Division is sharing out

Share it out fairly

You know division from life better than you think. You do it every time you share fairly with someone.

You have 12 sweets and you share them among three friends. One each, round and round: you, you, you, you again… until the sweets run out. Each has 4. You have just worked out 12 ÷ 3 = 4.

The sign ÷ is read divided by. The write-up 12 ÷ 3 means: split 12 things into 3 equal piles. The result says how many are in one pile.

Division can also be read the other way: how many times does three fit into twelve? Four times as well. Both readings are right and each is useful at a different time.

Today you will share out — sweets, cards, stickers. And you will see that division is just multiplying backwards.

Filip has a party and in a bag 15 chewing gums. Five children sit at the table and they all look at the bag. Filip does not want anyone to argue, so he shares in rounds: one to each, round, round again. When the bag is empty, each has 3 chewing gums in front of them and nobody complains. Mum comments: “Fifteen divided by five is three.” Filip stares — he was just calculating, and he did not even know. Sharing round and round is division live.

How to divide: share out, or ask backwards

Way 1: sharing (for understanding).

Example 12 ÷ 3:

1. Draw 3 circles — those are the piles (friends).
2. Share one mark into each circle, nicely round and round, until you have shared all 12.
3. Count the marks in one circle: 4.

Result: 12 ÷ 3 = 4.

Way 2: the backwards question (for speed).

Example 12 ÷ 3: I ask “3 × what = 12?” I go through the three row: 3, 6, 9, 12 — that is 3 × 4. So 12 ÷ 3 = 4.

The numbers in division have names: 12 is the dividend (what you share out), 3 is the divisor (how many piles), 4 is the quotient (how many each gets).

Watch one big difference from multiplying: in division you must not swap the numbers! 12 ÷ 3 = 4, but 3 ÷ 12 is definitely not four — three sweets among twelve children cannot be shared in wholes. Order in division matters. Always: what I share ÷ among how many.

Sharing with circles and marks

Example: 15 ÷ 5. Fifteen chewing gums for five children.

Step 1: I draw 5 circles.

Step 2: I share marks round and round: after the first round each has 1 (shared 5), after the second 2 (shared 10), after the third 3 (shared 15). All gone.

Step 3: in each circle there are 3 marks.

Result: 15 ÷ 5 = 3. Each child gets 3 chewing gums.

The backwards question

Example: 18 ÷ 6.

I ask: 6 × what = 18?

I go through the six row: 6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18. Here!

Result: 18 ÷ 6 = 3.

Check by multiplying: 3 × 6 = 18. It fits. This is the golden rule of division: the result times the divisor must give the dividend. If it does not, there is a mistake somewhere.

The other reading: how many times it fits

Example: 20 ÷ 4 — but differently. I have 20 Kč and one card costs 4 Kč. How many cards can I buy?

Here I am not sharing into piles. I ask: how many times does 4 fit into 20?

I count down in fours: 4, 8, 12, 16, 20 — five times.

Result: 20 ÷ 4 = 5. I buy 5 cards.

Same write-up, different story. Division can do both: split into piles and count how many times something fits.

Practice: now you do it 🎲

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

Divide using the backwards question: divisor times what gives the dividend?

Practise the questions

On paper

Draw circles and share. Hands understand division before the head does.

1. Draw the sharing for 12 ÷ 4: four circles, twelve marks round and round. Write the result.

2. Work out with the backwards question and write the question too: 21 ÷ 3 (I ask: 3 × what = 21?), 40 ÷ 5, 16 ÷ 8.

3. Make up and write your own story for 18 ÷ 3. Anything: stickers, rolls, marbles.

4. Check by multiplying: for all three questions from step 2 write the check (result × divisor = dividend).

Now you 💪

1. You can explain 12 ÷ 3 = 4 using sharing into circles.
2. You can turn division into a backwards question: 21 ÷ 3 → “3 × what = 21?”
3. You know that in division you cannot swap the numbers, and you can say why.

What to take from this lesson

• Division = fair sharing into equal piles.
• 12 ÷ 3 asks: share 12 among three — how many does each get? Or: how many times does 3 fit into 12?
• The fastest path: the backwards question through the times tables (3 × what = 12?).
• Division check: quotient × divisor = dividend. Always do it.
• In division you must not swap the numbers. Order matters.

© 2026 Ing. Martin Polak / AlgoRhino · 内容使用条款