Math worksheet for practicing operations with fractions, including addition, subtraction, multiplication, and division.

I'll solve each fraction problem step by step, checking my work carefully.

Problem 1: $\frac{7}{2} - \frac{9}{7}$
- Find common denominator: 2 × 7 = 14
- Convert: $\frac{7}{2} = \frac{49}{14}$ and $\frac{9}{7} = \frac{18}{14}$
- Subtract: $\frac{49}{14} - \frac{18}{14} = \frac{31}{14}$

Problem 2: $(-\frac{4}{3}) + (-\frac{6}{7})$
- This is the same as: $-\frac{4}{3} - \frac{6}{7}$
- Common denominator: 3 × 7 = 21
- Convert: $-\frac{4}{3} = -\frac{28}{21}$ and $-\frac{6}{7} = -\frac{18}{21}$
- Add: $-\frac{28}{21} + (-\frac{18}{21}) = -\frac{46}{21}$

Problem 3: $(-\frac{1}{2}) - (-\frac{6}{5})$
- Subtracting a negative becomes addition: $-\frac{1}{2} + \frac{6}{5}$
- Common denominator: 2 × 5 = 10
- Convert: $-\frac{1}{2} = -\frac{5}{10}$ and $\frac{6}{5} = \frac{12}{10}$
- Add: $-\frac{5}{10} + \frac{12}{10} = \frac{7}{10}$

Problem 4: $\frac{27}{7} \times (-\frac{2}{7})$
- Multiply numerators: 27 × (-2) = -54
- Multiply denominators: 7 × 7 = 49
- Result: $-\frac{54}{49}$

Problem 5: $\frac{7}{8} \div \frac{10}{9}$
- Division becomes multiplication by reciprocal: $\frac{7}{8} \times \frac{9}{10}$
- Multiply: $\frac{7 \times 9}{8 \times 10} = \frac{63}{80}$

Problem 6: $\frac{20}{7} - \frac{5}{2}$
- Common denominator: 7 × 2 = 14
- Convert: $\frac{20}{7} = \frac{40}{14}$ and $\frac{5}{2} = \frac{35}{14}$
- Subtract: $\frac{40}{14} - \frac{35}{14} = \frac{5}{14}$

Problem 7: $(-\frac{3}{2}) \div (-\frac{7}{3})$
- Division becomes multiplication by reciprocal: $(-\frac{3}{2}) \times (-\frac{3}{7})$
- Negative × negative = positive
- Multiply: $\frac{3 \times 3}{2 \times 7} = \frac{9}{14}$

Problem 8: $\frac{7}{3} \times (-\frac{13}{8})$
- Multiply numerators: 7 × (-13) = -91
- Multiply denominators: 3 × 8 = 24
- Result: $-\frac{91}{24}$

Problem 9: $(-\frac{7}{6}) \div \frac{16}{5}$
- Division becomes multiplication by reciprocal: $(-\frac{7}{6}) \times \frac{5}{16}$
- Multiply: $\frac{-7 \times 5}{6 \times 16} = -\frac{35}{96}$

Problem 10: $(-\frac{3}{2}) \times \frac{3}{2}$
- Multiply numerators: -3 × 3 = -9
- Multiply denominators: 2 × 2 = 4
- Result: $-\frac{9}{4}$

Final Answer:
1. $\frac{31}{14}$
2. $-\frac{46}{21}$
3. $\frac{7}{10}$
4. $-\frac{54}{49}$
5. $\frac{63}{80}$
6. $\frac{5}{14}$
7. $\frac{9}{14}$
8. $-\frac{91}{24}$
9. $-\frac{35}{96}$
10. $-\frac{9}{4}$