Fraction multiplication practice worksheet with 18 problems requiring students to multiply fractions without a calculator and simplify answers.

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

#### Step-by-Step Solution:

We will solve each multiplication problem step by step, simplifying where possible.

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Row 1:

1. $\frac{1}{5} \times \frac{15}{18}$
- Multiply numerators: $1 \times 15 = 15$
- Multiply denominators: $5 \times 18 = 90$
- Result: $\frac{15}{90}$
- Simplify: Both 15 and 90 are divisible by 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 numerators: $2 \times 12 = 24$
- Multiply denominators: $3 \times 22 = 66$
- Result: $\frac{24}{66}$
- Simplify: Both 24 and 66 are divisible by 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 numerators: $1 \times 10 = 10$
- Multiply denominators: $2 \times 12 = 24$
- Result: $\frac{10}{24}$
- Simplify: Both 10 and 24 are divisible by 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 numerators: $-3 \times 12 = -36$
- Multiply denominators: $4 \times 14 = 56$
- Result: $\frac{-36}{56}$
- Simplify: Both 36 and 56 are divisible by 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 numerators: $2 \times -5 = -10$
- Multiply denominators: $5 \times 10 = 50$
- Result: $\frac{-10}{50}$
- Simplify: Both 10 and 50 are divisible by 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 numerators: $-2 \times -3 = 6$ (negative times negative is positive)
- Multiply denominators: $7 \times 10 = 70$
- Result: $\frac{6}{70}$
- Simplify: Both 6 and 70 are divisible by 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 numerators: $-5 \times -6 = 30$ (negative times negative is positive)
- Multiply denominators: $6 \times 7 = 42$
- Result: $\frac{30}{42}$
- Simplify: Both 30 and 42 are divisible by 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 numerators: $3 \times 3 = 9$
- Multiply denominators: $5 \times 4 = 20$
- Result: $\frac{9}{20}$
- No further simplification needed.
- Final Answer: $\boxed{\frac{9}{20}}$

9. $\frac{-7}{8} \times \frac{5}{10}$
- Multiply numerators: $-7 \times 5 = -35$
- Multiply denominators: $8 \times 10 = 80$
- Result: $\frac{-35}{80}$
- Simplify: Both 35 and 80 are divisible by 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 numerators: $-3 \times 7 = -21$
- Multiply denominators: $5 \times 13 = 65$
- Result: $\frac{-21}{65}$
- No further simplification needed.
- Final Answer: $\boxed{\frac{-21}{65}}$

11. $\frac{3}{8} \times \frac{-5}{9}$
- Multiply numerators: $3 \times -5 = -15$
- Multiply denominators: $8 \times 9 = 72$
- Result: $\frac{-15}{72}$
- Simplify: Both 15 and 72 are divisible by 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 numerators: $-1 \times -9 = 9$ (negative times negative is positive)
- Multiply denominators: $3 \times 16 = 48$
- Result: $\frac{9}{48}$
- Simplify: Both 9 and 48 are divisible by 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 numerators: $-1 \times 9 = -9$
- Multiply denominators: $3 \times 14 = 42$
- Result: $\frac{-9}{42}$
- Simplify: Both 9 and 42 are divisible by 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 numerators: $-1 \times 16 = -16$
- Multiply denominators: $2 \times 28 = 56$
- Result: $\frac{-16}{56}$
- Simplify: Both 16 and 56 are divisible by 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 numerators: $3 \times 8 = 24$
- Multiply denominators: $4 \times 21 = 84$
- Result: $\frac{24}{84}$
- Simplify: Both 24 and 84 are divisible by 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 numerators: $-1 \times -8 = 8$ (negative times negative is positive)
- Multiply denominators: $2 \times 9 = 18$
- Result: $\frac{8}{18}$
- Simplify: Both 8 and 18 are divisible by 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 numerators: $-1 \times 16 = -16$
- Multiply denominators: $8 \times 17 = 136$
- Result: $\frac{-16}{136}$
- Simplify: Both 16 and 136 are divisible by 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 numerators: $0 \times -3 = 0$
- Multiply denominators: $4 \times 7 = 28$
- Result: $\frac{0}{28} = 0$
- Final Answer: $\boxed{0}$

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Final Answers:

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