The heaviest crown

Erklärus took a thick, old book down from the shelf. On the cover there was only one word: “Division”.

Liri: “I remember a stretch of 848 squares – but all I know is that I covered it in 4 jumps of equal size. How long was a single jump?”
Erklärus: “That is exactly what you need division for. This is the ultimate challenge – because you have to divide, multiply AND subtract all at once.”
Liri: “All at once?”
Erklärus: “One after another, step by step. When you know the length of one jump, you can recalculate your whole course home.”

🔁 The rhythm: Divide – Multiply – Subtract – Bring down

In long division the same routine repeats again and again, digit by digit from left to right:

1️⃣ Divide: how many times does the divisor go in?
2️⃣ Multiply: the check-back – how much has just been used up?
3️⃣ Subtract: what is left over as the remainder?
4️⃣ Bring down: bring down the next digit and start again from the beginning.

🔍 848 ÷ 4 – digit by digit

This is how you write it down: the remainder is noted as a little red box directly under the place you have divided, together with the next digit beside it. At the end comes the check.

8
4
8
÷
4
=
2
1
2
0
4
0
8
0
Check:
2
1
2
×
4
8
4
8

How to read the staircase: 8 ÷ 4 = 2, remainder 0 → write the next digit (4) beside it: “04”. 4 ÷ 4 = 1, remainder 0 → write the next digit (8) beside it: “08”. 8 ÷ 4 = 2, remainder 0. Done – and the check (212×4=848) confirms it!

Liri: “848 ÷ 4 = 212. So each of my four jumps was exactly 212 squares long!”

📝 Now you – another memory section

Liri remembers another stretch: 486 squares, this time covered in 2 jumps of equal size. Work it out as in the example above – fill in the digits of the answer and the remainders of the staircase, so that Liri knows the length of each jump:

4
8
6
÷
2
=
8
6
🌌 Dividing in the universe

A space telescope has 645 minutes of observing time, divided between 5 research teams – each gets the same amount of time.
Without long division, big missions couldn’t share their resources fairly between several teams or days.

❌ Common mistake

Bringing down is often forgotten, or a digit gets skipped.

Tip: after every subtraction, ask straight away: “Which digit comes down now?” – only then carry on dividing. And: if the divisor doesn’t go into a digit at all, a 0 still goes into the answer – it must not simply be skipped!

The crown fits

Liri had gone down the whole staircase once – dividing digit by digit, noting the remainder with the next digit – and at the end there was a clear, checked answer: 212 squares per jump.

Liri: “That really was the hardest task so far. But now I know the exact length of every single jump.”
Erklärus: “That is why it’s called the ultimate challenge. And that is exactly why it’s worth it: with this one number you can recalculate your whole course and know whether you are still on the right way home.”

Liri wrote 212 onto her star map – not just as the answer to a sum, but as a reliable building block of her way home.

“Long division: divide every digit separately, note the remainder + next digit underneath, carry on dividing. At the end the check: answer times divisor must give the starting number. That way I know exactly how long each jump home is.”
What you learned today
848 ÷ 4 = 212
Divide → Multiply → Subtract → Bring down → repeat
🌟

Chapter 22 mastered!

Liri has mastered the ultimate challenge – long division. Now she knows the exact length of every jump on her way home.

Erklärus’s notebook – page 22:
“Long division: divide every digit separately, note the remainder + next digit underneath, carry on dividing. At the end the check: answer times divisor = starting number. That way every memory on my star map stays checkable – and I know exactly how long every single jump home is.”
← Back to overview 22 – Long Division