🔢 Math

Division: sharing equally

Twelve sweets shared among three children, four each: 12 ÷ 3 = 4

📖 In short

Grandma gave 12 sweets to her three grandchildren and said: “Share them fairly.” How many does each get? 4! Division is sharing equally, and we write it with the ÷ sign: 12 ÷ 3 = 4. It's the opposite of multiplication, so if you know your times tables, you know division.

🤩 Did you know?

  • The ÷ sign first appeared in a Swiss book in 1659.
  • Any number ÷ 1 = the same number, and any number ÷ itself = 1.
  • The number 60 can be divided by 12 different numbers, which is why the Babylonians loved it.
  • In division, the number being shared is the “dividend”, the number we divide by is the “divisor”, and the answer is the “quotient”.

🔎 Find out more

🌟 Two questions for division

Division answers two questions: if we share 15 apples among 3 children, how many does each get? (5); and if we put 15 apples in bags of 3, how many bags do we need? (5 too).

🔍 Division undoes multiplication

Since 4 × 6 = 24, then 24 ÷ 6 = 4 and 24 ÷ 4 = 6. To work out 35 ÷ 7 we ask: 7 × what = 35? The answer is 5.

💡 Remainder

If we share 14 sweets among 4 children, each gets 3, and 2 are left, not enough for another round. We say: 14 ÷ 4 = 3 remainder 2. The remainder is always smaller than the number we divide by.

🎯 No dividing by zero

Can we share 10 sweets among zero children? That question makes no sense! That's why dividing by zero isn't allowed in math. But 0 ÷ 5 = 0: there's nothing to share.

📊 See it in a picture

Fourteen sweets on four plates: three on each plate and two left over
14 sweets on 4 plates: 3 on each plate, and 2 are left, not enough for another round.

🧮 Worked examples

  1. 20 ÷ 4 = 5Because 4 × 5 = 20.
  2. 17 ÷ 5 = 3 remainder 25 × 3 = 15, and 17 − 15 = 2.
  3. 100 ÷ 10 = 10When we divide by 10 we take a zero off the right.

📚 Key words

Division
Sharing a number into equal parts
Quotient
The answer to a division: each part's share
Remainder
What's left after sharing that isn't enough for a whole round

🧪 Try it at home

Count the sweets or nuts in a bag, then share them equally among your family. Is anything left? Write the calculation: the number ÷ the number of people = each share, and the remainder.

🧩 Test yourself

1 What is 18 ÷ 3?

2 If we share 10 pencils equally among 3 children, how many are left?

3 Division is the opposite of…

📚 Read next

🎮 Try it yourself