Adding and subtracting decimal numbers

Point under point and you are off

You already know column addition from Number kid: ones under ones, tens under tens. With decimal numbers the same holds — just one extra rule: the point must sit under the point.

Why? Because you can only add the same things. Korunas with korunas, hellers with hellers. When you line up the points, the wholes line up under wholes and the tenths under tenths on their own. When you do not line them up, you add korunas to hellers — and you get nonsense.

Second helper: pad with zeros. When you count 5 − 1.75, write the five as 5.00. Suddenly it has somewhere to borrow from and it counts just like whole numbers.

The rest you already know: you add by columns from the right, you carry a one, when subtracting you borrow. Nothing new under the sun — you just watch one point. Today we polish it on shopping and pocket money.

Jonáš is saving for a game that costs 250 Kč. In his tin he has 187.50. “How much am I short?” He takes paper and writes 250 minus 187.50 — but he throws the numbers under each other however they fall, and he gets nonsense over a hundred korunas. Sofie looks over his shoulder: “You have the point next to the point. Write 250 as 250.00 and line the points up under each other.” Jonáš rewrites it, subtracts by columns and gets 62.50. “So two lots of pocket money and I have it,” he grins. One straight point saved a lot of mess.

💡

始める前に counting, estimate the result to whole korunas: 12.90 + 4.50 is about 13 + 5 = 18. If you then get 174, you know at once that the point got lost.

Method: line up, pad, count

Adding and subtracting decimal numbers has three steps:

Step 1: Write the numbers under each other so the point sits under the point. That lines up wholes under wholes, tenths under tenths, hundredths under hundredths. Do not line the numbers up to the right like whole numbers — here the point is in charge.

Step 2: Pad the shorter number with zeros. From 2.5 + 1.25 you make 2.50 + 1.25. Zeros change nothing, but the columns are full and you have no holes where mistakes happen.

Step 3: Count from the right by columns like with whole numbers. Carrying a one works the same (10 hundredths = 1 tenth, 10 tenths = 1 whole). When subtracting you borrow just like before. At the end copy the point down to the same place — in the result it belongs exactly under the points above.

And always at the start or the end: an estimate. 187.50 + 62.50 should be about 190 + 60 = 250. The estimate is your detector of a lost point — the most common mistake is not in the adding, but in a shifted point.

Work out 2.5 + 1.25

I write them under each other, point under point, and pad with a zero:

  2.50
+ 1.25
------
  3.75

From the right: hundredths 0 + 5 = 5. Tenths 5 + 2 = 7. Wholes 2 + 1 = 3. I copy the point down.

Estimate to check: about 2.5 + 1.3 = not quite 4. The result 3.75 fits. If I did not line up the points and added 25 + 125, I would get nonsense.

Work out 5 − 1.75

Five is a whole number — I write it as 5.00 so it has columns:

  5.00
− 1.75
------
  3.25

Hundredths: 0 − 5 does not go, I borrow → 10 − 5 = 5. Tenths: 0 became 9 after the borrow… careful, step by step: from 0 tenths I also have to borrow from the wholes. Result by columns: 3.25.

Check by adding: 3.25 + 1.75 = 5.00. It fits — a check the other way round is the fastest check of subtraction.

Shopping: does Ema fit into a fifty-koruna note?

Ema buys a roll for 3.50, yoghurt for 12.90 and juice for 24.90.

First an estimate: 4 + 13 + 25 = 42. It should come out.

Exactly, in pairs: 3.50 + 12.90 = 16.40. Then 16.40 + 24.90 = 41.30.

Total 41.30 Kč — it fits into a fifty-koruna note and she has 50.00 − 41.30 = 8.70 Kč left. The estimate (42) and the result (41.30) match, so the point did not run off.

⚠️

Do not line decimal numbers up to the right. With whole numbers you line them up to the right edge, but 12.5 under 3.75 lined up right adds tenths to hundredths. The only right guide is point under point — then everything else sits.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. スタート with ten. When it goes well, add more.

Add and subtract decimal numbers on paper in columns. Write the answer with a decimal point, for example 12.5.

Practise the questions

On paper

Paper, pencil, straight columns. Points under each other like buttons on a shirt.

Work out in columns: 14.6 + 8.75 and 23.4 − 9.85. Before each question write an estimate to whole numbers.
Check Jonáš’s calculation from the story: is 250.00 − 187.50 really 62.50? Check it by adding.
Build your own shop of three things with prices to hellers (for example 19.90 + 7.50 + 32.40). Add them and find how much you get back from a hundred-koruna note.
Find the mistake: someone counted 6.3 + 1.48 = 2.11. Write what they did wrong and what the right result is.

Now you 💪

I can write 5 − 1.75 under each other correctly — with the five as 5.00.
Before counting I make an estimate and after the calculation I compare it with the result.
I can check subtraction: result + the number I subtracted = the original number.

✅

Done when: You add and subtract decimal numbers in columns with point under point, with padded zeros and with an estimate to check.

What to take from this lesson

Point under point — that lines up wholes with wholes and tenths with tenths.
Pad the shorter number with zeros: 5 → 5.00. It changes nothing, the columns are full.
You count from the right by columns, carries and borrows work like with whole numbers.
The point in the result belongs exactly under the points above.
An estimate to whole numbers finds a lost point before the teacher does.