we'd first off, convert the mixed fractions to "improper" and then do the subtraction from there, so let's do so,
[tex]\bf \stackrel{mixed}{7\frac{1}{7}}\implies \cfrac{7\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{49}{7}}
\\\\\\
\stackrel{mixed}{6\frac{13}{14}}\implies \cfrac{6\cdot 14+13}{14}\implies \stackrel{improper}{\cfrac{97}{14}}\\\\
-------------------------------\\\\
\cfrac{49}{7}-\cfrac{97}{14}\impliedby \textit{our LCD is 14}\implies \cfrac{(2)49~~-~~(1)97}{14}
\\\\\\
\cfrac{98~~-~~97}{14}\implies \cfrac{1}{14}[/tex]
