Question 1: Simplify the product of \(rac{2}{3} \) and \(\frac{3}{4}\).

Answer: 1/2

Question 2: Calculate and simplify: \(\frac{5}{8} \times \frac{16}{10} \).

Answer: 1/1

Question 3: Simplify the following product: \(\frac{9}{12} \times \frac{4}{6} \).

Answer: 1/2

Question 4: Construct a pair of fractions that multiply to \(\frac{1}{4}\) when simplified.

Answer: e.g., \(\frac{2}{8} \times \frac{2}{1}\)

Question 5: Multiply and simplify: \(\frac{7}{10} \times \frac{5}{14}\).

Answer: 1/4

Question 6: A recipe calls for \(\frac{3}{4} \) of a cup of sugar. If you multiply by \(\frac{2}{3}\) to adjust the recipe, what is the simplified amount needed?

Answer: \(\frac{1}{2}\) cup

Question 7: Simplify the product: \(\frac{15}{20} \times \frac{4}{5}\).

Answer: 3/5

Question 8: Identify and correct the mistake: \(\frac{3}{5} \times \frac{10}{15} = \frac{30}{75} = \frac{2}{5}\).

Answer: The mistake is in simplifying \(\frac{30}{75}\). Correct simplification yields \(\frac{2}{5}\) as shown, so the original calculation is correct.

Question 9: Calculate and simplify: \(\frac{8}{12} \times \frac{3}{4}\).

Answer: 1/2

Question 10: A student multiplies \(\frac{11}{22} \times \frac{4}{8}\) but leaves the answer as \(\frac{44}{176}\). Simplify the answer correctly.

Answer: 1/4

Question 11: Using the grid, construct a rectangle representing the product of \(\frac{2}{3}\) and \(\frac{3}{5}\). Then, simplify the product.

Answer: \(\frac{2}{5}\)

Question 12: Challenge: Simplify and verify if the product of \(\frac{18}{24} \) and \(\frac{12}{18} \) equals \(\frac{1}{2}\).

Answer: Yes, as \(\frac{3}{4} \times \frac{2}{3} = \frac{1}{2}\)