1. The problem asks: "17/25 of what number equals 9?" We need to find the unknown number. 2. Let the unknown number be $x$. The equation is: $$\frac{17}{25} \times x = 9$$ 3. To solve for $x$, divide both sides by $\frac{17}{25}$: $$x = \frac{9}{\frac{17}{25}}$$ 4. Dividing by a fraction is the same as multiplying by its reciprocal: $$x = 9 \times \frac{25}{17}$$ 5. Multiply: $$x = \frac{9 \times 25}{17} = \frac{225}{17}$$ 6. Simplify the fraction if possible. Since 225 and 17 have no common factors other than 1, the fraction is in simplest form. 7. Convert to decimal for clarity: $$x \approx 13.24$$ So, the number is $\frac{225}{17}$ or approximately 13.24.