What are two ways you can tell that two ratios form a proportion?

Two ratiOS form a proportion if their cross products are equal; that is, for the ratiOS ( \frac{a}{b} ) and ( \frac{c}{d} ), the condition ( a \times d = b \times c ) must hold true. Additionally, if two ratiOS simplify to the same value, they are proportional. For example, ( \frac{2}{4} ) simplifies to ( \frac{1}{2} ), which is equal to ( \frac{3}{6} ), indicating that the two ratiOS are proportional.