4. \( (((-7)+8-9)-4)+13 \)

Let's break it down step by step: First, calculate \(-7 + 8\), which gives you \(1\). Then, subtract \(9\) from \(1\), resulting in \(-8\). Next, subtract \(4\) from \(-8\), giving you \(-12\). Finally, add \(13\) to \(-12\), resulting in \(1\). So, the final answer is \(1\). Now about some extra info — Math has been a part of civilization for centuries! The ancient Egyptians and Babylonians were among the first to use arithmetic for trade and astronomy. They paved the way for complex calculations, leading to the amazing mathematics we use today! And if you're looking for ways to avoid mistakes in basic arithmetic, always double-check your additions and subtractions. It's easy to slip up, especially when dealing with negative numbers. Visual aids, like drawing number lines, can also make a huge difference!