Fraction Word
Problems
Learn to multiply and divide with fractions to solve real-world story problems.
What a Fraction Means
A fraction shows a part of a whole. The bottom number (denominator) tells how many equal pieces the whole is split into. The top number (numerator) tells how many of those pieces we have.
Key Words to Watch For
Word problems use signal words. Learning them helps you choose between multiplying and dividing.
Why This Matters
Fractions appear everywhere: in recipes, in sharing money, in measuring distance, and in telling time. The ISEE tests whether you can turn a story into the right math.
Rule: Multiplying Fractions
To multiply fractions, multiply the tops together and the bottoms together. A whole number can be written as a fraction over 1.
Rule: Dividing Fractions
To divide by a fraction, flip the second fraction (use its reciprocal) and then multiply. This is sometimes called "keep, change, flip."
Multiply vs. Divide
When do you multiply and when do you divide? Compare the meaning of each problem.
| Multiply | Divide | |
|---|---|---|
| Question type | Finding a part "of" a total | Splitting into equal groups |
| Signal word | "of" | "share", "how many in" |
| Result size | Usually smaller | Can be larger |
| Example | \( \frac{1}{2} \) of 6 | 6 \( \div \frac{1}{2} \) |
A Step-by-Step Plan
Example 1: "of" a Group
A class has 12 students. \( \frac{1}{3} \) of them walk to school. How many students walk?
Example 2: Fraction of a Fraction
A pizza has \( \frac{3}{4} \) left. Sam eats \( \frac{2}{3} \) of what's left. What fraction of the whole pizza did Sam eat?
Example 3: Dividing to Share
You have 4 cups of flour. Each batch of muffins needs \( \frac{1}{2} \) cup. How many batches can you make?
Example 4: A Two-Step Problem
A ribbon is 6 feet long. You cut it into pieces that are each \( \frac{3}{4} \) foot long. How many pieces do you get?
Common Mistakes
Quick Summary
| Operation | How To Do It | Signal |
|---|---|---|
| Multiply | Tops \( \times \) tops, bottoms \( \times \) bottoms | "of" |
| Divide | Keep, change, flip, then multiply | "share", "how many in" |
| Whole number | Write it over 1, e.g. \( 6 = \frac{6}{1} \) | any |
| Final step | Always simplify your answer | always |
Question 1 of 5
A box has 20 crayons. \( \frac{2}{5} \) of them are red. How many crayons are red?
Question 2 of 5
How many \( \frac{1}{3} \)-cup scoops are in 2 cups of rice?
Question 3 of 5
What is \( \frac{3}{4} \times \frac{2}{3} \) in simplest form?
Question 4 of 5
A pizza has \( \frac{1}{2} \) left. Three friends share it equally. What fraction of a whole pizza does each get?
Question 5 of 5
A rope is 8 feet long. It is cut into pieces each \( \frac{2}{3} \) foot long. How many pieces are made?
You've Got This!
You can now read a fraction word problem, find the signal words, choose multiply or divide, and simplify your answer.