Fraction word problems worksheet for practicing multiplication and division of fractions.

It seems you've uploaded a task involving multiplying and dividing fractions. Below, I will solve each problem step by step and explain the solution.

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Problem 6:

Question: Ethan ate $\frac{2}{3}$ of his popcorn. His friend John ate $\frac{2}{5}$ as much as Ethan. How much of the popcorn did John eat?

Solution:
1. Let's denote the total amount of popcorn Ethan ate as $\frac{2}{3}$.
2. John ate $\frac{2}{5}$ of what Ethan ate. To find out how much John ate, we multiply:
\[
\text{John's portion} = \frac{2}{5} \times \frac{2}{3}
\]
3. Multiply the numerators and the denominators:
\[
\frac{2}{5} \times \frac{2}{3} = \frac{2 \times 2}{5 \times 3} = \frac{4}{15}
\]

Answer:
\[
\boxed{\frac{4}{15}}
\]

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Problem 7:

Question: Tobias had 2 pounds of popcorn, and he split the popcorn into bags with $\frac{2}{5}$ pound in each bag. How many bags of popcorn did he fill?

Solution:
1. Tobias has a total of 2 pounds of popcorn.
2. Each bag contains $\frac{2}{5}$ pound of popcorn.
3. To find the number of bags, we divide the total amount of popcorn by the amount per bag:
\[
\text{Number of bags} = \frac{2}{\frac{2}{5}}
\]
4. Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{2}{\frac{2}{5}} = 2 \times \frac{5}{2} = \frac{2 \times 5}{2} = \frac{10}{2} = 5
\]

Answer:
\[
\boxed{5}
\]

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Problem 8:

Question: Guram ran $\frac{3}{4}$ of a mile on Saturday. He ran $\frac{2}{3}$ that much on Sunday. How much did he run on Sunday?

Solution:
1. Guram ran $\frac{3}{4}$ of a mile on Saturday.
2. On Sunday, he ran $\frac{2}{3}$ of what he ran on Saturday. To find out how much he ran on Sunday, we multiply:
\[
\text{Sunday's distance} = \frac{2}{3} \times \frac{3}{4}
\]
3. Multiply the numerators and the denominators:
\[
\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}
\]
4. Simplify the fraction:
\[
\frac{6}{12} = \frac{1}{2}
\]

Answer:
\[
\boxed{\frac{1}{2}}
\]

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Problem 9:

Question: The bakery paid $\frac{1}{2}$ of a cent for frosting on each cookie. They baked and frosted 7 cookies on Thursday. How much frosting did they use?

Solution:
1. The cost of frosting for one cookie is $\frac{1}{2}$ of a cent.
2. They baked and frosted 7 cookies. To find the total cost of frosting, we multiply:
\[
\text{Total frosting cost} = 7 \times \frac{1}{2}
\]
3. Perform the multiplication:
\[
7 \times \frac{1}{2} = \frac{7}{2} = 3.5
\]

Answer:
\[
\boxed{3.5}
\]

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Problem 10:

Question: Lily had $\frac{3}{4}$ of a gallon of lemonade. She poured $\frac{1}{3}$ of a gallon into cups for a party. How many cups did Lily fill?

Solution:
1. Lily had $\frac{3}{4}$ of a gallon of lemonade.
2. She poured $\frac{1}{3}$ of a gallon into cups. To find out how many cups she filled, we divide:
\[
\text{Number of cups} = \frac{\frac{3}{4}}{\frac{1}{3}}
\]
3. Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{\frac{3}{4}}{\frac{1}{3}} = \frac{3}{4} \times \frac{3}{1} = \frac{3 \times 3}{4 \times 1} = \frac{9}{4}
\]
4. Convert the improper fraction to a mixed number:
\[
\frac{9}{4} = 2 \frac{1}{4}
\]

Answer:
\[
\boxed{2 \frac{1}{4}}
\]

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Final Answers:

1. Problem 6: $\boxed{\frac{4}{15}}$
2. Problem 7: $\boxed{5}$
3. Problem 8: $\boxed{\frac{1}{2}}$
4. Problem 9: $\boxed{3.5}$
5. Problem 10: $\boxed{2 \frac{1}{4}}$