Column addition and subtraction

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 ¹
    2 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 ¹
    6 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.