Worksheet for practicing multiplying fractions using cross cancelling with real-world word problems.

Problem 1:

The closet in the foyer is $\frac{7}{8}$ feet high, and the closet in the bedroom is $\frac{3}{4}$ times as high as the closet in the foyer. What is the height of the closet in the bedroom?

#### Solution:
To find the height of the closet in the bedroom, we need to multiply the height of the closet in the foyer by $\frac{3}{4}$.

1. Height of the closet in the foyer: $\frac{7}{8}$ feet.
2. The closet in the bedroom is $\frac{3}{4}$ times as high as the closet in the foyer. Therefore, we calculate:
\[
\text{Height of the closet in the bedroom} = \frac{7}{8} \times \frac{3}{4}
\]

3. Multiply the fractions:
\[
\frac{7}{8} \times \frac{3}{4} = \frac{7 \times 3}{8 \times 4} = \frac{21}{32}
\]

Thus, the height of the closet in the bedroom is $\boxed{\frac{21}{32}}$ feet.

---

Problem 2:

Dolores picked $\frac{5}{6}$ of a bushel of corn last year. If she collected $\frac{3}{5}$ since the yield this year, how much corn did she harvest this year?

#### Solution:
To find out how much corn Dolores harvested this year, we need to multiply the amount of corn she picked last year by $\frac{3}{5}$.

1. Amount of corn picked last year: $\frac{5}{6}$ of a bushel.
2. This year, she collected $\frac{3}{5}$ of what she picked last year. Therefore, we calculate:
\[
\text{Amount of corn harvested this year} = \frac{5}{6} \times \frac{3}{5}
\]

3. Multiply the fractions:
\[
\frac{5}{6} \times \frac{3}{5} = \frac{5 \times 3}{6 \times 5} = \frac{15}{30}
\]

4. Simplify the fraction:
\[
\frac{15}{30} = \frac{1}{2}
\]

Thus, Dolores harvested $\boxed{\frac{1}{2}}$ of a bushel of corn this year.

---

Problem 3:

Percy's Earth-Day speech lasted $\frac{5}{6}$ minutes. If Naomi's speech was $\frac{2}{3}$ times longer than Percy's, how many minutes did Naomi speak for?

#### Solution:
To find the duration of Naomi's speech, we need to multiply the duration of Percy's speech by $\frac{2}{3}$.

1. Duration of Percy's speech: $\frac{5}{6}$ minutes.
2. Naomi's speech was $\frac{2}{3}$ times longer than Percy's. Therefore, we calculate:
\[
\text{Duration of Naomi's speech} = \frac{5}{6} \times \frac{2}{3}
\]

3. Multiply the fractions:
\[
\frac{5}{6} \times \frac{2}{3} = \frac{5 \times 2}{6 \times 3} = \frac{10}{18}
\]

4. Simplify the fraction:
\[
\frac{10}{18} = \frac{5}{9}
\]

Thus, Naomi spoke for $\boxed{\frac{5}{9}}$ minutes.

---

Problem 4:

The bird feeder had $\frac{11}{12}$ ounces of seeds in the morning. After a while, only $\frac{2}{3}$ of the seeds remained in the feeder. How many ounces of seeds remained?

#### Solution:
To find the amount of seeds remaining in the feeder, we need to multiply the initial amount of seeds by $\frac{2}{3}$.

1. Initial amount of seeds: $\frac{11}{12}$ ounces.
2. After some time, $\frac{2}{3}$ of the seeds remained. Therefore, we calculate:
\[
\text{Amount of seeds remaining} = \frac{11}{12} \times \frac{2}{3}
\]

3. Multiply the fractions:
\[
\frac{11}{12} \times \frac{2}{3} = \frac{11 \times 2}{12 \times 3} = \frac{22}{36}
\]

4. Simplify the fraction:
\[
\frac{22}{36} = \frac{11}{18}
\]

Thus, the amount of seeds remaining is $\boxed{\frac{11}{18}}$ ounces.

---

Problem 5:

Mr. Thompson wants to teach his daughters how to ride a bike. They cover $\frac{1}{4}$ of a mile on the first day. If they ride $2$ times the distance the next day, how many miles did they ride on the second day?

#### Solution:
To find the distance covered on the second day, we need to multiply the distance covered on the first day by $2$.

1. Distance covered on the first day: $\frac{1}{4}$ mile.
2. On the second day, they rode $2$ times the distance of the first day. Therefore, we calculate:
\[
\text{Distance covered on the second day} = \frac{1}{4} \times 2
\]

3. Multiply the fraction by $2$:
\[
\frac{1}{4} \times 2 = \frac{1 \times 2}{4} = \frac{2}{4}
\]

4. Simplify the fraction:
\[
\frac{2}{4} = \frac{1}{2}
\]

Thus, the distance covered on the second day is $\boxed{\frac{1}{2}}$ mile.

---

Final Answers:

1. $\boxed{\frac{21}{32}}$
2. $\boxed{\frac{1}{2}}$
3. $\boxed{\frac{5}{9}}$
4. $\boxed{\frac{11}{18}}$
5. $\boxed{\frac{1}{2}}$