Grade 8 Fraction Word Problems worksheet with a cake illustration, designed for educational practice.

Here is the solution to each problem from the worksheet, along with explanations:

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Problem 1:

A recipe for a cake requires 3/4 cup of sugar, 2/3 cup of flour, and 1/2 cup of butter. If you want to triple the recipe, how much of each ingredient do you need?

Solution:
To triple the recipe, multiply each ingredient by 3.

- Sugar: \( \frac{3}{4} \times 3 = \frac{9}{4} = 2\frac{1}{4} \) cups
- Flour: \( \frac{2}{3} \times 3 = 2 \) cups
- Butter: \( \frac{1}{2} \times 3 = \frac{3}{2} = 1\frac{1}{2} \) cups

Answer:
Sugar: \( 2\frac{1}{4} \) cups, Flour: 2 cups, Butter: \( 1\frac{1}{2} \) cups

---

Problem 2:

A rectangular swimming pool has a length of 20 meters and a width of 3/5 of the length. What is the area of the pool?

Solution:
1. Calculate the width:
\[
\text{Width} = \frac{3}{5} \times 20 = \frac{60}{5} = 12 \text{ meters}
\]

2. Calculate the area:
\[
\text{Area} = \text{Length} \times \text{Width} = 20 \times 12 = 240 \text{ square meters}
\]

Answer:
240 square meters

---

Problem 3:

In a school, 2/5 of the students play soccer, and 3/7 of the soccer players also play basketball. If there are 210 students in total, how many students play both soccer and basketball?

Solution:
1. Calculate the number of students who play soccer:
\[
\text{Students playing soccer} = \frac{2}{5} \times 210 = \frac{420}{5} = 84
\]

2. Calculate the number of students who play both soccer and basketball:
\[
\text{Students playing both} = \frac{3}{7} \times 84 = \frac{252}{7} = 36
\]

Answer:
36 students

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Problem 4:

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random and not replaced, what is the probability of selecting a blue marble followed by a red marble?

Solution:
1. Total marbles initially:
\[
5 + 3 + 2 = 10
\]

2. Probability of drawing a blue marble first:
\[
P(\text{Blue}) = \frac{3}{10}
\]

3. After drawing a blue marble, there are 9 marbles left (5 red, 2 blue, 2 green). Probability of drawing a red marble next:
\[
P(\text{Red after Blue}) = \frac{5}{9}
\]

4. Combined probability:
\[
P(\text{Blue then Red}) = P(\text{Blue}) \times P(\text{Red after Blue}) = \frac{3}{10} \times \frac{5}{9} = \frac{15}{90} = \frac{1}{6}
\]

Answer:
\( \frac{1}{6} \)

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Problem 5:

A rectangular box is 5/8 full with books. If the box can hold 48 books when full, how many books are in the box?

Solution:
1. Calculate the number of books when the box is 5/8 full:
\[
\text{Books in the box} = \frac{5}{8} \times 48 = \frac{240}{8} = 30
\]

Answer:
30 books

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Problem 6:

A pizza is divided into 16 equal slices. If Sara eats 3/4 of the pizza, how many slices does she eat?

Solution:
1. Calculate the number of slices Sara eats:
\[
\text{Slices eaten} = \frac{3}{4} \times 16 = \frac{48}{4} = 12
\]

Answer:
12 slices

---

Problem 7:

The ratio of boys to girls in a class is 5:3. If there are 64 students in total, how many girls are in the class?

Solution:
1. Let the number of boys be \( 5x \) and the number of girls be \( 3x \). The total number of students is:
\[
5x + 3x = 8x
\]

2. Given that the total number of students is 64:
\[
8x = 64 \implies x = \frac{64}{8} = 8
\]

3. Number of girls:
\[
3x = 3 \times 8 = 24
\]

Answer:
24 girls

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Problem 8:

A tank is filled with 2/3 of its total capacity. If the tank holds 90 liters when full, how many liters of water are in the tank?

Solution:
1. Calculate the amount of water in the tank:
\[
\text{Water in the tank} = \frac{2}{3} \times 90 = \frac{180}{3} = 60 \text{ liters}
\]

Answer:
60 liters

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Problem 9:

A car traveled 3/5 of a distance in 4 hours. If the car traveled at a constant speed, how many more hours will it take to complete the entire distance?

Solution:
1. Let the total distance be \( D \). The car traveled \( \frac{3}{5}D \) in 4 hours.
2. Time to travel the remaining \( \frac{2}{5}D \):
- Since the speed is constant, the time taken is proportional to the distance.
- Time for \( \frac{3}{5}D \) is 4 hours, so time for \( \frac{2}{5}D \) is:
\[
\text{Time for } \frac{2}{5}D = \frac{2}{3} \times 4 = \frac{8}{3} \approx 2.67 \text{ hours}
\]

Answer:
\( \frac{8}{3} \) hours or approximately 2.67 hours

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Problem 10:

Out of a class of 40 students, 3/8 of them are studying French, and 1/4 of the French students are also studying Spanish. How many students are studying both French and Spanish?

Solution:
1. Calculate the number of students studying French:
\[
\text{Students studying French} = \frac{3}{8} \times 40 = \frac{120}{8} = 15
\]

2. Calculate the number of students studying both French and Spanish:
\[
\text{Students studying both} = \frac{1}{4} \times 15 = \frac{15}{4} = 3.75
\]
Since the number of students must be a whole number, we round to the nearest whole number if necessary. However, in this context, it is reasonable to assume the problem implies exact fractions, so the answer is:
\[
3.75 \approx 4 \text{ (if rounding is allowed)}
\]
But strictly following the fraction, it's 3.75.

Answer:
3.75 students (or 4 if rounding is applied)

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Final Answers:

1. Sugar: \( 2\frac{1}{4} \) cups, Flour: 2 cups, Butter: \( 1\frac{1}{2} \) cups
2. 240 square meters
3. 36 students
4. \( \frac{1}{6} \)
5. 30 books
6. 12 slices
7. 24 girls
8. 60 liters
9. \( \frac{8}{3} \) hours
10. 3.75 students

Boxed Final Answer:
\[
\boxed{3.75}
\]