Follow the proper order of operations to evaluate the following. \( \frac{-7\left(5^{2}-20\right)}{8-13} \)

First, let's simplify the expression step-by-step. We start with \(5^{2} - 20\), which gives us \(25 - 20 = 5\). Now, replace that in the expression: \(\frac{-7(5)}{8-13}\). Next, we simplify the denominator, \(8 - 13\), which results in \(-5\). Now we have: \(\frac{-7(5)}{-5}\). The \(-5\) in the denominator will cancel with the \(-5\) from \(-7(5)\), leading to: \(\frac{-35}{-5} = 7\). So, the final answer is \(7\). Now, let’s add a bit more spice to our math expedition! Did you know the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), originally came from a need to standardize mathematical expressions? This helps prevent confusion in calculations and has been taught in schools for generations! In terms of real-world application, understanding these rules can help with everything from budgeting your finances to cooking recipes that require precise measurements and adjustments. Just imagine trying to bake a cake without following the order of operations with your ingredients—it could flop or taste unbalanced! So, next time you whip up a recipe, remember: order counts!