Division with Remainders • Topic 2 of 3

Interpreting Remainders in Word Problems

When solving word problems with division, the remainder can mean different things depending on the context. There are three rules:

  • Rule 1 — Ignore: When the question asks for 'full groups' or 'complete sets'. The remainder is not counted. E.g. how many full boxes?
  • Rule 2 — Round Up: When the question asks 'how many needed for everyone'. Even one extra person needs one more group. E.g. how many buses/taxis?
  • Rule 3 — Keep: When the question asks 'how much is left over' or 'how much does each get'. E.g. how many rupees each? How much left?
Remainder Rules: 100 / 8 = 12 R4Rule 1: IGNOREFull boxes: Answer 12(ignore the 4 left)Rule 2: ROUND UPBuses needed: Answer 13(+1 for the 4 extras)Rule 3: KEEPRs.12 each, Rs.4 left(keep remainder)Same calculation (12 R4) — different answers!Always READ CAREFULLY what the question asks for
Solved Examples
1
Worked Example
A farmer has 175 apples. He packs them in bags of 8 each. How many full bags can he make? How many apples are left?
Solution175 / 8 = 21 remainder 7. Full bags = 21 (Rule 1 - ignore the 7 leftover apples for the bag count). Apples left over = 7 (Rule 3 - keep the remainder). Answer: 21 full bags with 7 apples left.
2
Worked Example
175 people need to cross a river. Each boat carries 8 people. How many boat trips are needed?
Solution175 / 8 = 21 remainder 7. Since all 175 people must cross, the 7 extra people need one more trip. Apply Rule 2 (round up): 21 + 1 = 22. Answer: 22 boat trips.
3
Worked Example
Rs.1,000 is shared equally among 6 friends. How much does each get? How much is left?
Solution1000 / 6 = 166 remainder 4. Each friend gets Rs.166 (quotient). Rs.4 is left over (Rule 3 - keep remainder). Answer: Rs.166 each, Rs.4 remaining.

Key Points

  • Rule 1 (Ignore): Use when question asks for 'full' or 'complete' groups
  • Rule 2 (Round up): Use when everyone must be included (buses, taxis, rows)
  • Rule 3 (Keep): Use when question asks what is left over
  • The same division can have different answers depending on context!
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The remainder is what is left after:
Explanation: Equal sharing.
Q2."How many buses are needed?" usually means you should:
Explanation: Round up.
Q3."How many full boxes?" usually means you should:
Explanation: Drop the remainder.
Q4.$47\div5$ leaves a remainder of:
Explanation: $45+2$, so $2$.
Practice more MCQs → 📝 Assignment · 35 marks