5. Apply Math Models The world's smallest gecko is $$ \frac{3}{4} $$ inch long. An adult male Western Banded Gecko is $$ 7 \frac{1}{3} $$ times as long. How long is a Western Banded Gecko?

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To find the length of an adult male Western Banded Gecko, we need to multiply the length of the world's smallest gecko by the factor given.

1. **Identify the lengths:**
   - Length of the world's smallest gecko: $$ \frac{3}{4} $$ inch
   - Factor for the adult male Western Banded Gecko: $$ 7 \frac{1}{3} $$

2. **Convert the mixed number to an improper fraction:**
   - $$ 7 \frac{1}{3} = 7 + \frac{1}{3} = \frac{21}{3} + \frac{1}{3} = \frac{22}{3} $$

3. **Multiply the lengths:**
   - We need to calculate:
   $$
   \text{Length of Western Banded Gecko} = \frac{3}{4} \times \frac{22}{3}
   $$

4. **Perform the multiplication:**
   - The $$ 3 $$ in the numerator and denominator cancels out:
   $$
   = \frac{1}{4} \times 22 = \frac{22}{4}
   $$

5. **Simplify the fraction:**
   - $$ \frac{22}{4} = \frac{11}{2} $$

6. **Convert to a mixed number:**
   - $$ \frac{11}{2} = 5 \frac{1}{2} $$

Thus, the length of an adult male Western Banded Gecko is $$ 5 \frac{1}{2} $$ inches.
An adult male Western Banded Gecko is $$ 5 \frac{1}{2} $$ inches long.

5. Apply Math Models The world's smallest gecko is \( \frac{3}{4} \) inch long. An adult male Western Banded Gecko is \( 7 \frac{1}{3} \) times as long. How long is a Western Banded Gecko?

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