To find what the expression \( (x \% \text{ of } y) + (y \% \text{ of } x) \) is equivalent to, we need to understand how to convert percentages into mathematical expressions.

Percentage Conversion Basics

The term 'percent' literally means 'per one hundred'. So, \( P \% \) can be written as \( \frac{P}{100} \). When we say 'P % of Q', it means \( \frac{P}{100} \times Q \).

• Understanding 'x % of y':

  This expression can be written mathematically as:

  \( x \% \text{ of } y = \frac{x}{100} \times y = \frac{xy}{100} \)

• Understanding 'y % of x':

  Similarly, this expression can be written as:

  \( y \% \text{ of } x = \frac{y}{100} \times x = \frac{yx}{100} \)

Combining the Expressions

Now, let's add the two expressions together as given in the problem:

\( (x \% \text{ of } y) + (y \% \text{ of } x) = \frac{xy}{100} + \frac{yx}{100} \)

Since \( xy \) is the same as \( yx \) (due to the commutative property of multiplication), we can write:

\( \frac{xy}{100} + \frac{xy}{100} \)

When adding fractions with the same denominator, we add their numerators:

\( = \frac{xy + xy}{100} = \frac{2xy}{100} \)

Comparing with Options

We need to find an option that is equivalent to \( \frac{2xy}{100} \).

From the comparison, Option 1, which is \( 2 \% \text{ of } xy \), exactly matches our derived result of \( \frac{2xy}{100} \).

Final Conclusion

The expression \( (x \% \text{ of } y) + (y \% \text{ of } x) \) simplifies to \( \frac{2xy}{100} \), which is equivalent to \( 2 \% \text{ of } xy \). This demonstrates the fundamental rules of percentage calculation and algebraic manipulation.