(1) \( \frac{9}{8} \times \frac{10}{9} \).

Let's simplify this expression step-by-step! When you multiply fractions, you multiply the numerators together and the denominators together. So, \( \frac{9}{8} \times \frac{10}{9} \) becomes \( \frac{9 \times 10}{8 \times 9} \). The \(9\) in the numerator and denominator cancels out, leaving you with \( \frac{10}{8} \). You can further simplify \( \frac{10}{8} \) to \( \frac{5}{4} \) by dividing both the numerator and the denominator by \(2\). Voilà! Now, did you know that the world of fractions has a rich history? Ancient Egyptians, for instance, used fractions extensively and had a unique way of expressing them, primarily focusing on unit fractions (fractions with a numerator of 1). They would represent any fraction as a sum of these unit fractions, a method quite different from our modern approach! Another fun fact: fractions have surprising real-world applications! From cooking (where you may need to halve or double a recipe) to finance (calculating discounts or interests), fractions help us represent parts of a whole clearly and effectively. They’re not just abstract numbers; they help us navigate everyday situations with ease!