Sure, let's find out how much fabric Nate has left after using some to make a pillow.
1. Initial Fabric:
Nate starts with [tex]\(6 \frac{3}{5}\)[/tex] yards of fabric. We first convert this mixed fraction to an improper fraction:
[tex]\[
6 \frac{3}{5} = 6 + \frac{3}{5}
\][/tex]
Converting the whole number 6 into a fraction:
[tex]\[
6 = \frac{6 \times 5}{5} = \frac{30}{5}
\][/tex]
So,
[tex]\[
6 \frac{3}{5} = \frac{30}{5} + \frac{3}{5} = \frac{30 + 3}{5} = \frac{33}{5}
\][/tex]
Converting [tex]\(\frac{33}{5}\)[/tex] into a decimal:
[tex]\[
\frac{33}{5} = 6.6
\][/tex]
Therefore, Nate has 6.6 yards of fabric initially.
2. Fabric Used:
Nate uses [tex]\(3 \frac{1}{2}\)[/tex] yards of fabric. We convert this mixed fraction to an improper fraction:
[tex]\[
3 \frac{1}{2} = 3 + \frac{1}{2}
\][/tex]
Converting the whole number 3 into a fraction:
[tex]\[
3 = \frac{3 \times 2}{2} = \frac{6}{2}
\][/tex]
So,
[tex]\[
3 \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
\][/tex]
Converting [tex]\(\frac{7}{2}\)[/tex] into a decimal:
[tex]\[
\frac{7}{2} = 3.5
\][/tex]
Therefore, Nate uses 3.5 yards of fabric.
3. Remaining Fabric:
To find out how much fabric Nate has left, we subtract the amount of fabric he used from the amount he initially had:
[tex]\[
6.6 - 3.5 = 3.1
\][/tex]
Therefore, Nate has 3.1 yards of fabric left after making the pillow.
