1. The problem involves understanding how the fraction $\frac{4}{5}$ was obtained after dividing both sides of an equation by 625. 2. Suppose the original equation was $625x = 500$. 3. Dividing both sides by 625 gives: $$x = \frac{500}{625}$$ 4. Simplify the fraction $\frac{500}{625}$ by dividing numerator and denominator by their greatest common divisor, which is 125: $$\frac{500 \div 125}{625 \div 125} = \frac{4}{5}$$ 5. Therefore, $x = \frac{4}{5}$. This is how the fraction $\frac{4}{5}$ was obtained after dividing both sides by 625 and simplifying.