When solving problems involving percentages, it's important to translate the words into mathematical expressions accurately. For example, if a problem states that a number is 50% of 18, we represent the unknown number as x. The word "is" translates to an equals sign, so the equation becomes x = 50% of 18. Since percentages must be converted to decimals for calculations, 50% becomes 0.5. Therefore, the equation is x = 0.5 × 18, which simplifies to x = 9.

Similarly, if a number is 18% of 50, we again let the number be x and write x = 18% of 50. Converting 18% to decimal form gives 0.18, so the equation is x = 0.18 × 50, which also simplifies to x = 9.

The reason both parts yield the same result lies in the commutative property of multiplication, which states that the order of factors does not affect the product. Since percentages represent a fraction out of 100, converting 50% to decimal is equivalent to dividing 50 by 100, and similarly for 18%. Thus, the expressions can be rewritten as:

$$x = \frac{50}{100} \times 18$$

and

$$x = \frac{18}{100} \times 50$$

Both simplify to:

$$x = \frac{50 \times 18}{100}$$

This demonstrates that multiplying a percentage by a number is commutative in this context, leading to the same product regardless of the order. Understanding this property can simplify mental math, especially when calculating percentages without a calculator. For instance, calculating 18% of 50 might seem complex, but recognizing it as the same as 50% of 18 makes the problem easier to solve quickly.

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