Joanne has 13 1/4 yd of fabric to make 4.5 costumes. How many yards of fabric will Joanne use for each costume?(1 point) Responses 21718 2 and 17 over 18 1853 18 over 53 1734 17 and 3 fourths 834

Answer 1

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:

$$\frac{53}{4}÷\frac{9}{2}=\frac{53}{4}\times \frac{2}{9}=\frac{53\times 2}{4\times 9}=\frac{106}{36}$$

Now let's simplify $\frac{106}{36}$:

To simplify, we divide both the numerator and denominator by their greatest common divisor (which is 2):

$$\frac{106÷2}{36÷2}=\frac{53}{18}$$

This fraction $\frac{53}{18}$ can be converted back into a mixed number:

$$53÷18=2\text{ R }17$$

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.