Adding three-digit numbers is like adding two-digit numbers, with one more place: the hundreds. Add the ones, then the tens, then the hundreds.
Why it works
Each place holds 0 to 9. When the ones make 10 or more, 10 ones become a new ten. When the tens make 10 or more, 10 tens become a new hundred. Trading keeps the total the same and lets each place hold just one digit.
Worked example: No trades
Find $243 + 125$.
- Ones: $3 + 5 = 8$.
- Tens: $4 + 2 = 6$.
- Hundreds: $2 + 1 = 3$.
Answer: $368$
Worked example: Two trades
Find $367 + 258$.
- Ones: $7 + 8 = 15$. Write 5 and make a new ten.
- Tens: $6 + 5 + 1 = 12$ tens. Write 2 and make a new hundred.
- Hundreds: $3 + 2 + 1 = 6$.
Answer: $625$
Worked example: Add by place value
Find $467 + 258$ with expanded form.
- Hundreds: $400 + 200 = 600$.
- Tens: $60 + 50 = 110$.
- Ones: $7 + 8 = 15$.
- $600 + 110 + 15 = 725$.
Answer: $725$
Key idea
Add ones, tens, then hundreds. When a place gets 10 or more, trade 10 of them for 1 of the next place.
Common mistake
Squeezing a two-digit sum into one place. For $247 + 138$, the ones make $7 + 8 = 15$. Writing all of 15 in the answer gives 3715. A place holds only one digit: write 5 and trade the ten. The answer is 385. Check: 247 is close to 250 and 138 is close to 140, so the sum is close to 390, not thousands.
Grown-up tip: Graph paper helps keep the digits lined up in their places.