Adding and subtracting in columns

When the numbers are messy, the written column method always works. You write the digits one above the other, then go from right to left.

The setup

Always line up the same places under each other:

  2 4 5
+ 3 8 7
-------

Hundreds with hundreds, tens with tens, ones with ones. The bar separates the numbers from the answer.

Adding step by step

Step 1 — ones

Add the ones column: 5 + 7 = 12. The 12 is more than 9, so write 2 in the ones column and carry the 1 to the tens column (write a small "1" above the tens).

    ¹
  2 4 5
+ 3 8 7
-------
      2

Step 2 — tens

Add the tens column, including the carry: 4 + 8 + 1 = 13. Write 3 in the tens column and carry 1 to the hundreds.

  ¹ ¹
  2 4 5
+ 3 8 7
-------
    3 2

Step 3 — hundreds

Add the hundreds, including the carry: 2 + 3 + 1 = 6. Write 6 in the hundreds column.

  ¹ ¹
  2 4 5
+ 3 8 7
-------
  6 3 2

Done. 245 + 387 = 632.

What if the sum goes over 999?

Sometimes the hundreds column adds up to 10 or more. Then you carry one thousand — it appears as a 1 to the left of the hundreds.

  6 4 5
+ 4 7 8
-------
1 1 2 3

Step by step: 5 + 8 = 13 → write 3, carry 1. Then 4 + 7 + 1 = 12 → write 2, carry 1. Finally 6 + 4 + 1 = 11 → write 1 in hundreds and 1 in thousands.

Subtracting in columns

Subtraction is the same idea, but instead of carrying you borrow. If the top digit is smaller than the bottom one, take ten from the column to its left.

  4 2 3
- 1 5 8
-------

Step by step:

1. Ones: 3 − 8 doesn't work. Borrow 1 ten from the tens column — the ones become 13 and the tens column drops from 2 to 1. Now 13 − 8 = 5.
2. Tens: the 1 left there isn't enough — 1 − 5 doesn't work. Borrow from the hundreds — the tens become 11 and the hundreds column drops from 4 to 3. Now 11 − 5 = 6.
3. Hundreds: 3 are left. 3 − 1 = 2.

Final answer in columns:

  4 2 3
- 1 5 8
-------
  2 6 5

423 − 158 = 265.

Common mistakes

• Forgetting to carry / borrow. Always write the small "1" you carry; circle the digit you borrowed from.
• Lining up wrong. A 3-digit number under a 2-digit one needs the rightmost digits to match. Imagine an invisible 0 in front of the shorter number.

Try it

• ✏️ Column addition — 3 digits
• ✏️ Column subtraction — 3 digits

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