First, we must convert the mixed fraction 3 1/2 into a simple fraction form:
[tex]3\frac{1}{2}=\frac{2\cdot3+1}{2}=\frac{7}{2}[/tex]and now, we can apply the rule of three as
[tex]\begin{gathered} \frac{1}{4}\text{tsp paprika ------- }\frac{7}{2}tsp.\text{salt} \\ \frac{1}{2}\text{tsp paprika ------- x} \end{gathered}[/tex]then, x is given by
[tex]x=\frac{(\frac{1}{4})(\frac{7}{2})}{\frac{1}{2}}[/tex]the x is given by
[tex]\begin{gathered} x=\frac{\frac{1\cdot7}{4\cdot2}}{\frac{1}{2}} \\ x=\frac{\frac{7}{8}}{\frac{1}{2}} \end{gathered}[/tex]now, by appliying the sandwich law, we have
[tex]\begin{gathered} x=\frac{7\cdot2}{8\cdot1} \\ x=\frac{14}{8} \end{gathered}[/tex]this last result is equivalente to
[tex]x=\frac{7}{4}[/tex]in other words, we need 7/4 tsp of salt for 1/2 tsp of paprika.
