Question:
If \( a ⊙ b = \frac{ab}{4} \), evaluate:
\[ 3 ⊙ \left(\frac{1}{5} ⊙ \frac{1}{2}\right) \]
Options:
- (a) \( \frac{3}{160} \)
- (b) \( \frac{5}{160} \)
- (c) \( \frac{3}{10} \)
- (d) \( \frac{3}{40} \)
Solution:
Step 1: Compute inner operation
\[ \frac{1}{5} ⊙ \frac{1}{2} = \frac{\frac{1}{5} \cdot \frac{1}{2}}{4} = \frac{1}{10} \cdot \frac{1}{4} = \frac{1}{40} \]
Step 2: Compute outer operation
\[ 3 ⊙ \frac{1}{40} = \frac{3 \cdot \frac{1}{40}}{4} = \frac{3}{40} \cdot \frac{1}{4} = \frac{3}{160} \]
Final Answer:
\[ \boxed{\frac{3}{160}} \]
Correct Option: (a)