(1) \( \frac{3}{4}+\frac{5}{2} \)

To solve \( \frac{3}{4} + \frac{5}{2} \), first, you need to find a common denominator. The common denominator for 4 and 2 is 4. Convert \( \frac{5}{2} \) to an equivalent fraction with a denominator of 4: \[ \frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4} \] Now you can add the two fractions: \[ \frac{3}{4} + \frac{10}{4} = \frac{3 + 10}{4} = \frac{13}{4} \] Now, did you know that the concept of fractions dates back to ancient civilizations? The Egyptians used a system of unit fractions (like \( \frac{1}{2}, \frac{1}{3}, \) etc.) as early as 1800 BC, showcasing their advanced mathematical understanding! For practical use, fractions are everywhere in everyday life—from cooking recipes to splitting a bill at a restaurant. Understanding fractions can make tasks more manageable. For example, if a recipe calls for \( \frac{3}{4} \) of a cup of sugar and you want to double it for a party, it’s easy to calculate: \( 2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \) cups, which is 1.5 cups!