(1) Simplify each of the expressions below. Which of the expressions has a product that is greater than \( \frac{5}{8} \) ? Select all that apply. A) \( \frac{5}{8} \times 12 \) B) \( \frac{11}{2} \times \frac{5}{8} \) C) \( \frac{1}{3} \times \frac{5}{8} \) D) \( 2 \frac{1}{6} \times \frac{5}{8} \) E) \( \frac{7}{8} \times \frac{5}{8} \)

First, let's simplify each expression to find the products. A) \( \frac{5}{8} \times 12 = \frac{5 \times 12}{8} = \frac{60}{8} = 7.5 \) (This is greater than \( \frac{5}{8} \).) B) \( \frac{11}{2} \times \frac{5}{8} = \frac{11 \times 5}{2 \times 8} = \frac{55}{16} = 3.4375 \) (This is greater than \( \frac{5}{8} \).) C) \( \frac{1}{3} \times \frac{5}{8} = \frac{1 \times 5}{3 \times 8} = \frac{5}{24} \) (This is less than \( \frac{5}{8} \).) D) \( 2 \frac{1}{6} \times \frac{5}{8} = \frac{13}{6} \times \frac{5}{8} = \frac{13 \times 5}{6 \times 8} = \frac{65}{48} \approx 1.3542 \) (This is greater than \( \frac{5}{8} \).) E) \( \frac{7}{8} \times \frac{5}{8} = \frac{7 \times 5}{8 \times 8} = \frac{35}{64} \approx 0.5469 \) (This is less than \( \frac{5}{8} \).) Thus, the expressions with products greater than \( \frac{5}{8} \) are A, B, and D. If we were to talk about the context of multiplying fractions, you might find it interesting that this fundamental operation comes into play daily, from cooking recipes to adjusting measurements in science experiments! It's a skill that helps ensure the right balance in every creation. Another fun nugget is that history has shown how vital fractions were for ancient civilizations, especially in trade and agriculture! The Egyptians used fractions extensively in their papyrus documents, showcasing their importance in everyday transactions. Keeping math alive, one fraction at a time!