Dividing Fractions — Process & Examples

We can define the remainder for real numbers $x$ and $y$ (with $y \not= 0$) by $$\text{rem}(x,y) = x - y \left\lfloor \frac{x}{y} \right\rfloor$$ where $\left\lfloor \frac{x}{y} \right\rfloor$ denotes the greatest integer less than or equal to $\frac{x}{y}$. $\\$ What is the value of $\text{rem}(\frac{4}{7}, -\frac{1}{3})$?