Adding and subtracting decimals

Adding and subtracting decimals

Adding and subtracting decimals

You already know how to add and subtract whole numbers in columns: ones under ones, tens under tens, hundreds under hundreds. Decimals work the same way — you just have one extra rule.

The one rule that matters

When you write decimals one under the other, the decimal point goes under the decimal point. Once the points line up, every other column lines up too: tenths under tenths, hundredths under hundredths.

That blue dashed line shows the rule: the decimal point in the answer sits right under the decimal points in the two numbers above.

Adding decimals — worked example

Let's work out 3.47 + 2.85 step by step.

  1. Write the two numbers one under the other, decimal points lined up.
  2. Start at the rightmost column — hundredths. 7 + 5 = 12. Write 2 under the hundredths and carry 1 to the tenths.
  3. Tenths: 4 + 8 + 1 (carried) = 13. Write 3 and carry 1 to the ones.
  4. Ones: 3 + 2 + 1 = 6.
  5. The decimal point in the answer goes straight under the others.

3.47 + 2.85 = 6.32

That's it. The trickiest part isn't the maths — it's keeping the columns straight on the page.

Subtracting decimals — worked example

Now let's try 7.20 − 4.65.

A tip: if one number has fewer decimal places, add zeros on the right so both have the same number of decimal places. Adding zero on the right of a decimal doesn't change its value: 7.2 = 7.20.

  1. 7.20 − 4.65. Hundredths column: 0 − 5 — too small. Borrow 1 tenth (it becomes 10 hundredths). Now 10 − 5 = 5.
  2. Tenths column: the 2 became 1 after borrowing. 1 − 6 — too small. Borrow 1 one (it becomes 10 tenths). 11 − 6 = 5.
  3. Ones column: 7 became 6. 6 − 4 = 2.
  4. Decimal point goes under the others.

7.20 − 4.65 = 2.55

Common mistakes to avoid

  • Ignoring the decimal point. Adding 3.47 and 2.5 isn't 3.47 + 2.5 = 5.97 done by squishing digits together — line them up: 3.47 + 2.50 = 5.97.
  • Forgetting the carried digit. Just like with whole numbers, when a column total is 10 or more, the extra goes to the next column on the left.
  • Subtracting the larger digit from the smaller in a column. You can't "skip" the borrowing — if the top digit is smaller, you borrow from the column on its left.

Real-life moments

  • You spent £4.30 and £2.95. Total: £7.25.
  • A bottle holds 1.50 litres. You drink 0.75 l. Left: 0.75 l.
  • Your jump was 1.42 m on the first try, 1.58 m on the second. Better by 0.16 m.

Practice