Multiply & divide word problems

What is this skill?

Multiplication and division word problems are story problems about equal groups, arrays and fair sharing. "Amara has 6 bags with 7 marbles in each bag. How many marbles in all?" is a multiplication problem: 6 × 7 = 42. "Omar shares 36 cards equally among 4 friends. How many does each friend get?" is a division problem: 36 ÷ 4 = 9.

Third graders learn to recognize the structure of a problem: is it asking for the total of equal groups, the size of each group, or the number of groups? The same three numbers can appear in all three kinds of problems. Drawing a quick picture, an array or a bar split into equal parts is a strong strategy for deciding which operation to use.

Why it matters

Word problems show children why multiplication and division are worth learning. They come up whenever things are packed, shared, arranged or bought in equal amounts: packs of juice boxes, rows of seats, teams for a game or splitting a bill.

They also build reading and reasoning skills. Instead of looking for keywords, children have to understand the situation and decide what is unknown. That kind of thinking is needed for the multi-step problems in fourth and fifth grade, where equal groups are combined with addition and subtraction.

Common mistakes

• Adding the numbers instead of multiplying, such as answering 13 for 6 bags of 7. Asking "Are these equal groups?" points to multiplication.
• Mixing up the number of groups and the size of each group in division. In "36 cards shared among 4 friends," 4 is the number of groups, and the answer is how many in each group.
• Relying on keywords like "each," which can appear in both multiplication and division problems. Picturing the story works better than hunting for words.
• Not checking whether the answer makes sense. If 36 cards are shared and each friend gets 40, something has gone wrong.

How to help at home

• Make up equal-groups stories at meals or while shopping: "There are 4 packs with 6 yogurts in each. How many yogurts?"
• Ask your child to write their own multiplication and division story for a fact like 5 × 8 = 40.
• Act out sharing problems with small objects, dealing them out one at a time to check the answer.
• Ask your child to draw the story before solving it and to explain why they chose multiplication or division.
• Take one fact, like 4 × 9 = 36, and tell three stories with it: one where the total is unknown, one where the size of each group is unknown, and one where the number of groups is unknown.

Worked examples

These are real questions from the Tutorsaurus multiply & divide word problems practice, with the answers worked out.

1. Example 1

   Kenji shares 10 crayons equally among 2 friends. How many does each friend get?

   Answer: 5. 10 ÷ 2 = 5.

2. Example 2

   Maya shares 15 balloons equally among 3 friends. How many does each friend get?

   Answer: 5. 15 ÷ 3 = 5.

3. Example 3

   Eli shares 63 crayons equally among 7 friends. How many does each friend get?

   Answer: 9. 63 ÷ 7 = 9.