Simplify and leave your answer as a proper fraction or a mixed number. \( 5 \frac{5}{8}-4 \frac{1}{2}=\square \)

To simplify \( 5 \frac{5}{8} - 4 \frac{1}{2} \), first convert the mixed numbers to improper fractions. For \( 5 \frac{5}{8} \): \[ 5 \times 8 + 5 = 40 + 5 = 45 \] So, \( 5 \frac{5}{8} = \frac{45}{8} \). For \( 4 \frac{1}{2} \): \[ 4 \times 2 + 1 = 8 + 1 = 9 \] So, \( 4 \frac{1}{2} = \frac{9}{2} \). Now, find a common denominator to subtract the fractions. The common denominator between 8 and 2 is 8. Convert \( \frac{9}{2} \) to eighths: \[ \frac{9}{2} = \frac{9 \times 4}{2 \times 4} = \frac{36}{8} \] Now, subtract: \[ \frac{45}{8} - \frac{36}{8} = \frac{45 - 36}{8} = \frac{9}{8} \] Now, convert \( \frac{9}{8} \) back to a mixed number: \[ 9 \div 8 = 1 \, \text{R} \, 1 \] So, \( \frac{9}{8} = 1 \frac{1}{8} \). Thus, the answer is: \[ 1 \frac{1}{8} \]