1. The problem is to simplify the expression $\frac{625}{100} \times 100$. 2. The formula used here is basic arithmetic multiplication and division. 3. First, simplify the fraction $\frac{625}{100}$. 4. Both numerator and denominator can be divided by 25: $$\frac{\cancel{625}^{25}}{\cancel{100}^{25}} = \frac{25}{4}$$ 5. Now multiply the simplified fraction by 100: $$\frac{25}{4} \times 100$$ 6. Multiply numerator and denominator: $$\frac{25 \times 100}{4} = \frac{2500}{4}$$ 7. Simplify the fraction by dividing numerator and denominator by 4: $$\frac{\cancel{2500}^{4}}{\cancel{4}^{4}} = 625$$ 8. Therefore, the final answer is $625$.