The remainder can be defined for all real numbers $x$ and $y$ with $y\ne 0$ by $\mathrm{rem}(x,y)=x-y\lfloor \frac{x}{y}\rfloor$ where $\lfloor \frac{x}{y}\rfloor$ denotes the greatest integer less than or equal to $\frac{x}{y}$. What is the value of $\mathrm{rem}\left(\frac{7}{10},-\frac{1}{3}\right)$?