1. The problem asks to calculate $\frac{20}{40} \times 30$. 2. Simplify the fraction $\frac{20}{40}$ by dividing numerator and denominator by their greatest common divisor 20: $$\frac{20}{40} = \frac{20 \div 20}{40 \div 20} = \frac{1}{2}$$ 3. Now multiply the simplified fraction by 30: $$\frac{1}{2} \times 30 = \frac{30}{2}$$ 4. Simplify $\frac{30}{2}$: $$\frac{30}{2} = 15$$ 5. Final answer is $15$.