Fraction Word Problems Worksheets - 15 Worksheets Library - Free Printable

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

---

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

---

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

---

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 in the box:
\[
\text{Books in the box} = \frac{5}{8} \times 48 = \frac{240}{8} = 30
\]

Answer:
30 books

---

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

---

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

---

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

---

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 intends exact fractions, so we keep it as 3.75.

Answer:
3.75 students (or 4 if rounding up)

---

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:
\[
\boxed{2\frac{1}{4}, 2, 1\frac{1}{2}, 240, 36, \frac{1}{6}, 30, 12, 24, 60, \frac{8}{3}, 3.75}
\]