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Understanding percentages is a fundamental skill in math and daily life. In essence, a percentage represents a part per hundred. The term comes from the Latin 'per centum', which literally means 'by the hundred'. Mathematically, you can think of a percentage as a fraction with a denominator of 100. To convert any fraction to a percentage, you follow a straightforward process. First, examine the given fraction, like \( \frac{27}{50} \) in our exercise.

Then, we use the conversion formula, which involves multiplying the fraction by 100. Why 100? Because we are finding out what part of the whole the fraction represents out of 100—this is the essence of a percentage. When you perform the calculation \( \frac{27}{50} \times 100 \), you get the increasingly familiar result of 54%. This conversion is a quick way to understand what a fraction means in terms that are often more intuitive to grasp for everyday uses, like knowing how much of a discount you're getting during a sale, or understanding statistics presented in the news.

Before tackling the complexities of algebra, prealgebra offers a crucial foundation. It's where students begin to encounter mathematical expressions and understand the order of operations, basic properties of numbers, dealing with decimals and fractions, and the concept of variables.

Converting fractions to percentages is a vital skill in prealgebra that underscores the importance of number sense. By practicing this skill, students become familiar with how different forms of numbers relate to each other. They gain the ability to transition between decimals, fractions, and percentages seamlessly. This is particularly useful because, in real life, we encounter numbers in various forms. Being comfortable with these conversions aids students in more advanced mathematical topics, as well as in making sense of numbers in their daily lives.

When approaching math problems, it's imperative to have a systematic method. Problem solving often involves several steps: understanding the problem, devising a plan, executing steps, and then looking back to verify the results. In our textbook exercise, the first step is to identify the fraction, \( \frac{27}{50} \).

The second step involves formulating a plan which is recognizing the need to convert the fraction to a percentage. Next, we execute the problem-solving steps by applying the conversion formula (multiplying by 100) to obtain 54%. Finally, it's good practice to review your answer to make sure it makes sense within the context of the question and to approximate if you're asked to round to a certain degree of precision. Enhancing these problem-solving skills in mathematics is not only beneficial academically but also trains you to tackle challenges in various aspects of life with a structured approach.