Interpreting Remainders in Division Word Problems

Property When a division problem results in a remainder, the context of the word problem determines how to use it. Given a division $a \div b = q \text{ R } r$, where $q$ is the quotient and $r$ is the remainder, the answer to the problem could be the quotient $q$, the quotient rounded up ($q+1$), or the remainder $r$.

Examples Scenario 1: Round Up A group of 28 students is going on a field trip. If each van can hold 8 students, how many vans are needed? $$28 \div 8 = 3 \text{ R } 4$$ They will need 4 vans. 3 vans will be full, and a 4th van is needed for the remaining 4 students. Scenario 2: Use the Quotient You have 28 feet of ribbon to make bows. If each bow requires 8 feet of ribbon, how many complete bows can you make? $$28 \div 8 = 3 \text{ R } 4$$ You can make 3 complete bows. There is not enough ribbon for a 4th bow. Scenario 3: The Remainder is the Answer A farmer collects 28 eggs and puts them into cartons that hold 8 eggs each. After filling as many cartons as possible, how many eggs are left over? $$28 \div 8 = 3 \text{ R } 4$$ There are 4 eggs left over.

Explanation When solving division word problems, there is often a remainder. Carefully read the question to understand what to do with this remainder. Sometimes you must round your answer up to the next whole number to accommodate the leftover amount, like when seating people in vans. Other times, you only use the whole number quotient because you can only make complete items. In some cases, the question is specifically asking for the amount that is left over, which is the remainder itself.