To determine which amount of fabric is the greatest, we need to compare the given improper fractions. Here are the fractions we need to compare:
- [tex]\( \frac{22}{3} \)[/tex]
- [tex]\( \frac{43}{5} \)[/tex]
- [tex]\( \frac{78}{9} \)[/tex]
- [tex]\( \frac{33}{4} \)[/tex]
First, let's convert these improper fractions to decimal form:
1. Convert [tex]\( \frac{22}{3} \)[/tex] to a decimal:
[tex]\[
\frac{22}{3} = 22 \div 3 \approx 7.3333
\][/tex]
2. Convert [tex]\( \frac{43}{5} \)[/tex] to a decimal:
[tex]\[
\frac{43}{5} = 43 \div 5 = 8.6
\][/tex]
3. Convert [tex]\( \frac{78}{9} \)[/tex] to a decimal:
[tex]\[
\frac{78}{9} = 78 \div 9 \approx 8.6667
\][/tex]
4. Convert [tex]\( \frac{33}{4} \)[/tex] to a decimal:
[tex]\[
\frac{33}{4} = 33 \div 4 = 8.25
\][/tex]
Now, we compare these decimal values:
- [tex]\( \frac{22}{3} \approx 7.3333 \)[/tex]
- [tex]\( \frac{43}{5} = 8.6 \)[/tex]
- [tex]\( \frac{78}{9} \approx 8.6667 \)[/tex]
- [tex]\( \frac{33}{4} = 8.25 \)[/tex]
From the decimal forms, it is clear that [tex]\( \frac{78}{9} \approx 8.6667 \)[/tex] is the greatest value among the fractions.
Therefore, the amount with the greatest yardage is:
[tex]\[ C. \frac{78}{9} \][/tex]
