91Ó°ÊÓ

Algebraic fractions can often be intimidating, but they're just fractions that include variables. Solving them typically involves finding a value for the variable that makes the two sides of the equation equal. In our exercise, we dealt with an equation involving algebraic fractions, \(\frac{120}{n} = \frac{144}{25}\). The goal is to isolate the variable \(n\).
To do this effectively, we employed cross multiplication, which is a method where we multiply the numerator of one side by the denominator of the other side and vice versa, thus removing the fractions. This step helps us simplify the equation to an easier form without fractions, preparing it for further operations to solve for the variable. Simplification after cross multiplication is key, and it often leads us to a basic linear equation.

Simplification is a critical step in solving equations. It involves reducing complex expressions to the simplest form possible. After cross multiplying our equation, we obtained \(3000 = 144n\). The next step is to perform any arithmetic operations that are possible—like multiplication or division—to further simplify the equation.
In this case, we divided both sides by 144 to isolate the variable \(n\). The simplification resulted in \(n = \frac{3000}{144}\), which effectively uses inverse operations to break down the equation. Remember, simplifying equations isn't just about making them look nicer; it's necessary to clearly identify the next steps in solving the problem and ultimately finding the value of the variable.

In mathematics, particularly when dealing with real-life applications, we often need to round numbers to make them easier to work with. Rounding is a process of approximating a number to its nearest value based on a specific level of precision, which in this problem is to the nearest hundredth.
Upon solving the equation, we found the value of \(n\) to be a fraction, \(n = \frac{3000}{144}\). However, we are instructed to round \(n\) to the nearest hundredth for practical use. By using a calculator or long division, we determine that \(n \approx 20.83\), with \(83\) representing the hundredths place. Hence, \(20.83\) is a rounded approximation of the exact value of \(n\). This step is crucial in many scientific, statistical, or financial contexts where exact figures are impractical or unnecessary.