Question

write $9 \frac{1}{2}$ as an improper fraction.

Explanation:

Step1: Recall the formula for converting mixed numbers to improper fractions.

The formula is: For a mixed number \( a \frac{b}{c} \), the improper fraction is \( \frac{a \times c + b}{c} \), where \( a \) is the whole number part, \( b \) is the numerator of the fractional part, and \( c \) is the denominator of the fractional part.

Step2: Identify the values of \( a \), \( b \), and \( c \) for the given mixed number \( 9 \frac{1}{2} \).

Here, \( a = 9 \), \( b = 1 \), and \( c = 2 \).

Step3: Apply the formula.

First, calculate \( a \times c + b \): \( 9 \times 2 + 1 = 18 + 1 = 19 \).
Then, the denominator remains \( c = 2 \). So the improper fraction is \( \frac{19}{2} \).

Answer:

\(\frac{19}{2}\)