When the numbers are too big to do in your head, the column method comes to the rescue. You stack the digits in columns and work from right to left — ones first, then tens, hundreds, and thousands.
Set-up: line up the same places
The most important thing at the start — line up the same place values: ones under ones, tens under tens, hundreds under hundreds, and thousands under thousands.
2 4 7 5
+ 3 8 6 8
---------If one number is shorter, you can imagine a zero on the left:
0 4 9 6
+ 2 7 3 5
---------Column addition — with carrying
We add column by column from right to left. If a column sum is more than 9, you write the ones digit underneath and carry the ten over to the next column.
Example: 2,475 + 3,868
¹ ¹ ¹2 4 7 5
+ 3 8 6 8
─────────
6 3 4 3
Steps:
- Ones: 5 + 8 = 13 → write 3, carry 1 to the tens.
- Tens: 7 + 6 + 1 = 14 → write 4, carry 1 to the hundreds.
- Hundreds: 4 + 8 + 1 = 13 → write 3, carry 1 to the thousands.
- Thousands: 2 + 3 + 1 = 6 → write 6.
Answer: 6,343.
Column subtraction — with borrowing
In subtraction, the top digit in a column sometimes can't "afford" the bottom one. That's when we borrow ten from the column to the left.
Example: 6,042 − 2,875
⁵ ¹⁰ ³ ¹6 0 4 2
− 2 8 7 5
─────────
3 1 6 7
Steps:
- Ones: 2 − 5 doesn't work. Borrow from the tens: 4 → 3, the ones become 12. Then 12 − 5 = 7.
- Tens: After the borrow we have 3 − 7 — doesn't work. Borrow from the hundreds, but the hundreds are 0 — we have to borrow from the thousands instead. Hundreds become 10, then they lend on to the tens: hundreds 9, tens 13. Then 13 − 7 = 6.
- Hundreds: After the double borrow we have 9 − 8 = 1.
- Thousands: 6 shrank to 5 (because of the borrow). 5 − 2 = 3.
Answer: 3,167.
Borrowing across zeros is the trickiest part. It helps to say it out loud: "Can't borrow from zero, keep going left."
Estimate first to check yourself
Before you compute, round and estimate the answer. For 2,475 + 3,868 you'd round to 2,500 + 3,900 = 6,400. Your result 6,343 is close — the estimate matches.
If you'd somehow got 9,343, you'd know something went wrong — the answer should be near 6,400.
Related exercises
Try the column method in the generator:
- Add and subtract up to 10,000 — generates pairs of four-digit numbers.
- Find the missing number — the inverse of the same skill.
For the bigger picture: intro to this topic.