1. The problem is to calculate the value of $7\frac{1}{2} - 20\%$.\n\n2. First, convert the mixed number $7\frac{1}{2}$ to an improper fraction or decimal.\n$7\frac{1}{2} = 7 + \frac{1}{2} = 7 + 0.5 = 7.5$\n\n3. Convert $20\%$ to a decimal.\n$20\% = \frac{20}{100} = 0.2$\n\n4. Now subtract $0.2$ from $7.5$.\n$7.5 - 0.2 = 7.3$\n\n5. So, the final answer is $7.3$.