Solve Mixed Number Division: 1 5/13 ÷ 5/13

To solve this problem, we'll follow these steps:

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Multiply by the reciprocal of the fraction.
• Step 3: Simplify and express the result as a decimal if necessary.

Now, let's work through each step:
Step 1: Convert $1 \frac{5}{13}$ to an improper fraction. To do this, multiply the whole number 1 by the denominator 13 and add the numerator 5:
$1 \frac{5}{13} = \frac{1 \cdot 13 + 5}{13} = \frac{13 + 5}{13} = \frac{18}{13}$
Step 2: To divide by $\frac{5}{13}$, multiply by the reciprocal of the fraction $\frac{5}{13}$, which is $\frac{13}{5}$:
$\frac{18}{13} \times \frac{13}{5} = \frac{18 \cdot 13}{13 \cdot 5} = \frac{18}{5}$
Step 3: Simplify the fraction $\frac{18}{5}$ by dividing 18 by 5:
$\frac{18}{5} = 3.6$

Therefore, the solution to the problem is $3.6$.