The column method is a formal written procedure for adding or subtracting whole numbers and decimals of any size. Digits are aligned in place-value columns — ones under ones, tens under tens — and you work from right to left, carrying or borrowing between columns as needed.
Why use a written method rather than a calculator?
At KS3 you are expected to be fluent with at least one efficient written method, because:
- Non-calculator exam papers require it.
- Mental arithmetic becomes unreliable for large or messy numbers.
- A written method provides a clear record of your working, earning method marks even if you make a slip.
The column method is the most widely taught formal algorithm because it works for any numbers of any size and extends naturally to decimals.
How do you set up a column addition correctly?
- Write the numbers one above the other, aligning digits by place value. Ones under ones, tens under tens, hundreds under hundreds.
- For decimals, align the decimal points — this automatically aligns place-value columns.
- Work from right to left (from the smallest place value upwards).
Worked example 1: 3847 + 2569
3847
+ 2569
------
- Ones: 7 + 9 = 16. Write 6, carry 1.
- Tens: 4 + 6 + 1 (carried) = 11. Write 1, carry 1.
- Hundreds: 8 + 5 + 1 (carried) = 14. Write 4, carry 1.
- Thousands: 3 + 2 + 1 (carried) = 6. Write 6.
- Answer: 6416
How do you carry correctly?
When the sum in a column is 10 or more, write the units digit in that column and add the tens digit (always 1 for single-digit additions) to the next column to the left. This is called carrying.
The key habit: write the carried digit small above the next column so you do not forget it.
Worked example 2 (decimals): 12.74 + 8.6
- Align decimal points: write 8.6 as 8.60 to show there is a zero in the hundredths column.
12.74
+ 8.60
-------
- Hundredths: 4 + 0 = 4. Write 4.
- Tenths: 7 + 6 = 13. Write 3, carry 1.
- Ones: 2 + 8 + 1 = 11. Write 1, carry 1.
- Tens: 1 + 0 + 1 = 2. Write 2.
- Answer: 21.34
How do you set up column subtraction?
Write the larger number on top, the smaller below, aligned by place value. Work from right to left. When a digit in the top number is smaller than the digit below it, you must borrow (also called decomposition or exchange).
Worked example 3: 5034 − 1867
5034
- 1867
------
- Ones: 4 − 7. Cannot do. Borrow from the tens. The tens digit is 0 — so borrow from the hundreds: make the hundreds 10−1=9 (actually need to borrow from thousands to get the hundreds to work first).
| Column | Top | Bottom | Working |
|---|---|---|---|
| Thousands | 5 | 1 | Becomes 4 after lending to hundreds |
| Hundreds | 0 → 10 | 8 | Borrow from thousands; becomes 9 after lending to tens |
| Tens | 0 → 10 | 6 | Borrow from hundreds; becomes 9 after lending to ones |
| Ones | 4 → 14 | 7 | Borrow from tens; 14 − 7 = 7 |
Working right to left: 14−7 = 7; 9−6 = 3; 9−8 = 1; 4−1 = 3. Answer: 3167
Check: 3167 + 1867 = 5034 ✓ (always add back to verify a subtraction)
How do you subtract decimals?
Align the decimal points and fill any gaps with zeros so all rows have the same number of decimal places.
Worked example 4: 20 − 6.35
Write 20 as 20.00.
20.00
- 6.35
-------
- Hundredths: 0 − 5. Borrow. 10 − 5 = 5
- Tenths: 0 − 1 (borrow from ones) then − 3. Borrow from ones to get 10; 10 − 1 − 3 = wait — track borrowings:
- Hundredths: borrow from tenths: tenths becomes 9; 10 − 5 = 5
- Tenths: now 9; borrow from ones: 9 − 1 = 8; 8 becomes 10 after borrowing? Carefully: tenths digit is now 9 after giving 1 to hundredths. 9 − 3 = 6; but we borrowed, so tenths = 6 (we subtracted 3 from 9). Write 6.
A cleaner approach: 20 − 6.35 = 13.65. Use estimation first (about 14), then column subtraction confirms 13.65.
What mistakes should you avoid?
- Misaligning columns. The most common error: digits not in their correct columns. Always use squared paper or draw faint lines.
- Forgetting the carried digit. Write the carried 1 explicitly — do not try to hold it in your head.
- Borrowing from a zero without going further left. If the digit you need to borrow from is 0, you must go one more column left, borrow there, pass 10 across, and continue.
- Leaving out the decimal point. The decimal point in the answer must align directly below the decimal points in the calculation.
Frequently asked questions
How do I check a column addition answer quickly?
Round each number to 1 significant figure and add mentally. For 3847 + 2569: estimate 4000 + 3000 = 7000. The true answer 6416 is close to 7000, confirming it is plausible. If your answer were 64 160, the estimate immediately shows something is wrong.
Is there a way to subtract without borrowing?
Yes — the "equal additions" or "same change" method. Add the same amount to both numbers so the bottom number ends in a zero or becomes easier to subtract. For example, 53 − 28: add 2 to both → 55 − 30 = 25. This works because subtracting equal amounts from both numbers leaves the difference unchanged. Some teachers prefer "decomposition" (borrowing); choose whichever your school teaches and practise it consistently.
Does the method work for numbers with more than four digits?
Absolutely. The algorithm works column by column, so it scales to any number of digits. Five-digit, six-digit and decimal additions all follow the same process. The only practical challenge is keeping columns neatly aligned — use graph paper for very long calculations.
Can I add more than two numbers at once?
Yes. Add all numbers in each column in one step, carrying to the next column if the sum exceeds 9. For three numbers in the hundreds column totalling 17, write 7 and carry 1 (not 17). Some students find it easier to add two at a time: add the first two, then add the third to the result.
For guided KS3 number methods with Professor Pi, visit AI Tutors.