First, we find how is allotted for the \(\displaystyle{\frac{{{1}}}{{{8}}}}\) yard long pieces by finding the difference of \(\displaystyle{3}\ {y}{a}{r}{d}{s}\ {1}\times{\frac{{{1}}}{{{4}}}}\) yards:

\(\displaystyle{3}-{1}{\left(\times{\frac{{{1}}}{{{4}}}}\right)}={\left(\times{\frac{{{12}}}{{{4}}}}\right)}-{\left(\times{\frac{{{5}}}{{{4}}}}\right)}=\frac{{7}}{{4}}{y}{a}{r}{d}{s}\)

Then, we divide \(\times \frac{7}{4}\) yards by \(\times \frac{1}{8}\) yard to find the number of \(\frac{1}{8}\) yard long pieces:

\(\displaystyle{\left(\times{\frac{{{7}}}{{{4}}}}\right)}÷{\left({\frac{{{1}}}{{{8}}}}\right)}={\left(\times{\frac{{{7}}}{{{4}}}}\right)}\times{8}={14}\ pi{e}{c}{e}{s}\)