Written subtraction under each other

Subtract under each other: how much is missing?

You already know how to add under each other. Subtracting works in a similar way — numbers under each other, you calculate from the back by columns. Only the question in each column sounds different.

We will subtract by counting on. Instead of “how much is left when I take away” we ask: “how much is missing to the top number?” In the question 52 − 27, in the ones you ask: 7 and how many is 12? Five. That is exactly how they teach it at school and exactly how a shopkeeper gives change: they do not count the difference, they count on upwards.

And what if the bottom digit is bigger than the top one — like that 7 under 2? Then you make the top digit bigger by ten (from 2 you make 12) and as a balance you add one to the bottom number in the next column. It sounds like magic, but it is only a loan between floors: a ten moved over to the ones.

The check in subtraction is sweet: result + bottom number = top number. And that is already adding under each other, which you know.

Ema sells gingerbread at the school fair. A lady buys for 27 Kč and pays with a fifty and a two-crown coin — 52 Kč. Ema has to give change and freezes. The teacher whispers: “Count on. Twenty-seven… and three is thirty… and twenty is fifty… and two are fifty-two.” Ema gives back 3 + 20 + 2 = 25 Kč. At home she tries it under each other: 52 − 27, ones: 7 and how many is 12? 5. Tens: 2 and one is 3, 3 and how many is 5? 2. Result 25. Paper and the fair agree.

💡

The question for every column always sounds the same: “bottom and how many is top?” When you say it out loud, the hand writes almost by itself.

Method: count on by columns

I will show you on 52 − 27.

Step 1: write under each other, bigger number on top:

  52
− 27
----

Step 2: ones. I ask: 7 and how many is 2? It does not work — 7 is more than 2. So I make the top two bigger to 12 and I ask: 7 and how many is 12? 5. I write 5. For that borrowed ten I add one to the bottom number in the next column (at the two of the tens I picture a three).

Step 3: tens. Bottom 2 plus the balancing 1 = 3. I ask: 3 and how many is 5? 2. I write 2.

Result: 25.

Step 4: check by adding. 25 + 27 = 52? Ones 5 + 7 = 12, I write 2, one goes on. Tens 2 + 2 + 1 = 5. It gives 52. It fits!

The balancing one is the same as a carry in addition, only in the opposite direction. Write it tiny next to the bottom digit of the next column — never hold it in your head.

When the bottom digit is not bigger, there is no loan: you just ask “bottom and how many is top” and write.

With no loan

Example: 87 − 34.

  87
− 34
----

Ones: 4 and how many is 7? 3. I write 3.

Tens: 3 and how many is 8? 5. I write 5.

Result: 53.

Check: 53 + 34 = 87. It fits.

When the top digits are bigger everywhere, subtracting under each other is as easy as adding with no carry.

One loan

Example: 631 − 258.

Ones: 8 and how many is 1? It does not work. I make it 11: 8 and how many is 11? 3. I add 1 to the bottom five in the tens.

Tens: 5 + 1 = 6. 6 and how many is 3? It does not work. I make it 13: 6 and how many is 13? 7. I add 1 to the bottom two in the hundreds.

Hundreds: 2 + 1 = 3. 3 and how many is 6? 3.

Result: 373.

Check: 373 + 258 = 631. It fits (try it under each other).

Subtracting with zeros on top

Example: 500 − 137.

Ones: 7 and how many is 0? It does not work. I make it 10: 7 and how many is 10? 3. I add 1 to the three of the tens below.

Tens: 3 + 1 = 4. 4 and how many is 0? It does not work. I make it 10: 4 and how many is 10? 6. I add 1 to the one of the hundreds below.

Hundreds: 1 + 1 = 2. 2 and how many is 5? 3.

Result: 363.

Zeros on top mean a loan in almost every column — all the more reason to write the balancing ones on paper.

⚠️

The balancing one belongs to the bottom number of the next column, not the top one. And do not forget it: it is the most common mistake of the whole subtraction. A small one written in pencil next to the bottom digit will hold you.

Practice: now you do it 🎲

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

Calculate under each other on paper, by counting on. Here write only the result.

Practise the questions

On paper

Each question: calculation under each other and at once a check by adding.

Work out under each other and do the check: 74 − 38, 452 − 129, 823 − 456.
Work out 600 − 234 and 705 − 156. Watch for zeros on top.
Shopkeeper game: a customer pays with a hundred for shopping of 67 Kč. Count on out loud how much you give back, and check under each other (100 − 67).
Find the mistake: a friend calculated 531 − 278 = 353. Do the check by adding, say in which column the mistake is, and fix it.

Now you 💪

You know the column question: “bottom and how many is top?” — and you use it on 52 − 27.
You know what to do when the bottom digit is bigger: make the top one bigger by 10 and the bottom one in the next column by 1.
You check every subtraction: result + bottom number = top number.

✅

Done when: You subtract three-digit numbers under each other by counting on, you can handle loans and you do the check automatically.

What to take from this lesson

We subtract by counting on: bottom and how many is top?
When it does not work, make the top digit bigger by 10 and add 1 to the bottom number of the next column.
Write the balancing one on paper, not in your head.
The subtraction check is adding: result + smaller number = bigger number.
Counting on is also used by a shopkeeper when giving change.