To find out how many yards of fabric Joanne will use for each costume, you will divide the total amount of fabric she has by the number of costumes she is making.
Joanne has \(13 \frac{1}{4}\) yards of fabric. First, let's convert \(13 \frac{1}{4}\) to an improper fraction:
\[ 13 \frac{1}{4} = \frac{13 \times 4 + 1}{4} = \frac{52 + 1}{4} = \frac{53}{4} \]
Now, she is making 4.5 costumes, which can be converted into a fraction as well:
\[ 4.5 = \frac{9}{2} \]
Now we can find out how much fabric she uses per costume:
\[ \text{Fabric per costume} = \frac{\text{Total fabric}}{\text{Number of costumes}} = \frac{\frac{53}{4}}{\frac{9}{2}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \text{Fabric per costume} = \frac{53}{4} \times \frac{2}{9} = \frac{53 \times 2}{4 \times 9} = \frac{106}{36} \]
Now, simplify \(\frac{106}{36}\):
The greatest common divisor (GCD) of 106 and 36 is 2:
\[ \frac{106 \div 2}{36 \div 2} = \frac{53}{18} \]
Now, to convert \(\frac{53}{18}\) to a mixed number, we can perform the division:
\[ 53 \div 18 = 2 \quad \text{(with a remainder of } 17\text{)} \]
This means:
\[ \frac{53}{18} = 2 \frac{17}{18} \]
Therefore, Joanne will use \( \frac{53}{18}\) yards, or \( 2 \frac{17}{18} \) yards of fabric for each costume.
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