You know what multiplying and dividing mean, and you have your fact families. A word problem is just a story about equal groups, arrays or equal lengths. The skill is to picture the story, then decide what is missing.
Why it works
Every equal-groups story has three numbers: how many groups, how many in each group, and the total. The story gives you two of them. If the total is missing, multiply. If the total is known and one of the other two is missing, divide, because division finds a missing factor.
| What is missing? | Do this | Example |
|---|---|---|
| the total | multiply | 4 boxes of 6 eggs: $4 \times 6 = 24$ |
| how many in each group | divide | 24 eggs in 4 boxes: $24 \div 4 = 6$ each |
| how many groups | divide | 24 eggs, 6 per box: $24 \div 6 = 4$ boxes |
Key idea
Picture the story. Find the groups, the size of each group and the total. Multiply to find a missing total; divide to find a missing group size or number of groups.
Worked example: Total missing
A parking lot has 7 rows with 8 cars in each row. How many cars?
- An array: 7 rows of 8. The total is missing.
- $7 \times 8 = 56$.
Answer: $56$ cars
Worked example: Group size missing
A ribbon 36 inches long is cut into 4 equal pieces. How long is each piece?
- The total length (36) and the number of pieces (4) are known.
- Divide: $36 \div 4 = 9$, because $4 \times 9 = 36$.
Answer: $9$ inches
Worked example: Number of groups missing
Each box holds 6 eggs. How many boxes do 42 eggs fill?
- The total (42) and the size of each box (6) are known.
- Divide: $42 \div 6 = 7$.
Answer: $7$ boxes
Common mistake
Hunting for key words. "Each" shows up in multiplying stories ("each box has 6, how many in 7 boxes?") and in dividing stories ("each box holds 6, how many boxes for 42?"). Key words can fool you. Draw the groups instead, and ask which number is missing.