Comprehensive math worksheet designed to help students practice multiplying fractions, including negative values and simplification.

Problem: Multiply the fractions without a calculator. Show your work, be aware of the negative signs, and simplify your answers when possible.

We will solve each multiplication problem step by step.

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#### Row 1:

1. $\frac{1}{5} \times \frac{15}{18}$
- Multiply the numerators: $1 \times 15 = 15$
- Multiply the denominators: $5 \times 18 = 90$
- Result: $\frac{15}{90}$
- Simplify by dividing both numerator and denominator by their greatest common divisor (GCD), which is 15:
$$
\frac{15 \div 15}{90 \div 15} = \frac{1}{6}
$$
- Final answer: $\boxed{\frac{1}{6}}$

2. $\frac{2}{3} \times \frac{12}{22}$
- Multiply the numerators: $2 \times 12 = 24$
- Multiply the denominators: $3 \times 22 = 66$
- Result: $\frac{24}{66}$
- Simplify by dividing both numerator and denominator by their GCD, which is 6:
$$
\frac{24 \div 6}{66 \div 6} = \frac{4}{11}
$$
- Final answer: $\boxed{\frac{4}{11}}$

3. $\frac{1}{2} \times \frac{10}{12}$
- Multiply the numerators: $1 \times 10 = 10$
- Multiply the denominators: $2 \times 12 = 24$
- Result: $\frac{10}{24}$
- Simplify by dividing both numerator and denominator by their GCD, which is 2:
$$
\frac{10 \div 2}{24 \div 2} = \frac{5}{12}
$$
- Final answer: $\boxed{\frac{5}{12}}$

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#### Row 2:

4. $-\frac{3}{4} \times \frac{12}{14}$
- Multiply the numerators: $-3 \times 12 = -36$
- Multiply the denominators: $4 \times 14 = 56$
- Result: $\frac{-36}{56}$
- Simplify by dividing both numerator and denominator by their GCD, which is 4:
$$
\frac{-36 \div 4}{56 \div 4} = \frac{-9}{14}
$$
- Final answer: $\boxed{-\frac{9}{14}}$

5. $\frac{2}{5} \times \frac{-5}{10}$
- Multiply the numerators: $2 \times -5 = -10$
- Multiply the denominators: $5 \times 10 = 50$
- Result: $\frac{-10}{50}$
- Simplify by dividing both numerator and denominator by their GCD, which is 10:
$$
\frac{-10 \div 10}{50 \div 10} = \frac{-1}{5}
$$
- Final answer: $\boxed{-\frac{1}{5}}$

6. $-\frac{2}{7} \times \frac{-3}{10}$
- Multiply the numerators: $-2 \times -3 = 6$ (negative times negative gives positive)
- Multiply the denominators: $7 \times 10 = 70$
- Result: $\frac{6}{70}$
- Simplify by dividing both numerator and denominator by their GCD, which is 2:
$$
\frac{6 \div 2}{70 \div 2} = \frac{3}{35}
$$
- Final answer: $\boxed{\frac{3}{35}}$

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#### Row 3:

7. $-\frac{5}{6} \times \frac{-6}{7}$
- Multiply the numerators: $-5 \times -6 = 30$ (negative times negative gives positive)
- Multiply the denominators: $6 \times 7 = 42$
- Result: $\frac{30}{42}$
- Simplify by dividing both numerator and denominator by their GCD, which is 6:
$$
\frac{30 \div 6}{42 \div 6} = \frac{5}{7}
$$
- Final answer: $\boxed{\frac{5}{7}}$

8. $\frac{3}{5} \times \frac{3}{4}$
- Multiply the numerators: $3 \times 3 = 9$
- Multiply the denominators: $5 \times 4 = 20$
- Result: $\frac{9}{20}$
- This fraction is already in simplest form.
- Final answer: $\boxed{\frac{9}{20}}$

9. $-\frac{7}{8} \times \frac{5}{10}$
- Multiply the numerators: $-7 \times 5 = -35$
- Multiply the denominators: $8 \times 10 = 80$
- Result: $\frac{-35}{80}$
- Simplify by dividing both numerator and denominator by their GCD, which is 5:
$$
\frac{-35 \div 5}{80 \div 5} = \frac{-7}{16}
$$
- Final answer: $\boxed{-\frac{7}{16}}$

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#### Row 4:

10. $-\frac{3}{5} \times \frac{7}{13}$
- Multiply the numerators: $-3 \times 7 = -21$
- Multiply the denominators: $5 \times 13 = 65$
- Result: $\frac{-21}{65}$
- This fraction is already in simplest form.
- Final answer: $\boxed{-\frac{21}{65}}$

11. $\frac{3}{8} \times \frac{-5}{9}$
- Multiply the numerators: $3 \times -5 = -15$
- Multiply the denominators: $8 \times 9 = 72$
- Result: $\frac{-15}{72}$
- Simplify by dividing both numerator and denominator by their GCD, which is 3:
$$
\frac{-15 \div 3}{72 \div 3} = \frac{-5}{24}
$$
- Final answer: $\boxed{-\frac{5}{24}}$

12. $-\frac{1}{3} \times \frac{-9}{16}$
- Multiply the numerators: $-1 \times -9 = 9$ (negative times negative gives positive)
- Multiply the denominators: $3 \times 16 = 48$
- Result: $\frac{9}{48}$
- Simplify by dividing both numerator and denominator by their GCD, which is 3:
$$
\frac{9 \div 3}{48 \div 3} = \frac{3}{16}
$$
- Final answer: $\boxed{\frac{3}{16}}$

---

#### Row 5:

13. $-\frac{1}{3} \times \frac{9}{14}$
- Multiply the numerators: $-1 \times 9 = -9$
- Multiply the denominators: $3 \times 14 = 42$
- Result: $\frac{-9}{42}$
- Simplify by dividing both numerator and denominator by their GCD, which is 3:
$$
\frac{-9 \div 3}{42 \div 3} = \frac{-3}{14}
$$
- Final answer: $\boxed{-\frac{3}{14}}$

14. $-\frac{1}{2} \times \frac{16}{28}$
- Multiply the numerators: $-1 \times 16 = -16$
- Multiply the denominators: $2 \times 28 = 56$
- Result: $\frac{-16}{56}$
- Simplify by dividing both numerator and denominator by their GCD, which is 8:
$$
\frac{-16 \div 8}{56 \div 8} = \frac{-2}{7}
$$
- Final answer: $\boxed{-\frac{2}{7}}$

15. $\frac{3}{4} \times \frac{8}{21}$
- Multiply the numerators: $3 \times 8 = 24$
- Multiply the denominators: $4 \times 21 = 84$
- Result: $\frac{24}{84}$
- Simplify by dividing both numerator and denominator by their GCD, which is 12:
$$
\frac{24 \div 12}{84 \div 12} = \frac{2}{7}
$$
- Final answer: $\boxed{\frac{2}{7}}$

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#### Row 6:

16. $-\frac{1}{2} \times \frac{-8}{9}$
- Multiply the numerators: $-1 \times -8 = 8$ (negative times negative gives positive)
- Multiply the denominators: $2 \times 9 = 18$
- Result: $\frac{8}{18}$
- Simplify by dividing both numerator and denominator by their GCD, which is 2:
$$
\frac{8 \div 2}{18 \div 2} = \frac{4}{9}
$$
- Final answer: $\boxed{\frac{4}{9}}$

17. $-\frac{1}{8} \times \frac{16}{17}$
- Multiply the numerators: $-1 \times 16 = -16$
- Multiply the denominators: $8 \times 17 = 136$
- Result: $\frac{-16}{136}$
- Simplify by dividing both numerator and denominator by their GCD, which is 8:
$$
\frac{-16 \div 8}{136 \div 8} = \frac{-2}{17}
$$
- Final answer: $\boxed{-\frac{2}{17}}$

18. $\frac{0}{4} \times \frac{-3}{7}$
- Multiply the numerators: $0 \times -3 = 0$
- Multiply the denominators: $4 \times 7 = 28$
- Result: $\frac{0}{28} = 0$
- Final answer: $\boxed{0}$

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Final Answers:

$$
\boxed{
\begin{array}{ccc}
\frac{1}{6} & \frac{4}{11} & \frac{5}{12} \\
-\frac{9}{14} & -\frac{1}{5} & \frac{3}{35} \\
\frac{5}{7} & \frac{9}{20} & -\frac{7}{16} \\
-\frac{21}{65} & -\frac{5}{24} & \frac{3}{16} \\
-\frac{3}{14} & -\frac{2}{7} & \frac{2}{7} \\
\frac{4}{9} & -\frac{2}{17} & 0
\end{array}
}
$$