Respuesta :
In order to check if a comparison such as this is true, you can use this logical equivalence:
[tex] \dfrac{a}{b} > \dfrac{c}{d} \iff ad > bc,\quad \dfrac{a}{b} < \dfrac{c}{d} \iff ad < bc [/tex]
Anyway, it's not always necessary to make this check. We know that every proper fraction represents a number between 0 and 1, and any improper fraction represents a number greater than 1. So, every proper fraction is less than every improper fraction.
So, the first two options are surely wrong, because they ask for a proper fraction to be more than an improper fraction.
The third option compares two proper fractions, so we actually have to check:
[tex] \dfrac{16}{26}>\dfrac{30}{31} \iff 16 \cdot 31 > 26 \cdot 30 \iff 496 > 780[/tex]
which is false.
Last option:
[tex] \dfrac{35}{30}<\dfrac{22}{12} \iff 35 \cdot 12 < 30 \cdot 22 \iff 420 < 660[/tex]
Which is true.
