Final answer:
The equation (\(\frac{x}{2} \times \frac{2}{x} = 1\)) exemplifies the outcome when a fraction is multiplied by its reciprocal. The correct answer blends with the concept of multiplicative identity and reciprocals, which is not listed among the provided options. The closest related property from the options is the multiplication property of equality.
Step-by-step explanation:
The student's question asks which property is illustrated by the equation (\(\frac{x}{2} \times \frac{2}{x} = 1\)). This equation demonstrates that when you multiply a fraction by its reciprocal, you get 1. This is because the numerator and denominator in each fraction are the same but inverted, and when the same non-zero number is divided by itself, the result is 1.
The correct property that describes this situation is not specifically listed in the given options, as it is a fundamental property of the multiplicative identity and reciprocals. However, if we must choose from the given options, none of them perfectly fit this property. The closest would be the multiplication property of equality, which holds that if you multiply both sides of an equation by the same non-zero number, the equality of the equation remains unchanged.
However, in this case, since we are not comparing two separate sides of an equation or applying an operation to both sides to maintain equality, the multiplication property of equality isn't exactly what is demonstrated here. This is more about the property of reciprocals and the identity element of multiplication.