3-digit addition with regrouping, step by step
To add 3-digit numbers, line them up by place value and add the ones, then the tens, then the hundreds. When a column makes 10 or more, regroup (carry): write the ones digit and move the ten to the next column. This page shows why with base-ten pictures, works five examples, covers the mistakes children make, and has a tool that walks through any problem.
3-digit addition: the big idea
Adding 3-digit numbers is adding hundreds to hundreds, tens to tens and ones to ones. The only new part is what happens when a place gets 10 or more: 10 ones make 1 ten, and 10 tens make 1 hundred. That trade is regrouping.
How to add 3-digit numbers with regrouping
- Line up hundreds, tens and ones in columns.
- Add the ones. If the total is 10 or more, write the ones digit and carry 1 above the tens column.
- Add the tens, including any carried 1. Carry again if the total is 10 or more.
- Add the hundreds, including any carry.
- Check with an estimate, or subtract to undo it.
Try any addition problem
Type the problem from homework. The tool adds one column at a time and shows every carry.
Worked examples: 3-digit addition
Red 1s are carried digits.
Example 1: No regrouping
Each column adds to less than 10: 2 + 5 = 7, 4 + 3 = 7, 3 + 1 = 4.
Example 2: Regroup once, in the ones
8 + 7 = 15: write 5, carry 1 ten. Tens: 5 + 3 + 1 = 9. Hundreds: 2 + 1 = 3.
Example 3: Regroup twice
Ones: 8 + 6 = 14, write 4, carry 1. Tens: 7 + 5 + 1 = 13, write 3, carry 1. Hundreds: 4 + 2 + 1 = 7.
Example 4: Regroup into the thousands
Ones: 5 + 8 = 13, carry 1. Tens: 9 + 0 + 1 = 10, write 0, carry 1. Hundreds: 6 + 3 + 1 = 10. The answer has four digits: 1,003.
Example 5: Different lengths
Line up the ones: 7 + 6 = 13, carry. Tens: 0 + 9 + 1 = 10, carry. Hundreds: 4 + 1 = 5. The answer is 503.
Other ways to add 3-digit numbers
Partial sums
Add each place separately, then combine: 478 + 256 = (400 + 200) + (70 + 50) + (8 + 6) = 600 + 120 + 14 = 734. Many schools teach this before the column method.
Round and adjust
298 + 145: add 300 instead (445), then take away the extra 2: 443.
Common mistakes in 3-digit addition
How to teach 3-digit addition at home
Use money
$1 bills, dimes and pennies are hundreds, tens and ones. Ten pennies are swapped for a dime: that is carrying.
Estimate first
478 + 256 is about 500 + 250 = 750. An answer of 6,124 or 624 is obviously wrong.
Add up a receipt
Add two or three prices in whole dollars, like $145 + $238, then check with the receipt.
Partner check
One person adds, the other checks by subtracting. Swap roles.
3-digit addition by grade
- Grade 2 (2.NBT.B.7): add within 1,000 using models, drawings and place value.
- Grade 3 (3.NBT.A.2): add within 1,000 fluently.
- Grade 4 (4.NBT.B.4): the standard method for multi-digit addition.
The partner skill is 3-digit subtraction. Before this, children need addition facts to 20.
3-digit addition worksheets
3-digit addition worksheet: 50 problems with an answer key.
Make a fresh 3-digit addition test · Addition chart · All addition
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Questions parents ask
How do you add 3-digit numbers?
Line the numbers up by place value and add one column at a time, starting with the ones. If a column adds up to 10 or more, write the ones digit and carry the ten to the next column.
What is regrouping in addition?
Trading 10 of one place for 1 of the next: 10 ones for 1 ten, or 10 tens for 1 hundred. In 478 + 256, the 14 ones become 1 ten and 4 ones. Regrouping is the newer name for carrying.
Why do you start with the ones column?
Because carrying moves to the left. If you start on the left, a carry from the ones or tens would change a digit you have already written.
How can my child check a 3-digit addition?
Subtract one number from the answer; you should get the other number. For 478 + 256 = 734, check that 734 − 256 = 478. Estimating first also helps: about 500 + 250 = 750.
Can you add 3-digit numbers in your head?
Often, yes. Add the hundreds, then the tens, then the ones: 245 + 132 = 300 + 70 + 7 = 377. For numbers near a hundred, round and adjust: 298 + 145 = 300 + 145 − 2 = 443.
What grade learns 3-digit addition?
Grade 2 adds within 1,000 using blocks, drawings and place value (2.NBT.B.7). Grade 3 is expected to do it fluently (3.NBT.A.2), and grade 4 uses the standard method for any size of number.