If we have two fractions a/b and c/d:
[tex]\frac{a}{b}(\text{ })\frac{c}{d}[/tex]To determine which one of them is greater we make the cross product:
[tex]ad(\text{ })bc[/tex]We have 3 cases:
- If ad is greater than bc, then a/b is greater than c/d
- If bc is greater than ad, then c/d is greater than a/b
- If ad is equal to bc, then a/b is equal to c/d
For 1/2 and 2/7:
[tex]\begin{gathered} \frac{1}{2}(\text{ })\frac{2}{7} \\ 7\cdot1(_{\square})2\cdot2 \\ 7>4 \\ \Rightarrow\frac{1}{2}>\frac{2}{7} \end{gathered}[/tex]