The ability to add and subtract decimal numbers accurately is essential for KS3 maths and for everyday tasks such as handling money and recording measurements. The column method makes the process straightforward, provided you follow one golden rule: always line up the decimal points before you begin.
What is the key rule for adding and subtracting decimals?
The golden rule is this: write the numbers in a column so that every decimal point is directly beneath the one above. This ensures that digits of the same place value — ones under ones, tenths under tenths, hundredths under hundredths — are in the same column and can be added or subtracted correctly.
Why does this matter? If you misalign the columns, you end up adding tenths to ones or hundredths to tenths, which gives a completely wrong answer. Getting the alignment right takes a moment to set up, but it prevents the most common errors in decimal arithmetic.
The decimal point in the answer goes directly below the decimal points in the question — never move it left or right.
How do I set up the column calculation for decimals?
Follow these three preparation steps before you begin any column calculation with decimals:
- Write the numbers in a column, decimal points aligned.
- Fill any gaps with zeros as placeholders so every number has the same number of decimal places. For example, 4.3 becomes 4.30 when the other number has two decimal places.
- Draw a line beneath the last number and write the decimal point of your answer directly below the column of decimal points.
Using zero placeholders does not change the value of a number — 4.3 and 4.30 are identical — but they prevent you from accidentally adding into an empty column.
Place-value column headings
| Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|
| 1 | 2 | . | 6 | 0 |
| 4 | . | 3 | 7 |
This layout shows 12.60 and 4.37 correctly aligned, ready for column addition.
How do I add decimals step by step?
Worked Example 1 — Calculate 3.47 + 2.85
3.47
+ 2.85
------
Work from right to left, exactly as with whole numbers:
- Hundredths: 7 + 5 = 12. Write 2, carry 1.
- Tenths: 4 + 8 + 1 (carried) = 13. Write 3, carry 1.
- Ones: 3 + 2 + 1 (carried) = 6.
- Tens: none.
Answer: 6.32 ✓
Check by estimation: 3.47 ≈ 3.5 and 2.85 ≈ 3; estimated total ≈ 6.5. The answer 6.32 is close, so it is plausible.
Worked Example 2 — Calculate 12.6 + 4.37
Write 12.6 as 12.60 (add a zero placeholder in the hundredths column):
12.60
+ 4.37
-------
- Hundredths: 0 + 7 = 7.
- Tenths: 6 + 3 = 9.
- Ones: 2 + 4 = 6.
- Tens: 1 + 0 = 1.
Answer: 16.97 ✓
Check by estimation: 12.6 ≈ 13 and 4.37 ≈ 4; estimated total ≈ 17. The answer 16.97 is sensible.
Worked Example 3 — Add three amounts: £24.60 + £7.85 + £3.09
24.60
+ 7.85
+ 3.09
-------
- Hundredths: 0 + 5 + 9 = 14. Write 4, carry 1.
- Tenths: 6 + 8 + 0 + 1 (carried) = 15. Write 5, carry 1.
- Ones: 4 + 7 + 3 + 1 (carried) = 15. Write 5, carry 1.
- Tens: 2 + 0 + 0 + 1 (carried) = 3.
Answer: £35.54 ✓
Check: £24.60 + £7.85 = £32.45; £32.45 + £3.09 = £35.54 ✓
How do I subtract decimals using the column method?
Subtraction with decimals follows exactly the same column method as subtraction with whole numbers — with the same alignment rule applied first.
Worked Example 4 — Calculate 8.5 − 3.27
Write 8.5 as 8.50 (add a zero placeholder in the hundredths column):
8.50
- 3.27
------
Work right to left, borrowing (exchanging) when needed:
- Hundredths: 0 − 7. Cannot subtract. Borrow 1 from the tenths column (tenths becomes 4). Hundredths becomes 10. 10 − 7 = 3.
- Tenths: 4 − 2 = 2.
- Ones: 8 − 3 = 5.
Answer: 5.23 ✓
Check: 3.27 + 5.23 → hundredths: 7+3=10 write 0 carry 1; tenths: 2+2+1=5; ones: 3+5=8 → 8.50 ✓
Worked Example 5 — Calculate 15.04 − 6.78
15.04
- 6.78
-------
- Hundredths: 4 − 8. Cannot subtract. Borrow from tenths. Tenths is 0, so borrow from ones (ones becomes 4, tenths becomes 10). Now borrow 1 for hundredths: tenths becomes 9, hundredths becomes 14. 14 − 8 = 6.
- Tenths: 9 − 7 = 2.
- Ones: 4 − 6. Cannot subtract. Borrow from tens. Tens becomes 0, ones becomes 14. 14 − 6 = 8.
- Tens: 0 − 0 = 0 (write nothing in the tens place).
Answer: 8.26 ✓
Check: 6.78 + 8.26 → hundredths: 8+6=14 write 4 carry 1; tenths: 7+2+1=10 write 0 carry 1; ones: 6+8+1=15 write 5 carry 1; tens: 0+0+1=1 → 15.04 ✓
How do I check my decimal calculation?
Three reliable checking strategies:
-
Estimate first. Round each number to the nearest whole number (or to one decimal place) and add or subtract mentally. If your exact answer differs significantly from the estimate, recheck your column work.
Example: 6.94 + 3.18 ≈ 7 + 3 = 10. Exact answer: 10.12. Sensible ✓.
-
Use the inverse operation. If you calculated A − B = C, verify by checking that B + C = A. This is demonstrated in the worked examples above.
-
Re-examine the decimal point. A very common slip is writing the answer without the decimal point, or placing it one column too far left or right. After every calculation, confirm the decimal point is directly below the column of decimal points in the question.
Where does decimal addition and subtraction appear in real life?
Mastering this skill opens up a wide range of real-world applications:
- Money: calculating the total cost of several items, working out change, splitting a bill between friends.
- Measurements in science: recording masses on a balance (e.g. 12.6 g + 4.37 g), calculating lengths in centimetres and millimetres, finding the difference between two temperatures.
- Sports and athletics: comparing race times (e.g. 9.58 s − 9.69 s), adding up distances in a triathlon.
- Engineering and construction: summing lengths of materials where fractions of a metre matter.
In each of these contexts, a misaligned decimal point can lead to an answer that is 10 or 100 times too large or too small — so the column-alignment habit is genuinely important beyond the exam hall.
Frequently Asked Questions
What happens if the numbers have different numbers of decimal places?
Write zero placeholders so that both (or all) numbers have the same number of decimal places, then proceed with the column method as usual. For example, when adding 5.4 and 2.136, write 5.400 so that all three decimal places are filled. The zero placeholders do not change the values — they simply ensure every column has a digit in it and nothing is accidentally left empty.
Can I use the column method for negative decimals?
At KS3 the column method is applied to positive numbers. When a subtraction would produce a negative result (for example 2.3 − 5.7), the approach is to swap the numbers (calculate 5.7 − 2.3 = 3.4) and then place a minus sign in front of the answer: −3.4. Full work with negative decimals and directed numbers is covered separately in the KS3 curriculum.
Is estimation always a good idea?
Yes — estimation is a quick sanity check that takes only a few seconds and catches the majority of careless errors. In an exam, show your estimate alongside your working; some mark schemes award a method mark for a reasonable estimate even if the exact calculation contains a slip. Always round to convenient values (nearest whole number, nearest 10, etc.) that you can calculate mentally.
Why do I need a zero placeholder — can I not just leave the space blank?
Leaving a column blank is risky because it is easy to slip a digit into the wrong column when working down a calculation. The zero acts as a visual anchor, keeping every digit in its correct place. In particular, subtracting from a blank space (as in Worked Example 4 above) requires a borrowing chain that is much easier to follow when you can see the 0 written in the column.
Struggling with a decimal calculation? Ask Professor Pi at aitutors.me for a step-by-step hint — without just being given the answer.