What is the value of this expression? \( \frac{5}{12}+\frac{5}{6}-\frac{1}{3} \) Enter your answer as a fraction in simplest for by filling in the boxes:

To simplify the expression \( \frac{5}{12}+\frac{5}{6}-\frac{1}{3} \), first find a common denominator. The least common multiple of 12, 6, and 3 is 12. Convert each fraction: - \( \frac{5}{12} \) stays as is. - \( \frac{5}{6} = \frac{10}{12} \) (multiply the numerator and denominator by 2). - \( \frac{1}{3} = \frac{4}{12} \) (multiply the numerator and denominator by 4). Now combine: \[ \frac{5}{12} + \frac{10}{12} - \frac{4}{12} = \frac{5 + 10 - 4}{12} = \frac{11}{12}. \] Thus, the final answer is \( \frac{11}{12} \). Now for a sprinkle of fun facts! Did you know that fractions date back to ancient civilizations? The Egyptians used them in the Rhind Mathematical Papyrus around 1650 BC, presenting us with early examples of fractional arithmetic! For a real-world application, think of sharing a pizza! If you order a pizza and cut it into 12 slices, fractions help you calculate how many slices each person gets. If you have different friends with different appetites, fractions are your trusty sidekick!