ANSWER
[tex] \frac{1}{6} \: yards[/tex]
EXPLANATION
It was given that, Joan has
[tex] \frac{1}{2} \: yard \: of \: felt[/tex]
and she will use
[tex] \frac{1}{3} [/tex]
of it to make place cards.
We want to find how felt she will use for place cards.
We just have to find,
[tex] = \frac{1}{3} \: of \: \frac{1}{2} [/tex]
[tex] = \frac{1}{3} \times \frac{1}{2} [/tex]
[tex] = \frac{1}{6} [/tex]
Therefore Joan will use
[tex] \frac{1}{6} [/tex]
yards of felt for the place cards.