Twelve star stones, three friends

Erklärus had collected twelve glow-stones – and three friends who all wanted the same number.

Erklärus: “Twelve stones, shared fairly between three friends. How many does each one get?”
Liri: “One, one, one… then start again from the beginning…”
Erklärus: “That’s called dividing. In short: 12 ÷ 3.”

🍬 Sharing – dividing fairly

12 sweets are shared fairly between 3 children. Each child gets one in turn, until they are all gone.

🍬🍬🍬🍬
Child 1
🍬🍬🍬🍬
Child 2
🍬🍬🍬🍬
Child 3

12 ÷ 3 = 4 — each child gets 4 sweets.

📦 Grouping – circling groups

A different problem, the same sum: “Always put 3 sweets in a bag. How many bags do you need for 12 sweets?”

🍬🍬🍬
Bag 1
🍬🍬🍬
Bag 2
🍬🍬🍬
Bag 3
🍬🍬🍬
Bag 4

Here too: 12 ÷ 3 = 4 — this time it is 4 bags.

Liri: “Both times the answer is 4 – even though the questions were different?”
Erklärus: “Exactly. Whether you share fairly or split into groups – the sum behind it is the same: division.”

🔄 The inverse operation

Division is the opposite of multiplication – the best trick for checking a division!

Erklärus: “I work out 12 ÷ 3 = 4 because I know: 4 × 3 = 12.”
20 ÷ 4 = (Hint: which number times 4 makes 20?)
🌌 Dividing in the universe

A rocket has 15 compartments for astronaut equipment, shared fairly between 3 astronauts – each gets 5 compartments.
A star catalogue with 20 photos is sorted into albums of 4 photos each – that makes 5 albums.
Division helps astronomers share telescope observing time fairly between several research teams.

❌ Common mistake

With “12 ÷ 3”, people sometimes mix up which number is being divided and which number it is divided by.

12 ÷ 3 means: 12 things are split into groups of 3 (or between 3 people) – not the other way round!

Tip: the first number is always the total amount; the second tells you how many parts it is split into.

🍬 Exercise 1 – Sharing
16 star biscuits are shared fairly between 4 astronauts. How many does each one get?
📦 Exercise 2 – Grouping
You have 18 moon rocks and always pack 3 into a sample box. How many boxes do you need?
🔄 Exercise 3 – The inverse
You know: 7 × 4 = 28. So what is 28 ÷ 4?

Shared fairly

Liri had shared out all twelve glow-stones fairly – and in doing so had understood something bigger.

Liri: “Dividing and multiplying are like two sides of the same coin.”
Erklärus: “That is exactly why you can check any division with a multiplication.”
Liri: “I could even use it to divide the sky into search areas of equal size – then I’d find out faster which part my home is in.”
“Division: sharing fairly OR splitting into groups – both lead to the same answer. Inverse: 12÷3=4, because 4×3=12.”
What you learned today
12 ÷ 3 = 4, because 4 × 3 = 12
Sharing (dividing fairly) or grouping (making groups) – the same sum
🌟

Chapter 10 mastered!

Liri can now share fairly – and check every answer with the inverse calculation.

Erklärus’s notebook – page 10:
“Division: sharing (dividing fairly) or grouping (making groups) – both lead to the same answer. Inverse operation: 12÷3=4, because 4×3=12. That is how you can check any division.”
← Back to overview 10 – Division, Part 1