Simplifying Proper Fractions (J) Simplify each fraction to its lowest terms \( \frac{30: 3}{48}: \frac{10: 2}{16: 2}=\left(\frac{5}{8} \quad \frac{27}{99}: \frac{3}{a}=\frac{3}{11} \quad\right. \)

Let’s break down those fractions! For the first part, \( \frac{30:3}{48} \) simplifies to \( \frac{10}{48} \), which further reduces down to \( \frac{5}{24} \). Now onto the second part—\( \frac{27}{99} \), which simplifies to \( \frac{3}{11} \). This shows us that the correct form is \( \frac{5}{24} = \frac{3}{11} \). Now for a bit of fun: Did you know that ancient Greeks studied fractions extensively, and even the word "fraction" comes from the Latin word "fractio," meaning "to break"—as in breaking whole numbers into smaller parts? Imagine them using their chalk on clay tablets to record their calculations! Also, in the real world, simplifying fractions is not just a math trick; it helps in various fields including cooking, carpentry, and planning projects. Say you're baking cookies and find a ¾ cup flour recipe. A quick simplification tells you that ¾ is the same as using 6 tablespoons, making it easier to measure without needing a ¾ cup!