G8 Basic math worksheet on multiplying algebraic fractions with a bonus question about over-the-counter medicines.

Problem Analysis:

The task involves solving eight multiplication problems involving fractions with variables in the denominators. After solving these, there is a bonus question asking for three commonly used over-the-counter (OTC) medicines and their functions.

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Step-by-Step Solution:

#### 1. $\frac{5}{x} \cdot \frac{3}{x} = ?$

- Multiply the numerators: $5 \cdot 3 = 15$.
- Multiply the denominators: $x \cdot x = x^2$.
- Result: $\frac{15}{x^2}$.

$$
\boxed{\frac{15}{x^2}}
$$

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#### 2. $\frac{2}{3x} \cdot \frac{7}{3x} = ?$

- Multiply the numerators: $2 \cdot 7 = 14$.
- Multiply the denominators: $3x \cdot 3x = 9x^2$.
- Result: $\frac{14}{9x^2}$.

$$
\boxed{\frac{14}{9x^2}}
$$

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#### 3. $\frac{3}{2x} \cdot \frac{9}{2x} = ?$

- Multiply the numerators: $3 \cdot 9 = 27$.
- Multiply the denominators: $2x \cdot 2x = 4x^2$.
- Result: $\frac{27}{4x^2}$.

$$
\boxed{\frac{27}{4x^2}}
$$

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#### 4. $\frac{-3}{x^2} \cdot \frac{6}{x^2} = ?$

- Multiply the numerators: $-3 \cdot 6 = -18$.
- Multiply the denominators: $x^2 \cdot x^2 = x^4$.
- Result: $\frac{-18}{x^4}$.

$$
\boxed{\frac{-18}{x^4}}
$$

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#### 5. $\frac{2}{xy} \cdot \frac{10}{xy} = ?$

- Multiply the numerators: $2 \cdot 10 = 20$.
- Multiply the denominators: $xy \cdot xy = x^2y^2$.
- Result: $\frac{20}{x^2y^2}$.

$$
\boxed{\frac{20}{x^2y^2}}
$$

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#### 6. $\frac{-5}{3x^2} \cdot \frac{-7}{3x^2} = ?$

- Multiply the numerators: $-5 \cdot -7 = 35$.
- Multiply the denominators: $3x^2 \cdot 3x^2 = 9x^4$.
- Result: $\frac{35}{9x^4}$.

$$
\boxed{\frac{35}{9x^4}}
$$

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#### 7. $\frac{1}{x^2y^3} \cdot \frac{-2}{x^2y^3} = ?$

- Multiply the numerators: $1 \cdot -2 = -2$.
- Multiply the denominators: $x^2y^3 \cdot x^2y^3 = x^4y^6$.
- Result: $\frac{-2}{x^4y^6}$.

$$
\boxed{\frac{-2}{x^4y^6}}
$$

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#### 8. $\frac{-3}{-5x^2} \cdot \frac{-8}{-5x^2} = ?$

- Multiply the numerators: $-3 \cdot -8 = 24$.
- Multiply the denominators: $-5x^2 \cdot -5x^2 = 25x^4$.
- Result: $\frac{24}{25x^4}$.

$$
\boxed{\frac{24}{25x^4}}
$$

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Bonus Question:

Give three most commonly used OTC medicines and their functions.

1. Acetaminophen (e.g., Tylenol):
- Function: Pain reliever and fever reducer. Commonly used for headaches, muscle aches, and fevers.

2. Ibuprofen (e.g., Advil or Motrin):
- Function: Nonsteroidal anti-inflammatory drug (NSAID) that reduces pain, inflammation, and fever. Used for conditions like arthritis, menstrual cramps, and minor injuries.

3. Antihistamines (e.g., Benadryl):
- Function: Relieves symptoms of allergies, such as sneezing, itching, and runny nose, by blocking histamine receptors.

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Final Answer:

$$
\boxed{
\begin{array}{ll}
1. & \frac{15}{x^2} \\
2. & \frac{14}{9x^2} \\
3. & \frac{27}{4x^2} \\
4. & \frac{-18}{x^4} \\
5. & \frac{20}{x^2y^2} \\
6. & \frac{35}{9x^4} \\
7. & \frac{-2}{x^4y^6} \\
8. & \frac{24}{25x^4} \\
\end{array}
}
$$

Bonus Answer:
1. Acetaminophen: Pain reliever and fever reducer.
2. Ibuprofen: NSAID for pain, inflammation, and fever.
3. Antihistamines: Allergy symptom relief.