$\frac{1}{2} : \frac{1}{4} = \frac{1}{2} * 4 = 2$;
$2\frac{3}{4} : \frac{1}{4} = \frac{11}{4} * 4 = 11$;
$1 : \frac{1}{4} = 1 * 4 = 4$;
$\frac{5}{16} : \frac{1}{4} = \frac{5}{16} * 4 = \frac{5}{4} = 1\frac{1}{4}$;
$\frac{1}{8} : \frac{1}{4} = \frac{1}{8} * 4 = \frac{1}{2}$;
$\frac{3}{4} : \frac{1}{4} = \frac{3}{4} * 4 = 3$;
$2 : \frac{1}{4} = 2 * 4 = 8$;
$\frac{1}{4} : \frac{1}{4} = 1$.

$-\frac{1}{2} + \frac{1}{6} = -\frac{3}{6} + \frac{1}{6} = -\frac{2}{6} = -\frac{1}{3}$;
$\frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$;
$-\frac{1}{12} + \frac{1}{6} = -\frac{1}{12} + \frac{2}{12} = \frac{1}{12}$;
$-1 + \frac{1}{6} = -\frac{5}{6}$;
$\frac{5}{12} + \frac{1}{6} = \frac{5}{12} + \frac{2}{12} = \frac{7}{12}$;
$-\frac{1}{3} + \frac{1}{6} = -\frac{2}{6} + \frac{1}{6} = -\frac{1}{6}$;
$\frac{1}{2} + \frac{1}{6} = \frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3}$;
$-\frac{1}{6} + \frac{1}{6} = 0$.