Training Fractions Word Problems with Fractions
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Word Problems with Fractions

24 min Fractions

Word Problems with Fractions

Fractions become truly useful when you apply them to real-world problems. Whether you are halving a recipe, splitting a bill, or calculating how much of a project is complete, fraction word problems test your ability to translate everyday language into mathematical operations.

The key to solving word problems is reading carefully, identifying what operation is needed, and setting up the calculation before reaching for a pencil. This lesson presents a variety of practical scenarios that require addition, subtraction, multiplication, or division of fractions.

Key Phrases
PhraseOperation
"of"Multiplication
"how much more / less"Subtraction
"total," "combined"Addition
"split equally," "per person"Division
Example 1

A recipe calls for $2\dfrac{1}{2}$ cups of flour. You make $\dfrac{2}{3}$ of the recipe. How much flour?

$$\frac{2}{3} \times \frac{5}{2} = \frac{5}{3} = 1\frac{2}{3} \text{ cups}$$

Example 2

A board is $8\dfrac{3}{4}$ ft long. You cut off $3\dfrac{1}{2}$ ft. Remaining length?

$$8\frac{3}{4} - 3\frac{2}{4} = 5\frac{1}{4} \text{ feet}$$

Example 3

A 6-foot ribbon is cut into $\dfrac{3}{4}$-ft pieces. How many pieces?

$$6 \div \frac{3}{4} = 6 \times \frac{4}{3} = 8 \text{ pieces}$$

Example 4

Maria spent $\dfrac{1}{4}$ of her savings on books and $\dfrac{1}{3}$ on clothes. Total fraction spent?

$$\frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12}$$

Example 5

A class of 30 students: $\dfrac{3}{5}$ play a sport. Of those, $\dfrac{1}{3}$ play basketball. How many play basketball?

$$\frac{1}{3} \times \frac{3}{5} \times 30 = \frac{1}{5} \times 30 = 6 \text{ students}$$

Example 6

A pipe fills $\dfrac{1}{6}$ of a pool per hour. Time to fill $\dfrac{3}{4}$ of the pool?

$$\frac{3}{4} \div \frac{1}{6} = \frac{3}{4} \times 6 = \frac{18}{4} = 4\frac{1}{2} \text{ hours}$$

Practice Problems

1. You have $\dfrac{3}{4}$ pizza and eat $\dfrac{1}{3}$ of it. How much of a whole pizza did you eat?
2. A rope is 12 ft. Cut off $3\dfrac{5}{8}$ ft. How long is the rest?
3. $4\dfrac{1}{2}$ cups of sugar; recipe needs $1\dfrac{3}{4}$ cups. How many full recipes?
4. Walk $\dfrac{2}{3}$ mi to school, then $\dfrac{3}{4}$ mi to the store. Total?
5. Plant flowers on $\dfrac{2}{5}$ of a $\dfrac{5}{6}$-acre garden. How many acres?
6. 24 cookies shared, $1\dfrac{1}{2}$ each. How many people?
7. Study $2\dfrac{1}{4}$ hr Mon, $1\dfrac{1}{2}$ hr Tue, $\dfrac{3}{4}$ hr Wed. Total?
8. Tank $\dfrac{7}{8}$ full; $\dfrac{3}{4}$ of the water used. Fraction used?
9. Recipe needs $\dfrac{2}{3}$ cup oil. Making $2\dfrac{1}{2}$ batches. How much oil?
10. Marathon = $26\dfrac{1}{5}$ mi. Runner completed $\dfrac{3}{4}$. Miles run?
Show Answer Key

1. $\dfrac{1}{4}$ pizza

2. $8\dfrac{3}{8}$ ft

3. $\dfrac{9}{2} \div \dfrac{7}{4} = \dfrac{18}{7} \approx 2\dfrac{4}{7}$ → 2 full recipes

4. $1\dfrac{5}{12}$ mi

5. $\dfrac{1}{3}$ acre

6. 16 people

7. $4\dfrac{1}{2}$ hours

8. $\dfrac{21}{32}$

9. $1\dfrac{2}{3}$ cups

10. $19\dfrac{13}{20}$ mi

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