\begin{tabular}{l|l} 3. \( \frac{2}{3} \cdot 5 \frac{3}{4} \)\end{tabular}

To solve \( \frac{2}{3} \cdot 5 \frac{3}{4} \), start by converting the mixed number \( 5 \frac{3}{4} \) into an improper fraction. This means you multiply the whole number (5) by the denominator (4) and add the numerator (3), resulting in \( \frac{23}{4} \). Now, the expression becomes \( \frac{2}{3} \cdot \frac{23}{4} \). Multiply the numerators together (2 and 23) and the denominators together (3 and 4) to get \( \frac{46}{12} \). Simplifying gives you \( \frac{23}{6} \), or \( 3 \frac{5}{6} \) when converted back to a mixed number! Math-related problems have been tackled for centuries, making it a fascinating subject not just for students but also for historians. The journey of fractions dates back to ancient Egyptian mathematics, where they had unique ways of handling them. Fast forward to today, and fractions are pivotal in everything, from cooking to construction, reflecting how math evolves but remains an essential part of our daily interactions!