[tex]sugar \: \: 3 \frac{1}{4} \ \times \frac{1}{2} = \frac{13}{4} \times \frac{1}{2} \\ = \frac{13}{8} =1 \frac{5}{8 \: cups} [/tex]
[tex]floor \: \\ \frac{1}{2} of 1 \frac{1}{2} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} [/tex]
[tex]sugar \: \frac{1}{2} of \: \frac{3}{4} = \frac{1}{2} \times \frac{3}{4} \\ = \frac{3}{8} cup[/tex]