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?

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.