First, we'll convert the mixed number of fabric Joanne has into an improper fraction for easier calculations.
Joanne has 13 1/4 yards of fabric:
\[ 13 \frac{1}{4} = \frac{13 \times 4 + 1}{4} = \frac{52 + 1}{4} = \frac{53}{4} \text{ yards} \]
Next, to find out how much fabric is used for each costume, we divide the total fabric by the number of costumes:
\[ \text{Fabric per costume} = \frac{\text{Total fabric}}{\text{Number of costumes}} = \frac{\frac{53}{4}}{4.5} \]
We can convert \(4.5\) into a fraction:
\[ 4.5 = \frac{9}{2} \]
Now we will perform the division:
\[ \frac{53}{4} \div \frac{9}{2} = \frac{53}{4} \times \frac{2}{9} = \frac{53 \times 2}{4 \times 9} = \frac{106}{36} \]
Now let's simplify \( \frac{106}{36} \):
To simplify, we divide both the numerator and denominator by their greatest common divisor (which is 2):
\[ \frac{106 \div 2}{36 \div 2} = \frac{53}{18} \]
This fraction \( \frac{53}{18} \) can be converted back into a mixed number:
\[ 53 \div 18 = 2 \text{ R } 17 \]
So, \( \frac{53}{18} = 2 \frac{17}{18} \).
Thus, the amount of fabric used for each costume is \( 2 \frac{17}{18} \) yards.
Among the options provided, the corresponding answer is 2 and 17 over 18.