Worksheet with fraction word problems on multiplication and division.

Let's solve each of these word problems involving fraction multiplication and division step by step.

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Problem 1:

A wire of length $10\frac{1}{2}$ m is cut into 7 equal pieces. What is the length of each piece of the wire?

#### Step 1: Convert mixed number to improper fraction
$$
10\frac{1}{2} = \frac{21}{2}
$$

#### Step 2: Divide by 7
$$
\frac{21}{2} \div 7 = \frac{21}{2} \times \frac{1}{7} = \frac{21}{14} = \frac{3}{2}
$$

#### Final Answer:
$$
\boxed{\frac{3}{2}} \text{ m or } 1\frac{1}{2} \text{ m}
$$

Each piece is $1\frac{1}{2}$ meters long.

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Problem 2:

A rectangle is $12\frac{1}{2}$ m long and $\frac{4}{5}$ m wide. Find its area.

#### Step 1: Convert mixed number to improper fraction
$$
12\frac{1}{2} = \frac{25}{2}
$$

#### Step 2: Multiply length × width
$$
\text{Area} = \frac{25}{2} \times \frac{4}{5} = \frac{100}{10} = 10
$$

#### Final Answer:
$$
\boxed{10} \text{ m}^2
$$

The area of the rectangle is 10 square meters.

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Problem 3:

Lucy uses $\frac{8}{5}$ cups of sugar to make 24 brownies. How much sugar did she use to make one brownie?

#### Step 1: Divide total sugar by number of brownies
$$
\frac{8}{5} \div 24 = \frac{8}{5} \times \frac{1}{24} = \frac{8}{120} = \frac{1}{15}
$$

#### Final Answer:
$$
\boxed{\frac{1}{15}} \text{ cups}
$$

She used $\frac{1}{15}$ cup of sugar per brownie.

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Problem 4:

There are 25 water bottles. Each bottle is $\frac{3}{5}$-filled with water. If we empty all the bottles in a container, how many bottles can we fill with the same amount of water?

#### Step 1: Total water in all bottles
Each bottle has $\frac{3}{5}$ of its capacity.
So total water = $25 \times \frac{3}{5} = \frac{75}{5} = 15$ full bottles' worth.

#### Final Answer:
$$
\boxed{15} \text{ bottles}
$$

We can fill 15 full bottles with that amount of water.

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Problem 5:

How can $\frac{6}{11}$ of a cake be divided equally among 5 people?

We need to divide $\frac{6}{11}$ by 5:
$$
\frac{6}{11} \div 5 = \frac{6}{11} \times \frac{1}{5} = \frac{6}{55}
$$

#### Final Answer:
$$
\boxed{\frac{6}{55}} \text{ of the cake per person}
$$

Each person gets $\frac{6}{55}$ of the whole cake.

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Problem 6:

If one sheet of paper is $\frac{3}{4}$ cm thick, how thick is a pad containing 80 sheets?

Multiply thickness per sheet by number of sheets:
$$
80 \times \frac{3}{4} = \frac{240}{4} = 60
$$

#### Final Answer:
$$
\boxed{60} \text{ cm}
$$

The pad is 60 cm thick.

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✔ Summary of Answers:

| Problem | Answer |
|--------|--------|
| 1 | $1\frac{1}{2}$ m |
| 2 | $10$ m² |
| 3 | $\frac{1}{15}$ cups |
| 4 | $15$ bottles |
| 5 | $\frac{6}{55}$ of the cake per person |
| 6 | $60$ cm |

Let me know if you'd like visual explanations or diagrams for any of these!