Question 1: Calculate: 2 1/2 × 3 1/4.

Answer: 8 1/8

Question 2: Convert the mixed number 4 2/3 to an improper fraction.

Answer: 14/3

Question 3: Multiply: 1 3/4 × 2 2/3.

Answer: 4 5/6

Question 4: Explain why multiplying mixed numbers requires converting them to improper fractions first.

Answer: Because multiplication of mixed numbers is easiest when they are expressed as improper fractions, which facilitates straightforward multiplication of numerators and denominators.

Question 5: Calculate: 3 1/5 × 2 3/4.

Answer: 8 1/20

Question 6: A recipe calls for 1 1/2 cups of sugar. If you want to make half the recipe, how much sugar do you need?

Answer: 3/4 cups

Question 7: Multiply: 5/8 × 2 1/2.

Answer: 1 5/16

Question 8: Identify and correct the mistake in this student solution: 2 1/3 × 3 2/5 = 7/3 × 17/5 = 119/15 = 7 14/15.

Answer: The mistake is in the multiplication of mixed numbers without converting to improper fractions. Correct approach: 2 1/3 = 7/3, 3 2/5 = 17/5; then multiply to get 7/3 × 17/5 = 119/15, which simplifies to 7 14/15, so the calculation is correct. But if any step was incorrect, students should identify it.

Question 9: Construct a rectangle on the grid with length 2 1/2 units and width 3 1/4 units. Find the area.

Answer: 8 1/8 units squared

Question 10: Challenge: If you multiply 7 1/4 by 4 2/3, what is the product in mixed number form?

Answer: 33 1/12