Concept 5 of 7
Sharing Fairly: Division
Today's big idea
Dividing hands things out one round at a time until there is not enough for another.
Whatever cannot make a full round is the remainder, not a mistake.
How it works
👀 What's going on?
You have 30 sweets and 6 friends, and everyone is watching to see that it is fair. You could hand them out one at a time until the bag is empty. Division tells you the answer before you start.
💡 Here's the trick
Look at the sharing above. Dividing splits a total into equal groups, which is exactly multiplication run backwards. Knowing 6 × 5 = 30 hands you 30 divided by 6 is 5, and 30 divided by 5 is 6. One fact, read three ways.
🪄 How to do it
- 1.Read the division as a question, the way the sharing above asks it: how many fit into the total?
- 2.Run your times tables backwards until you find what multiplies up to the total.
- 3.Whatever will not make a full group is the remainder.
✍️ Try it
Work out 30 divided by 6. Then share 26 stickers equally among 4 children. Finally share 84 pencils equally among 6 children.
Counting 6, 12, 18, 24, 30 takes five sixes, so 30 divided by 6 is 5. For the stickers, 4 × 6 is 24 and 4 × 7 is 28, which is too many. So each child gets 6, and 2 stickers are left over. For 84 ÷ 6, work left to right: 6 goes into 8 once with 2 left over, so write 1 and carry the 2 to make 24; then 6 goes into 24 four times, giving 14. Taking the tens first, then the ones, is the short-division method.
⚠️ Watch out
You might be thinking division works either way round, the way multiplication does. It does not. 30 divided by 6 is 5, but 6 divided by 30 is not even a whole number. The total always goes first.
🌟 Why this matters
Splitting a bill, sharing a packet, working out how many boxes you need: these are the questions division was invented for. It is the other half of every times table you learn.
Exam tip: When a division does not come out exactly, the leftover is usually the point of the question.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Share 30 candies fairly among 6 friends. How many each?”
- 1
What is 'share'?
Split 30 into 6 EQUAL groups. 🍬
- 2
Think tables
Find a number × 6 that gives 30. 5 × 6 = 30 ✓
- 3
Write as division
30 ÷ 6 = 5
- 4
Each friend gets ✓
Each friend gets 5 candies
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Share 12 fairly among 3 plates. Give one to every plate each round until the pile is empty.
DIVIDE · ROUND 1 OF 3
12 ÷ 3
PILE TO SHARE
🍪12
Every plate is empty — start dealing!
Quick check
✅ VERIFICATION
Which multiplication fact would you use to work out 42 ÷ 7?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Remainders in Real Life
26 kids, cars of 4 → 7 cars, not 6.