1. The problem is to subtract the fractions $\frac{9}{10}$ and $\frac{1}{2}$. 2. To subtract fractions, they must have a common denominator. The denominators here are 10 and 2. 3. Find the least common denominator (LCD) of 10 and 2, which is 10. 4. Convert $\frac{1}{2}$ to a fraction with denominator 10: multiply numerator and denominator by 5 to get $\frac{5}{10}$. 5. Now subtract the fractions: $\frac{9}{10} - \frac{5}{10} = \frac{9-5}{10} = \frac{4}{10}$. 6. Simplify $\frac{4}{10}$ by dividing numerator and denominator by their greatest common divisor, 2: $\frac{4 \div 2}{10 \div 2} = \frac{2}{5}$. 7. The final answer is $\frac{2}{5}$.