Joanne has 13 1/4 yd of fabric to make 4.5 costumes. How many yards of fabric will Joanne use for each costume?

Question

Which operation will you use?

Answer 1

To find out how many yards of fabric Joanne will use for each costume, you need to divide the total amount of fabric she has by the number of costumes she is making.

The total amount of fabric Joanne has is \( 13 \frac{1}{4} \) yards, and she is making \( 4.5 \) costumes.

First, convert \( 13 \frac{1}{4} \) to an improper fraction: \[ 13 \frac{1}{4} = \frac{13 \times 4 + 1}{4} = \frac{52 + 1}{4} = \frac{53}{4} \text{ yards} \]

Next, you can perform the division: \[ \text{Fabric per costume} = \frac{\text{Total fabric}}{\text{Number of costumes}} = \frac{\frac{53}{4}}{4.5} \]

To make this division easier, convert \( 4.5 \) to a fraction: \[ 4.5 = \frac{9}{2} \]

Now, perform the division: \[ \frac{\frac{53}{4}}{\frac{9}{2}} = \frac{53}{4} \times \frac{2}{9} = \frac{53 \times 2}{4 \times 9} = \frac{106}{36} \]

Now, simplify the fraction \( \frac{106}{36} \):

• Divide the numerator and denominator by 2: \[ \frac{106 ÷ 2}{36 ÷ 2} = \frac{53}{18} \]

Thus, the amount of fabric Joanne will use for each costume is \( \frac{53}{18} \) yards.

To summarize, the operation you will use is division.

Answer 2

Joanne has 13 1/4 yd of fabric to make 4.5 costumes. How many yards of fabric will Joanne use for each costume?
a. 2 17/18
b. 18/53
c. 17 3/4
d 8 3/4

Answer 3

To find out how many yards of fabric Joanne will use for each costume, we can first convert the mixed number and decimal into fractions, then perform the division.

1. Convert \( 13 \frac{1}{4} \) to an improper fraction: \[ 13 \frac{1}{4} = \frac{13 \times 4 + 1}{4} = \frac{52 + 1}{4} = \frac{53}{4} \text{ yards} \]

2. Convert \( 4.5 \) to a fraction: \[ 4.5 = \frac{9}{2} \]

3. Now, divide the total fabric by the number of costumes: \[ \text{Fabric per costume} = \frac{\frac{53}{4}}{\frac{9}{2}} = \frac{53}{4} \times \frac{2}{9} = \frac{53 \times 2}{4 \times 9} = \frac{106}{36} \]

4. Simplify \( \frac{106}{36} \):

   • Find the greatest common divisor (GCD) for 106 and 36.
   • The GCD is 2.

   \[ \frac{106 \div 2}{36 \div 2} = \frac{53}{18} \]

5. Convert \( \frac{53}{18} \) to a mixed number:

   • \( 53 \div 18 = 2 \) with a remainder of \( 17 \).
   • So, \( \frac{53}{18} = 2 \frac{17}{18} \).

Therefore, the amount of fabric Joanne uses for each costume is \( 2 \frac{17}{18} \).

The correct answer is: a. \( 2 \frac{17}{18} \).