Written division · Kode bersama Martin

Split a big number floor by floor

How much is 156 ÷ 6? Families will not help you — 156 is not in the small times tables. But you can divide with a remainder, and that is enough. Written division is nothing but division with a remainder repeated floor by floor.

The idea roughly: you share 156 crowns among six children. First you share the hundreds, then the tens, then the crowns. What cannot be shared on one floor, you change into smaller and add to the next floor.

In writing it goes from the left (watch — the opposite of adding and multiplying!): you take the first digit, try to divide, you “stick” the remainder onto the next digit and divide on.

It is the hardest of the four written operations — that is why it comes last. But it is built only from things you know: division with a remainder and the small times tables. We will go slowly and out loud.

Jonáš has 156 marbles from a raffle and shares them with two brothers and three cousins — there are six of them. He tries sharing one by one, but at the fortieth he loses track. Dad stops him: “By floors. One hundred and fifty-six is 15 tens and 6 marbles. Fifteen tens for six people — each two tens, three tens left.” The leftover three tens he changes: 30 and 6 is 36 marbles. “Thirty-six for six — six each.” Each has 26 marbles. In the evening Jonáš writes it under each other and finds that the paper did exactly what dad did.

💡

Written division is read from the left, from the biggest floor — exactly the opposite of adding, subtracting and multiplying. You share the big notes first, then the small change.

Method: divide, write, stick the remainder to the next

I will show you on 156 ÷ 6.

Step 1: take digits from the left until you can divide them. The one on its own: 1 ÷ 6 does not work (1 < 6). Take the next digit too: 15.

Step 2: divide with a remainder. 15 ÷ 6 = 2, remainder 3. (Nearest smaller multiple: 12.) Into the result I write 2.

Step 3: stick the remainder onto the next digit. Remainder 3 and the next digit 6 give 36.

Step 4: divide on. 36 ÷ 6 = 6, remainder 0. Into the result I write 6.

The digits have run out. Result: 26, remainder 0.

Step 5: check by multiplying. 26 × 6 = 156? Under each other: 6 × 6 = 36, I write 6, three goes on; 2 × 6 = 12, plus 3 = 15. It gives 156. It fits!

When a non-zero remainder is left at the end, it belongs to the result: 157 ÷ 6 = 26, remainder 1. The check then sounds: 26 × 6 + 1 = 157.

The rhythm of each floor is always the same: divide with a remainder, write the quotient, stick the remainder onto the next digit. Three steps round and round, until the digits run out. Out loud say: “fifteen divided by six is two, remainder three… thirty-six divided by six is six.”

Smooth division

Example: 84 ÷ 4.

Floor 1: first digit 8. 8 ÷ 4 = 2, remainder 0. I write 2.

Floor 2: remainder 0 and digit 4 give 4. 4 ÷ 4 = 1, remainder 0. I write 1.

Result: 21.

Check: 21 × 4 = 84. It fits.

Here each floor could be shared with no remainder — the nicest case.

Remainders between floors

Example: 738 ÷ 3.

Floor 1: 7 ÷ 3 = 2, remainder 1. I write 2.

Floor 2: remainder 1 + digit 3 → 13. 13 ÷ 3 = 4, remainder 1. I write 4.

Floor 3: remainder 1 + digit 8 → 18. 18 ÷ 3 = 6, remainder 0. I write 6.

Result: 246.

Check: 246 × 3 = 738 (work it out under each other — 6 × 3 = 18, I write 8, one goes on…). It fits.

Division with a remainder at the end

Example: 95 ÷ 4.

Floor 1: 9 ÷ 4 = 2, remainder 1. I write 2.

Floor 2: remainder 1 + digit 5 → 15. 15 ÷ 4 = 3, remainder 3. I write 3.

The digits have run out, the last remainder stays: 95 ÷ 4 = 23, remainder 3.

Check: 23 × 4 + 3 = 92 + 3 = 95. It fits.

As a story: 95 eggs into cartons of four — 23 full cartons and 3 eggs extra.

⚠️

Do not forget to write the quotient at every floor, even when it comes out zero. 612 ÷ 3: six gives 2, one divided by three gives 0 (you write it!), remainder 1 you stick onto two → 12 ÷ 3 = 4. Result 204, not 24. A skipped zero shrinks the number ten times.

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.

Divide on paper floor by floor, out loud. Here write only the result.

Practise the questions

On paper

Check every division at once by multiplying. The pair of calculations belong together.

Work out and check: 96 ÷ 4, 84 ÷ 7, 372 ÷ 3.
Work out with a remainder at the end: 89 ÷ 6, 250 ÷ 4. Check: quotient × divisor + remainder.
Watch for a zero in the quotient: 618 ÷ 6, 812 ÷ 4.
Marble problem: 156 marbles for 6 children. Write the whole method floor by floor like Jonáš’s dad and the answer in a sentence.

Now you 💪

You know the floor rhythm: divide with a remainder, write the quotient, stick the remainder onto the next digit.
You work out 738 ÷ 3 = 246 and back it with the check 246 × 3 = 738.
You know when a zero belongs in the quotient, and you do not skip it.

✅

Done when: You divide a three-digit number by a one-digit number floor by floor, you pass remainders on and you check every result by multiplying.

What to take from this lesson

Written division goes from the left, from the biggest floor.
Rhythm: divide with a remainder, write the quotient, stick the remainder onto the next digit.
The last remainder belongs to the result: 95 ÷ 4 = 23, remainder 3.
Check: quotient × divisor (+ remainder) = dividend. Always.
A zero in the quotient is written — skipping it means a ten times smaller result.