1. The problem is to simplify the fraction $\frac{75}{120}$ to its simplest form. 2. To simplify a fraction, we divide both the numerator and denominator by their greatest common divisor (GCD). 3. Find the GCD of 75 and 120. - Prime factors of 75: $3 \times 5 \times 5$ - Prime factors of 120: $2 \times 2 \times 2 \times 3 \times 5$ - Common factors: $3$ and $5$ - GCD is $3 \times 5 = 15$ 4. Divide numerator and denominator by 15: $$\frac{\cancel{15} \times 5}{\cancel{15} \times 8} = \frac{5}{8}$$ 5. Therefore, the simplest form of $\frac{75}{120}$ is $\frac{5}{8}$.