Multiplying fractions word problems worksheet with illustrated examples for math practice.

Let's solve each problem step by step.

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Problem 1:

Lucy is training for a long distance race. She runs \(\frac{5}{8}\) of a kilometer every day during her first week of training. How many kilometers did she run during that first week?

#### Solution:
- Lucy runs \(\frac{5}{8}\) km each day.
- There are 7 days in a week.
- Total distance run in one week = \(7 \times \frac{5}{8}\).

\[
7 \times \frac{5}{8} = \frac{7 \times 5}{8} = \frac{35}{8}
\]

- Convert \(\frac{35}{8}\) to a mixed number:
\[
\frac{35}{8} = 4 \frac{3}{8} \text{ km}
\]

#### Final Answer:
\[
\boxed{4 \frac{3}{8}}
\]

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Problem 2:

If it takes Micah 4 minutes to swim \(\frac{1}{10}\) of a kilometer, how long would it take him to swim 2 kilometers?

#### Solution:
- Micah swims \(\frac{1}{10}\) km in 4 minutes.
- To find the time to swim 1 km, multiply the time for \(\frac{1}{10}\) km by 10:
\[
4 \times 10 = 40 \text{ minutes per km}
\]
- To find the time to swim 2 km, multiply the time for 1 km by 2:
\[
40 \times 2 = 80 \text{ minutes}
\]

#### Final Answer:
\[
\boxed{80}
\]

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Problem 3:

There are 27 players on the JV baseball team. Out of all of the players, \(\frac{2}{9}\) of them are left-handed. Of those left-handed players, \(\frac{2}{3}\) of them are over 6 feet tall. How many players on the JV baseball team are left-handed and over 6 feet tall?

#### Solution:
1. Find the number of left-handed players:
\[
\text{Left-handed players} = \frac{2}{9} \times 27 = \frac{2 \times 27}{9} = \frac{54}{9} = 6
\]

2. Find the number of left-handed players who are over 6 feet tall:
\[
\text{Left-handed and over 6 feet tall} = \frac{2}{3} \times 6 = \frac{2 \times 6}{3} = \frac{12}{3} = 4
\]

#### Final Answer:
\[
\boxed{4}
\]

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Problem 4:

Danny ordered 16 pizzas for a party. \(\frac{3}{4}\) of the pizzas have toppings and the rest are plain. Of the pizzas with toppings, \(\frac{1}{3}\) of them have olives and the rest have only mushrooms. How many pizzas have only mushrooms?

#### Solution:
1. Find the number of pizzas with toppings:
\[
\text{Pizzas with toppings} = \frac{3}{4} \times 16 = \frac{3 \times 16}{4} = \frac{48}{4} = 12
\]

2. Find the number of pizzas with olives:
\[
\text{Pizzas with olives} = \frac{1}{3} \times 12 = \frac{1 \times 12}{3} = \frac{12}{3} = 4
\]

3. Find the number of pizzas with only mushrooms:
\[
\text{Pizzas with only mushrooms} = \text{Pizzas with toppings} - \text{Pizzas with olives} = 12 - 4 = 8
\]

#### Final Answer:
\[
\boxed{8}
\]

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Problem 5:

There is \(\frac{3}{5}\) of a birthday cake left over from last night's party. Mariah ate \(\frac{1}{3}\) of the leftover cake for breakfast this morning. How much of the cake did she eat?

#### Solution:
1. Mariah ate \(\frac{1}{3}\) of the leftover cake, which is \(\frac{3}{5}\) of the original cake.
\[
\text{Amount Mariah ate} = \frac{1}{3} \times \frac{3}{5} = \frac{1 \times 3}{3 \times 5} = \frac{3}{15} = \frac{1}{5}
\]

#### Final Answer:
\[
\boxed{\frac{1}{5}}
\]

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Problem 6:

Tina is making bags of homemade cookies to share with her coworkers. She plans on making 36 cookies, where each cookie will weigh \(\frac{1}{5}\) pounds. If she puts 4 cookies in each box, how much will each box weigh?

#### Solution:
1. Each cookie weighs \(\frac{1}{5}\) pounds.
2. Each box contains 4 cookies.
3. Weight of each box:
\[
\text{Weight of each box} = 4 \times \frac{1}{5} = \frac{4 \times 1}{5} = \frac{4}{5} \text{ pounds}
\]

#### Final Answer:
\[
\boxed{\frac{4}{5}}
\]

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Final Answers:

1. \(\boxed{4 \frac{3}{8}}\)
2. \(\boxed{80}\)
3. \(\boxed{4}\)
4. \(\boxed{8}\)
5. \(\boxed{\frac{1}{5}}\)
6. \(\boxed{\frac{4}{5}}\)