Fraction word problems worksheet for educational use, designed to help students practice solving real-world math problems involving fractions.

Let's solve each of these fraction word problems step by step and explain the reasoning.

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Problem 1:

Rocky finished a 200-meter race in $ \frac{5}{12} $ of a minute. The winner of the race used $ \frac{21}{25} $ of Rocky’s time to finish the race. How much time did the winner use to finish the race?

#### Step-by-step solution:

We are told:
- Rocky's time = $ \frac{5}{12} $ minutes
- Winner's time = $ \frac{21}{25} $ of Rocky’s time

So, we multiply:
$$
\text{Winner's time} = \frac{21}{25} \times \frac{5}{12}
$$

Multiply numerators and denominators:
$$
= \frac{21 \times 5}{25 \times 12} = \frac{105}{300}
$$

Simplify:
$$
\frac{105}{300} = \frac{7}{20} \quad \text{(divided numerator and denominator by 15)}
$$

✔ Answer: $ \boxed{\frac{7}{20}} $ minutes

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Problem 2:

Patrick decided to run every day to keep himself healthy. He ended up running $ \frac{3}{5} $ of a kilometer every day. How much did he run in a week?

A week has 7 days.

So total distance = $ 7 \times \frac{3}{5} $

$$
= \frac{21}{5} = 4 \frac{1}{5} \text{ kilometers}
$$

✔ Answer: $ \boxed{4 \frac{1}{5}} $ km

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Problem 3:

Scarlett usually rides her bike about $ 1\frac{1}{5} $ hours every day. The distance between the library and school is $ \frac{7}{8} $ mile. Yesterday the bike had a problem and Scarlett only rode her bike $ \frac{2}{3} $ of the way from school to the library and walked the rest of the way. How far did she ride her bike?

We are only asked for the distance she rode, not the time.

Total distance = $ \frac{7}{8} $ mile
She rode $ \frac{2}{3} $ of this distance.

So:
$$
\text{Distance ridden} = \frac{2}{3} \times \frac{7}{8} = \frac{14}{24} = \frac{7}{12} \text{ miles}
$$

✔ Answer: $ \boxed{\frac{7}{12}} $ miles

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Problem 4:

It takes Olivia one minute to swim $ \frac{1}{60} $ of a kilometer. How far can she swim in 12 minutes?

In 1 minute → $ \frac{1}{60} $ km
In 12 minutes → $ 12 \times \frac{1}{60} = \frac{12}{60} = \frac{1}{5} $ km

✔ Answer: $ \boxed{\frac{1}{5}} $ km

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Problem 5:

The tallest basketball player in the school’s basketball team is 6 feet tall. Jacob’s height is $ \frac{11}{12} $ of the height of the tallest basketball player. What is Jacob’s height?

Tallest player = 6 feet
Jacob’s height = $ \frac{11}{12} \times 6 $

$$
= \frac{11 \times 6}{12} = \frac{66}{12} = 5.5 \text{ feet}
$$

Or as a fraction: $ \frac{66}{12} = \frac{11}{2} = 5 \frac{1}{2} $ feet

✔ Answer: $ \boxed{5 \frac{1}{2}} $ feet

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Problem 6:

Mila is a professional marathon runner. She spends 38 hours each week training. She spends $ \frac{2}{5} $ of her training time running and $ \frac{3}{8} $ of her training time in the gym. How many hours does she spend in the gym every week?

We need to find $ \frac{3}{8} $ of 38 hours.

$$
\frac{3}{8} \times 38 = \frac{3 \times 38}{8} = \frac{114}{8} = 14.25 \text{ hours}
$$

Or as a mixed number:
$$
\frac{114}{8} = \frac{57}{4} = 14 \frac{1}{4} \text{ hours}
$$

✔ Answer: $ \boxed{14 \frac{1}{4}} $ hours

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✔ Final Answers Summary:

1. $ \frac{7}{20} $ minutes
2. $ 4 \frac{1}{5} $ km
3. $ \frac{7}{12} $ miles
4. $ \frac{1}{5} $ km
5. $ 5 \frac{1}{2} $ feet
6. $ 14 \frac{1}{4} $ hours

Let me know if you'd like these explained visually or with diagrams!