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Understanding percentage calculations is crucial in solving proportion problems effectively. Percentages represent a way to express a number as a fraction of 100. For example, 16% can be seen as 16 parts out of 100 parts. When a problem asks "what is 16% of a number?", it translates to "16/100 of that number".
Percentages are used widely in many daily applications such as calculating discounts, interest rates, and more. To find what 16% of a number is, convert the percentage to a decimal by dividing by 100, so 16% becomes 0.16. Then multiply this by the number to find the result; in this case, 0.16 times the unknown number equals 48.
This concept is foundational in pre-algebra and sets the stage for more complex algebraic manipulations.

Cross-multiplication is an essential method in solving proportions, which are equations that state two ratios are equal. When you have a proportion such as \(\frac{a}{b} = \frac{c}{d}\), you can cross-multiply by multiplying the outer terms and the inner terms: \(a \times d = b \times c\).
In our exercise, we set up the proportion \(\frac{16}{100} = \frac{48}{n}\). Cross-multiplying gives us \(16 \times n = 100 \times 48\), resulting in the equation \(16n = 4800\).
This technique simplifies the process, especially with non-integer results, by eliminating the fractions at first glance, allowing you to work with whole numbers or direct multiplication results. It’s a clear, quick method, widely used in pre-algebra.

To solve equations, especially simple algebraic ones found in pre-algebra, the key is to isolate the variable. Once you’ve set up your equation through proportion and cross-multiplication, you likely have a linear equation such as \(16n = 4800\).
To isolate \(n\), divide both sides of the equation by the coefficient attached to \(n\), which in this case is 16. So, \(n = \frac{4800}{16}\). Calculating this gives \(n = 300\).
This method shows the solution step-by-step, making sure to keep the balance of the equation equal. Understanding how to manipulate these equations is fundamental to tackling more complex algebraic problems as students progress.

Pre-algebra serves as the foundation for all higher-level algebra, offering tools and techniques needed for solving real-world mathematical problems. The focus is often on understanding numbers, how they relate to each other, and how they can be manipulated.
In pre-algebra, it's common to solve problems involving fractions, percentages, proportions, and basic equations like the one in our exercise. These exercises are designed to teach logical thinking and systematic problem-solving approaches, building confidence in students before they tackle more challenging algebraic concepts.
By reinforcing the basics, such as converting percentages to decimals, setting up proportions, cross-multiplying, and solving equations, students develop a strong mathematical foundation, readying them for more complex algebraic tasks in the future.