Unit fraction word problems - Math Worksheets - MathsDiary.com - Free Printable

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

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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?

#### Step-by-step Solution:

- Time to make one pair = $ \frac{1}{3} $ hour
- So, in 1 hour, one line can make $ \frac{1}{\frac{1}{3}} = 3 $ pairs.
- In 8 hours, one line makes:
$ 3 \times 8 = 24 $ pairs
- With 24 lines:
$ 24 \times 24 = 576 $ pairs

✔ Answer: 576 pairs of headphones per day.

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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?

#### Step-by-step Solution:

- Total silicone for 30 headphones = $ \frac{1}{3} $ gram
- Silicone per pair = $ \frac{1}{3} \div 30 = \frac{1}{3} \times \frac{1}{30} = \frac{1}{90} $

✔ Answer: $ \frac{1}{90} $ gram of silicone per pair.

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Problem 3:

To make sure the machines run smoothly, mechanics need to add $ \frac{1}{5} $ liter of oil to each machine every Monday. One Monday, a mechanic finds 12 liters of oil. Is there enough oil for 65 machines?

#### Step-by-step Solution:

- Oil needed per machine = $ \frac{1}{5} $ liter
- For 65 machines:
$ 65 \times \frac{1}{5} = \frac{65}{5} = 13 $ liters
- Available oil = 12 liters
- Since 12 < 13 → Not enough

✔ Answer: No, there is not enough oil. They need 13 liters but only have 12.

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Problem 4:

A team of 6 workers has $ \frac{1}{2} $ hour to test 15 randomly selected headphones. How many minutes do the workers have to test each pair?

#### Step-by-step Solution:

- Total time available = $ \frac{1}{2} $ hour = 30 minutes
- Number of headphones to test = 15
- Time per headphone = $ \frac{30}{15} = 2 $ minutes

✔ Answer: 2 minutes per pair.

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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?

#### Step-by-step Solution:

Let total number tested = $ x $

Given:
$$
\frac{1}{1000} \times x = 5
$$

Solve for $ x $:
$$
x = 5 \times 1000 = 5000
$$

✔ Answer: 5000 headphones were tested.

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Problem 6:

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

#### Step-by-step Solution:

- Volume of one box = $ \frac{1}{4} $ ft³
- Total volume = 60 ft³
- Number of boxes = $ 60 \div \frac{1}{4} = 60 \times 4 = 240 $

✔ Answer: 240 boxes can fit.

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✔ Final Answers Summary:

1. 576 pairs
2. $ \frac{1}{90} $ gram of silicone per pair
3. No, not enough oil (need 13 L, have 12 L)
4. 2 minutes per pair
5. 5000 headphones tested
6. 240 boxes

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