write 1 in the tens place and carry 1 hundred. Finally the hundreds: 1 (carried) + 1 + 1 = 3. Answer: 312. The key is that "carrying" isn't magic — it's the same trade you've always made, just happening inside the written algorithm.
The most common mistake is forgetting the carried digit. A good habit: before moving to the next column, check that you've written the carry mark above it. When you need to regroup twice in one problem — once in the ones and once in the tens — do it one column at a time, left to right from smallest place to largest. Each column is its own mini-problem; the only connection is the digit you carry forward. Keep that carry visible and the rest follows naturally.
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