In order to determine which comparisson is correct, you take into account the least common multiple of the denominators of the fractions. Then, you mutltiply the inequality or the equation by the least common multiple to cancel out the denominators. In this way it is going to be more clear if the comparisson are correct or not.
You rewrite the given inequalities as follow:
First inequality:
[tex]\frac{1}{2}<\frac{1}{3}[/tex]multiply both sides by 6:
[tex]\begin{gathered} 6(\frac{1}{2})<6(\frac{1}{3}) \\ 3<2 \end{gathered}[/tex]The previous result is inconsecuent, so, the comparisson is incorrect.
Second inequality: here you multiply both sides by 48
[tex]\begin{gathered} \frac{3}{8}>\frac{1}{6} \\ 48(\frac{3}{8})>48(\frac{1}{6}) \\ 18>8 \end{gathered}[/tex]The last result is consecuent, so, the comparisson is correct.
Third inequality: here you multiply by 24
[tex]\begin{gathered} \frac{5}{6}<\frac{3}{4} \\ 24(\frac{5}{6})<24(\frac{3}{4}) \\ 20<18 \end{gathered}[/tex]The last result is inconsecuent, so, the comparisson is incorrect.
Fourth equation: here, you multiply both sides by 35:
[tex]\begin{gathered} \frac{3}{5}=\frac{5}{7} \\ 35(\frac{3}{5})=35(\frac{5}{7}) \\ 21=25 \end{gathered}[/tex]It is evident that the previous result is wrong. Then, the comparisson is incorrect.
