Fraction word problems worksheet for students, featuring school-related math questions.

Let's solve each problem step by step.

---

Problem 1: How many girls are there in the school?

#### Given:
- Total number of students = 864
- Fraction of students who are boys = \(\frac{5}{8}\)

#### Solution:
1. Calculate the number of boys:
\[
\text{Number of boys} = \frac{5}{8} \times 864 = \frac{5 \times 864}{8} = \frac{4320}{8} = 540
\]

2. Calculate the number of girls:
\[
\text{Number of girls} = \text{Total students} - \text{Number of boys} = 864 - 540 = 324
\]

#### Answer:
\[
\boxed{324}
\]

---

Problem 2: How many boys are there in the soccer team?

#### Given:
- Total number of boys = 540 (from Problem 1)
- Fraction of boys who joined the basketball team = \(\frac{1}{6}\)
- Fraction of boys who joined the soccer team = \(\frac{2}{9}\)

#### Solution:
1. Calculate the number of boys in the soccer team:
\[
\text{Number of boys in soccer team} = \frac{2}{9} \times 540 = \frac{2 \times 540}{9} = \frac{1080}{9} = 120
\]

#### Answer:
\[
\boxed{120}
\]

---

Problem 3: What fraction of all students take the school bus to school?

#### Given:
- Total number of students = 864
- Fraction of students in grades 1 and 2 = \(\frac{5}{24}\)
- Fraction of grades 1 and 2 students who take the school bus = \(\frac{4}{7}\)

#### Solution:
1. Calculate the number of students in grades 1 and 2:
\[
\text{Number of students in grades 1 and 2} = \frac{5}{24} \times 864 = \frac{5 \times 864}{24} = \frac{4320}{24} = 180
\]

2. Calculate the number of students in grades 1 and 2 who take the school bus:
\[
\text{Number of students taking the bus} = \frac{4}{7} \times 180 = \frac{4 \times 180}{7} = \frac{720}{7} \approx 102.86
\]
Since the number of students must be a whole number, we assume the exact fraction is used without rounding.

3. Calculate the fraction of all students who take the school bus:
\[
\text{Fraction of all students taking the bus} = \frac{\text{Number of students taking the bus}}{\text{Total number of students}} = \frac{\frac{720}{7}}{864} = \frac{720}{7 \times 864} = \frac{720}{6048} = \frac{5}{42}
\]

#### Answer:
\[
\boxed{\frac{5}{42}}
\]

---

Problem 4: What was the fraction of all students that called in to inform the school about missing school this day?

#### Given:
- Total number of students = 864
- Fraction of students who attended school = \(\frac{7}{12}\)
- Fraction of students who missed school = \(1 - \frac{7}{12} = \frac{5}{12}\)
- Fraction of students who missed school and called in = \(\frac{4}{5}\)

#### Solution:
1. Calculate the number of students who missed school:
\[
\text{Number of students who missed school} = \frac{5}{12} \times 864 = \frac{5 \times 864}{12} = \frac{4320}{12} = 360
\]

2. Calculate the number of students who missed school and called in:
\[
\text{Number of students who called in} = \frac{4}{5} \times 360 = \frac{4 \times 360}{5} = \frac{1440}{5} = 288
\]

3. Calculate the fraction of all students who called in:
\[
\text{Fraction of all students who called in} = \frac{\text{Number of students who called in}}{\text{Total number of students}} = \frac{288}{864} = \frac{1}{3}
\]

#### Answer:
\[
\boxed{\frac{1}{3}}
\]

---

Problem 5: How many staff members are invited to the meeting?

#### Given:
- Total number of staff members = 80
- Fraction of staff members who are teaching staff = \(\frac{13}{16}\)

#### Solution:
1. Calculate the number of teaching staff members:
\[
\text{Number of teaching staff members} = \frac{13}{16} \times 80 = \frac{13 \times 80}{16} = \frac{1040}{16} = 65
\]

#### Answer:
\[
\boxed{65}
\]

---

Problem 6: How many staff members were at the meeting?

#### Given:
- Total number of staff members = 80
- Fraction of teaching staff not in school for a field trip = \(\frac{1}{5}\)

#### Solution:
1. Calculate the number of teaching staff members:
\[
\text{Number of teaching staff members} = 65 \quad (\text{from Problem 5})
\]

2. Calculate the number of teaching staff members who were not in school:
\[
\text{Number of teaching staff not in school} = \frac{1}{5} \times 65 = \frac{65}{5} = 13
\]

3. Calculate the number of teaching staff members who were in school:
\[
\text{Number of teaching staff in school} = 65 - 13 = 52
\]

4. Calculate the number of non-teaching staff members:
\[
\text{Number of non-teaching staff members} = 80 - 65 = 15
\]

5. Calculate the total number of staff members at the meeting:
\[
\text{Total staff members at the meeting} = \text{Teaching staff in school} + \text{Non-teaching staff} = 52 + 15 = 67
\]

#### Answer:
\[
\boxed{67}
\]

---

Final Answers:

1. \(\boxed{324}\)
2. \(\boxed{120}\)
3. \(\boxed{\frac{5}{42}}\)
4. \(\boxed{\frac{1}{3}}\)
5. \(\boxed{65}\)
6. \(\boxed{67}\)