To compare 13/19 and 17/25 a student cross-multiplies and gets $13\times 25=325$ and $17\times 19=323$. The correct conclusion is:

In cross-multiplication each product belongs to the fraction whose numerator was used: 325 goes with 13/19 and 323 goes with 17/25. The larger product marks the larger fraction, so 13/19 > 17/25. As decimals, 13/19 ≈ 0.6842 and 17/25 = 0.68, which agrees. Attaching each product to the wrong fraction is the usual error.