Hello Donnella.
Before I show you how to answer this question, I want to point out some of the words in the question and how they translate into a mathematical equation.
"She used 1/3 of the material."
This means you multiply whatever you are starting with by 1/3.
So in this case Mineko begins with 3/5 yd.
So,
3/5 • 1/3 = 1/5
She used 1/5 yard to make the pillow.
She has 2/5 yard left.