(b) \( \frac{2}{3}+\frac{3}{4} \)

To add the fractions \( \frac{2}{3} \) and \( \frac{3}{4} \), first, find a common denominator, which is 12. Then, convert each fraction: \( \frac{2}{3} = \frac{8}{12} \) and \( \frac{3}{4} = \frac{9}{12} \). Now, add them together: \( \frac{8}{12} + \frac{9}{12} = \frac{17}{12} \). So, \( \frac{2}{3} + \frac{3}{4} = \frac{17}{12} \) or \( 1 \frac{5}{12} \). Also, this mathematical operation stems from the ancient Babylonians, who were some of the first to use fractions. They used a base-60 numeral system, so when you’re maneuvering through fractions today, remember the pioneering spirit of those early mathematicians who laid the groundwork for a system that still shapes our calculations! Want to avoid common pitfalls in adding fractions? Always ensure that your denominators are the same before combining. Many learners mistakenly add numerators first and forget that finding a common denominator is crucial. This small step can save you from unwittingly producing incorrect answers and demystifies the art of fraction addition!