Fraction word problems worksheet focusing on real-world applications of fractions in a headphone manufacturing context.

Let's solve each problem step by step.

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Problem 1:

The time to manufacture a pair of headphones on each assembly line is \(\frac{1}{3}\) hour. If there are 24 assembly lines and they operate 8 hours a day, how many pairs of headphones can be manufactured in a day?

#### Solution:
1. Time to manufacture one pair of headphones per line: \(\frac{1}{3}\) hour.
2. Number of pairs manufactured per line in 1 hour:
\[
\text{Pairs per line per hour} = \frac{1}{\frac{1}{3}} = 3
\]
3. Number of pairs manufactured per line in 8 hours:
\[
\text{Pairs per line in 8 hours} = 3 \times 8 = 24
\]
4. Total number of pairs manufactured by 24 lines in 8 hours:
\[
\text{Total pairs} = 24 \times 24 = 576
\]

Answer:
\[
\boxed{576}
\]

---

Problem 2:

\(\frac{1}{8}\) gram of copper and \(\frac{1}{3}\) gram of silicone is used to manufacture 30 headphones. How much silicone is used in each pair of headphones?

#### Solution:
1. Total silicone used for 30 headphones: \(\frac{1}{3}\) gram.
2. Silicone used per pair of headphones:
\[
\text{Silicone per pair} = \frac{\frac{1}{3}}{30} = \frac{1}{3} \times \frac{1}{30} = \frac{1}{90}
\]

Answer:
\[
\boxed{\frac{1}{90}}
\]

---

Problem 3:

To make sure the machines in the factory run smoothly, the mechanics need to add \(\frac{1}{5}\) liter of oil to the machine every Monday. One Monday, a mechanic can only find 12 liters of oil in the storage. Is there enough oil for 65 machines?

#### Solution:
1. Oil required per machine: \(\frac{1}{5}\) liter.
2. Total oil required for 65 machines:
\[
\text{Total oil required} = 65 \times \frac{1}{5} = \frac{65}{5} = 13 \text{ liters}
\]
3. Oil available: 12 liters.
4. Comparison:
\[
12 \text{ liters} < 13 \text{ liters}
\]
Therefore, there is not enough oil.

Answer:
\[
\boxed{\text{No}}
\]

---

Problem 4:

A team of 6 workers at the factory is responsible to check the quality of the headphones manufactured. They have \(\frac{1}{2}\) hour to do quick tests on 15 randomly selected headphones. How many minutes do the workers have to test each pair of headphones?

#### Solution:
1. Total time available for testing: \(\frac{1}{2}\) hour.
2. Convert \(\frac{1}{2}\) hour to minutes:
\[
\frac{1}{2} \text{ hour} = \frac{1}{2} \times 60 = 30 \text{ minutes}
\]
3. Number of headphones to test: 15.
4. Time per headphone:
\[
\text{Time per headphone} = \frac{30 \text{ minutes}}{15} = 2 \text{ minutes}
\]

Answer:
\[
\boxed{2}
\]

---

Problem 5:

Usually, \(\frac{1}{1000}\) of the headphones cannot pass the tests. If they found 5 headphones failing, how many headphones did the workers test?

#### Solution:
1. Fraction of failing headphones: \(\frac{1}{1000}\).
2. Number of failing headphones: 5.
3. Let \(x\) be the total number of headphones tested.
\[
\frac{1}{1000} \times x = 5
\]
4. Solve for \(x\):
\[
x = 5 \times 1000 = 5000
\]

Answer:
\[
\boxed{5000}
\]

---

Problem 6:

After the headphones are tested, each pair of headphones are packed in a small box. Each small box is \(\frac{1}{4}\) cubic foot. How many boxes of headphones can fit into a truck with a cargo compartment of 60 cubic feet?

#### Solution:
1. Volume of one box: \(\frac{1}{4}\) cubic foot.
2. Total volume of the truck: 60 cubic feet.
3. Number of boxes that can fit:
\[
\text{Number of boxes} = \frac{60}{\frac{1}{4}} = 60 \times 4 = 240
\]

Answer:
\[
\boxed{240}
\]

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Final Answers:

1. \(\boxed{576}\)
2. \(\boxed{\frac{1}{90}}\)
3. \(\boxed{\text{No}}\)
4. \(\boxed{2}\)
5. \(\boxed{5000}\)
6. \(\boxed{240}\)