1. **State the problem:** Solve for $x$ in the equation $\frac{x}{13} = \frac{7}{91}$.\n\n2. **Formula and rule:** To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, cross-multiply to get $a \times d = b \times c$.\n\n3. **Apply cross-multiplication:** Multiply both sides: $x \times 91 = 13 \times 7$.\n\n4. **Calculate the right side:** $13 \times 7 = 91$. So, $91x = 91$.\n\n5. **Solve for $x$:** Divide both sides by 91: $x = \frac{91}{91} = 1$.\n\n**Final answer:** $x = 1$.