A remainder is a real amount: people, inches, dollars. After you divide, read the question again and decide what the remainder means.
Key idea
There are three common cases. Round up when the leftovers still need something (one more van). Drop it when the leftovers cannot make a whole one (a piece too short to use). Report it when the question asks what is left over.
Why it works
The quotient counts full groups. In "30 people, 7 per van," $30 \div 7 = 4$ R 2: four vans are full and 2 people are still waiting. They need a van too, so the answer is 5. The math is the same each time; the story decides the answer.
Worked example: Round up
30 people go on a trip. Each van holds 7. How many vans are needed?
- $30 \div 7 = 4$ R 2.
- The 2 extra people need a seat, so add a van.
Answer: 5 vans
Worked example: Drop the remainder
A ribbon is 46 inches long. How many 6-inch pieces can you cut?
- $46 \div 6 = 7$ R 4.
- The 4 inches left is too short for another piece.
Answer: 7 pieces
Worked example: The remainder is the answer
29 cookies are shared equally by 4 friends, as many as possible each. How many are left over?
- $29 \div 4 = 7$ R 1.
- Each friend gets 7, and the question asks what is left.
Answer: 1 cookie
Common mistake
Answering "4 R 2 vans" or "4 vans." A number with an R is not an answer to "how many vans?", and 4 vans leaves 2 people behind. Picture the story and ask: what happens to the leftovers?