Word Problems
Division word problems test two skills at once: picking the right operation and then reading the remainder sensibly. The first move is to decide whether the problem is sharing or grouping. If a known number of people or boxes is given and you want how many each gets, it is sharing and the divisor is the number of groups. If a group size is given and you want how many such groups fit, it is grouping and the divisor is the group size. The harder, and more heavily tested, skill is interpreting the remainder, because the maths alone does not tell you what to do with the leftover. Sometimes you ignore it -- 50 students in full teams of 11 makes 4 teams with 6 left out. Sometimes you must round the quotient up -- to carry 125 students in buses of 40, 125 divided by 40 is 3 remainder 5, but 3 buses hold only 120, so you need a 4th bus for the last 5. The right answer depends entirely on the real situation, so children should always write the answer as a full sentence that makes sense in context, not just a bare number.
✅ Solved examples
✏️ Practice — try these, take hints as needed
📝 Topic test — 8 questions
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Key Concepts — Quick Reference
Division relationships
| The four terms | Dividend / Divisor = Quotient, with Remainder left over |
|---|---|
| Fundamental relation | Dividend = (Divisor x Quotient) + Remainder |
| Remainder rule | Remainder is ALWAYS less than the Divisor |
| Inverse of multiplication | If a x b = c, then c / a = b and c / b = a |
Sharing vs grouping (same sentence, two meanings)
| Sharing | Total / Number of groups = Size of each group ("how many each?") |
|---|---|
| Grouping | Total / Size of each group = Number of groups ("how many groups?") |
| Repeated subtraction | Grouping = subtract the group size until you hit 0; the count of subtractions is the quotient |