Each problem shows two bars of the same width, divided into their own number of equal parts and shaded, and the student writes <, > or = between them. Because both bars are the same width, the one shaded further along is the larger fraction - no common denominator or cross-multiplying required.
The two bars usually have different numbers of parts on purpose: two bars split the same way is just counting, not comparing. About one problem in ten is a genuine equality - two bars with different numbers of parts shaded exactly as far, like 2/4 next to 1/2 - which is the case that makes the visual method worth trusting: it agrees with the arithmetic every time.
Since both bars are the same total width, compare how far the shading reaches. The bar shaded further along represents the larger fraction - the number of parts each bar is cut into does not matter for comparing, only the total length shaded.
Yes, and it happens on purpose about one time in ten - a bar cut into quarters with two shaded reaches exactly as far as a bar cut in half with one shaded, because 2/4 and 1/2 are the same value.
Sometimes, but not most of the time on purpose - two bars split into the same number of parts turns the question into simple counting rather than a real comparison.
That page writes both fractions as numbers and expects a common-denominator or cross-multiplication method. This page answers by looking at two pictures instead - the visual method most curricula teach before the numeric one.