Share it out in rounds
There are 12 sweets to share fairly between 3 friends, and fairly means everyone gets the same number. The sure way is to deal them out like cards: give one sweet to each friend in turn, go round again, and keep going until the pile is gone.
Each full round gives every friend one more sweet, so the shares stay level the whole time. When the pile is empty, count what one friend has.
12 ÷ 3 asks how many each friend gets: hand the pile round in turn, one to each friend per round
Deal out the whole pile, one to each friend in turn
Each round hands one counter to every friend, so after each full round the shares are level again.
Sharing is dividing
Sharing 12 equally between 3 is written 12 ÷ 3 and read "12 divided by 3". The answer is how many each friend gets. It took 4 full rounds to empty the pile, so each friend has 4, and 12 ÷ 3 = 4.
Multiplying checks a share: 3 friends with 4 sweets each have 3 × 4 = 12, the whole pile. When a pile does not share out exactly, stop when there are too few left for another full round. The ones left are left over, because giving them to some friends and not others would make the shares unequal.
Worked example: Sweets Shared Equally Among Children
Question 12 sweets are shared equally among 3 children. (a) How many sweets does each child get? (b) One more child comes, and the 12 sweets are shared equally among the 4 children instead. How many sweets does each child get now?
1.Draw 3 plates, one for each child. Give 1 sweet to each child in turn. One round uses 3 sweets.
One plate for each child. The first round gives each child 1 sweet. 2.Keep going until all 12 sweets are given out. That takes 4 rounds, so each plate has 4 sweets.
After 4 rounds all 12 sweets are given out. Each plate has 4. 3.(a) 12 ÷ 3 = 4. Each child gets 4 sweets. Check: 3 × 4 = 12.
(a) 12 ÷ 3 = 4 sweets each. Check: 3 × 4 = 12. 4.(b) Now draw 4 plates and share the 12 sweets again. Each plate gets 3 sweets, so 12 ÷ 4 = 3. Each child gets 3 sweets.
(b) With 4 children, 12 ÷ 4 = 3 sweets each.
Answer: (a) 4 sweets; (b) 3 sweets
Common mistakes
- Subtracting: 12 − 3 = 9. That takes away 3 sweets once. Sharing among 3 children means making 3 equal groups, which is 12 ÷ 3.
- Thinking that more children means more sweets each. The 12 sweets do not change, so when 4 children share them each child gets fewer: 3 instead of 4.
More multiplication and division problems, worked step by step →
Worked example: Stickers Shared with Some Left Over
Question A teacher has 14 stickers. She shares them equally among 4 children and gives each child as many as she can. (a) How many stickers does each child get? (b) How many stickers are left over?
1.Draw 4 plates, one for each child. Give 1 sticker to each child in turn. One round uses 4 stickers.
One plate for each child. The first round gives each child 1 sticker. 2.After 3 rounds, 3 × 4 = 12 stickers are given out and 14 − 12 = 2 are left. Another round needs 4 stickers, and 2 is not enough.
After 3 rounds, 12 stickers are given out. The 2 that are left are not enough for another round. 3.(a) Each child gets 3 stickers.
(a) Each child gets 3 stickers. 4.(b) 2 stickers are left over. Check: 4 × 3 + 2 = 14.
(b) 2 stickers are left over. Check: 4 × 3 + 2 = 14.
Answer: (a) 3 stickers; (b) 2 stickers
Common mistakes
- Giving the 2 stickers that are left to two of the children. Then two children have 4 stickers and two have 3, and the sharing is no longer equal.
- Stopping after 2 rounds and saying that 6 stickers are left over. 6 is enough for another round of 4. What is left over must be smaller than the number of children.
More multiplication and division problems, worked step by step →