Fraction arithmetic worksheet for practicing addition and subtraction of positive and negative fractions.

To solve the given problems, we need to perform addition and subtraction of fractions. The key steps involve:

1. Finding a common denominator when adding or subtracting fractions.
2. Simplifying the result to ensure it is in its simplest form (proper or improper fraction).

Let's solve each problem step by step.

---

Problem 1:

\[
(-\frac{5}{6}) - (-\frac{7}{8}) - (-\frac{4}{6})
\]

#### Step 1: Simplify the expression
\[
-\frac{5}{6} + \frac{7}{8} + \frac{4}{6}
\]

#### Step 2: Combine like terms
\[
-\frac{5}{6} + \frac{4}{6} = -\frac{1}{6}
\]
So the expression becomes:
\[
-\frac{1}{6} + \frac{7}{8}
\]

#### Step 3: Find a common denominator
The denominators are 6 and 8. The least common denominator (LCD) is 24.
\[
-\frac{1}{6} = -\frac{4}{24}, \quad \frac{7}{8} = \frac{21}{24}
\]

#### Step 4: Add the fractions
\[
-\frac{4}{24} + \frac{21}{24} = \frac{17}{24}
\]

#### Final Answer:
\[
\boxed{\frac{17}{24}}
\]

---

Problem 2:

\[
\frac{8}{2} - \frac{3}{5}
\]

#### Step 1: Simplify \(\frac{8}{2}\)
\[
\frac{8}{2} = 4
\]
So the expression becomes:
\[
4 - \frac{3}{5}
\]

#### Step 2: Convert 4 to a fraction with denominator 5
\[
4 = \frac{20}{5}
\]
So the expression becomes:
\[
\frac{20}{5} - \frac{3}{5} = \frac{17}{5}
\]

#### Final Answer:
\[
\boxed{\frac{17}{5}}
\]

---

Problem 3:

\[
\frac{9}{4} - (-\frac{7}{8})
\]

#### Step 1: Simplify the expression
\[
\frac{9}{4} + \frac{7}{8}
\]

#### Step 2: Find a common denominator
The denominators are 4 and 8. The LCD is 8.
\[
\frac{9}{4} = \frac{18}{8}
\]

#### Step 3: Add the fractions
\[
\frac{18}{8} + \frac{7}{8} = \frac{25}{8}
\]

#### Final Answer:
\[
\boxed{\frac{25}{8}}
\]

---

Problem 4:

\[
(-\frac{4}{3}) + \frac{6}{7} + (-\frac{8}{3})
\]

#### Step 1: Combine like terms
\[
-\frac{4}{3} - \frac{8}{3} = -\frac{12}{3} = -4
\]
So the expression becomes:
\[
-4 + \frac{6}{7}
\]

#### Step 2: Convert -4 to a fraction with denominator 7
\[
-4 = -\frac{28}{7}
\]
So the expression becomes:
\[
-\frac{28}{7} + \frac{6}{7} = -\frac{22}{7}
\]

#### Final Answer:
\[
\boxed{-\frac{22}{7}}
\]

---

Problem 5:

\[
\frac{9}{7} + (-\frac{6}{3})
\]

#### Step 1: Simplify \(-\frac{6}{3}\)
\[
-\frac{6}{3} = -2
\]
So the expression becomes:
\[
\frac{9}{7} - 2
\]

#### Step 2: Convert -2 to a fraction with denominator 7
\[
-2 = -\frac{14}{7}
\]
So the expression becomes:
\[
\frac{9}{7} - \frac{14}{7} = -\frac{5}{7}
\]

#### Final Answer:
\[
\boxed{-\frac{5}{7}}
\]

---

Problem 6:

\[
(-\frac{2}{8}) + \frac{7}{4} + (-\frac{9}{8})
\]

#### Step 1: Simplify \(-\frac{2}{8}\)
\[
-\frac{2}{8} = -\frac{1}{4}
\]
So the expression becomes:
\[
-\frac{1}{4} + \frac{7}{4} - \frac{9}{8}
\]

#### Step 2: Combine \(-\frac{1}{4}\) and \(\frac{7}{4}\)
\[
-\frac{1}{4} + \frac{7}{4} = \frac{6}{4} = \frac{3}{2}
\]
So the expression becomes:
\[
\frac{3}{2} - \frac{9}{8}
\]

#### Step 3: Find a common denominator
The denominators are 2 and 8. The LCD is 8.
\[
\frac{3}{2} = \frac{12}{8}
\]
So the expression becomes:
\[
\frac{12}{8} - \frac{9}{8} = \frac{3}{8}
\]

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

---

Problem 7:

\[
\frac{8}{2} + (-\frac{6}{4})
\]

#### Step 1: Simplify \(\frac{8}{2}\) and \(-\frac{6}{4}\)
\[
\frac{8}{2} = 4, \quad -\frac{6}{4} = -\frac{3}{2}
\]
So the expression becomes:
\[
4 - \frac{3}{2}
\]

#### Step 2: Convert 4 to a fraction with denominator 2
\[
4 = \frac{8}{2}
\]
So the expression becomes:
\[
\frac{8}{2} - \frac{3}{2} = \frac{5}{2}
\]

#### Final Answer:
\[
\boxed{\frac{5}{2}}
\]

---

Problem 8:

\[
(-\frac{7}{3}) + (-\frac{6}{5}) + \frac{4}{3}
\]

#### Step 1: Combine \(-\frac{7}{3}\) and \(\frac{4}{3}\)
\[
-\frac{7}{3} + \frac{4}{3} = -\frac{3}{3} = -1
\]
So the expression becomes:
\[
-1 + (-\frac{6}{5})
\]

#### Step 2: Convert -1 to a fraction with denominator 5
\[
-1 = -\frac{5}{5}
\]
So the expression becomes:
\[
-\frac{5}{5} - \frac{6}{5} = -\frac{11}{5}
\]

#### Final Answer:
\[
\boxed{-\frac{11}{5}}
\]

---

Problem 9:

\[
\frac{3}{4} - \frac{7}{2} - (-\frac{9}{4})
\]

#### Step 1: Simplify the expression
\[
\frac{3}{4} - \frac{7}{2} + \frac{9}{4}
\]

#### Step 2: Combine \(\frac{3}{4}\) and \(\frac{9}{4}\)
\[
\frac{3}{4} + \frac{9}{4} = \frac{12}{4} = 3
\]
So the expression becomes:
\[
3 - \frac{7}{2}
\]

#### Step 3: Convert 3 to a fraction with denominator 2
\[
3 = \frac{6}{2}
\]
So the expression becomes:
\[
\frac{6}{2} - \frac{7}{2} = -\frac{1}{2}
\]

#### Final Answer:
\[
\boxed{-\frac{1}{2}}
\]

---

Problem 10:

\[
\frac{7}{5} + \frac{2}{9}
\]

#### Step 1: Find a common denominator
The denominators are 5 and 9. The LCD is 45.
\[
\frac{7}{5} = \frac{63}{45}, \quad \frac{2}{9} = \frac{10}{45}
\]

#### Step 2: Add the fractions
\[
\frac{63}{45} + \frac{10}{45} = \frac{73}{45}
\]

#### Final Answer:
\[
\boxed{\frac{73}{45}}
\]

---

Problem 11:

\[
(-\frac{7}{6}) + (-\frac{8}{3}) + (-\frac{4}{6})
\]

#### Step 1: Combine \(-\frac{7}{6}\) and \(-\frac{4}{6}\)
\[
-\frac{7}{6} - \frac{4}{6} = -\frac{11}{6}
\]
So the expression becomes:
\[
-\frac{11}{6} + (-\frac{8}{3})
\]

#### Step 2: Find a common denominator
The denominators are 6 and 3. The LCD is 6.
\[
-\frac{8}{3} = -\frac{16}{6}
\]
So the expression becomes:
\[
-\frac{11}{6} - \frac{16}{6} = -\frac{27}{6} = -\frac{9}{2}
\]

#### Final Answer:
\[
\boxed{-\frac{9}{2}}
\]

---

Problem 12:

\[
\frac{7}{3} - (-\frac{8}{9}) - (-\frac{2}{3})
\]

#### Step 1: Simplify the expression
\[
\frac{7}{3} + \frac{8}{9} + \frac{2}{3}
\]

#### Step 2: Combine \(\frac{7}{3}\) and \(\frac{2}{3}\)
\[
\frac{7}{3} + \frac{2}{3} = \frac{9}{3} = 3
\]
So the expression becomes:
\[
3 + \frac{8}{9}
\]

#### Step 3: Convert 3 to a fraction with denominator 9
\[
3 = \frac{27}{9}
\]
So the expression becomes:
\[
\frac{27}{9} + \frac{8}{9} = \frac{35}{9}
\]

#### Final Answer:
\[
\boxed{\frac{35}{9}}
\]

---

Problem 13:

\[
(-\frac{7}{8}) + (-\frac{9}{6})
\]

#### Step 1: Simplify \(-\frac{9}{6}\)
\[
-\frac{9}{6} = -\frac{3}{2}
\]
So the expression becomes:
\[
-\frac{7}{8} - \frac{3}{2}
\]

#### Step 2: Find a common denominator
The denominators are 8 and 2. The LCD is 8.
\[
-\frac{3}{2} = -\frac{12}{8}
\]
So the expression becomes:
\[
-\frac{7}{8} - \frac{12}{8} = -\frac{19}{8}
\]

#### Final Answer:
\[
\boxed{-\frac{19}{8}}
\]

---

Problem 14:

\[
(-\frac{5}{8}) - \frac{9}{2} - \frac{3}{8}
\]

#### Step 1: Combine \(-\frac{5}{8}\) and \(-\frac{3}{8}\)
\[
-\frac{5}{8} - \frac{3}{8} = -\frac{8}{8} = -1
\]
So the expression becomes:
\[
-1 - \frac{9}{2}
\]

#### Step 2: Convert -1 to a fraction with denominator 2
\[
-1 = -\frac{2}{2}
\]
So the expression becomes:
\[
-\frac{2}{2} - \frac{9}{2} = -\frac{11}{2}
\]

#### Final Answer:
\[
\boxed{-\frac{11}{2}}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{17}{24} \\
2. & \frac{17}{5} \\
3. & \frac{25}{8} \\
4. & -\frac{22}{7} \\
5. & -\frac{5}{7} \\
6. & \frac{3}{8} \\
7. & \frac{5}{2} \\
8. & -\frac{11}{5} \\
9. & -\frac{1}{2} \\
10. & \frac{73}{45} \\
11. & -\frac{9}{2} \\
12. & \frac{35}{9} \\
13. & -\frac{19}{8} \\
14. & -\frac{11}{2} \\
\end{array}
}
\]