Erica bought 312 yars of fabric. If she uses 23 of the fabric to make...

Step 1
You know, I really don’t like the ${\displaystyle 3\frac{1}{2}}$ notation, I think it’s a lot more confusing than writing 3.5 or even ${\displaystyle \frac{7}{2}}$. I’ll use the latter here, to make the math easier.
Okay, Erica started with ${\displaystyle \frac{7}{2}}$ yards of fabric. Then, she uses ${\displaystyle \frac{2}{3}}$ of that. But how much is ${\displaystyle \frac{2}{3}}$ of ${\displaystyle \frac{7}{2}?}$ All you have to do is multiply!
${\displaystyle \frac{7}{2}\cdot \frac{2}{3}=\frac{14}{6}=\frac{7}{3}}$
Alright, she used ${\displaystyle \frac{7}{3}}$ yards of fabric in the curtain, if you take that out of the total how much will be left?
${\displaystyle \frac{7}{2}-\frac{7}{3}=\frac{21-14}{6}=\frac{7}{6}}$
Here it is, she will have ${\displaystyle \frac{7}{6}}$ yards of fabricleft. If you want the answer in that notation, it is ${\displaystyle 1\frac{1}{6}}$

Step 1
So, Erica bought ${\displaystyle 3\frac{1}{2}}$ yards of fabric. o make this easier to work with, we convert it to an improper fraction. Now we know Erica has ${\displaystyle \frac{7}{2}}$ yards of fabric.
Next, she uses ${\displaystyle \frac{2}{3}}$ of it. This means that ${\displaystyle \frac{1}{3}(=1-\frac{2}{3})}$ of the fabric is remaining.
To get ${\displaystyle \frac{1}{3}}$ of ${\displaystyle \frac{7}{2}}$, we just multiply them:
${\displaystyle (\frac{1}{3}(\left(\frac{7}{2}\right)=\frac{7}{6}}$
So now we know Erica has ${\displaystyle \frac{7}{6}}$ yards of fabric remaining. This is equivalent to ${\displaystyle 1\frac{1}{6}}$ yards, or 1 yard and 6 inches.

Step 1
She has
$3\frac{1}{2}=\frac{7}{2}=3.5$
yards and uses
$\frac{2}{3}=0.6$
So she has $\frac{1}{3}=0.3$
left that's
$\frac{7}{2}\times \frac{1}{3}=\frac{7}{6}$
$1\frac{1}{6}=1.16$ yards,