Question 1: Calculate and simplify: (2/3) × (3/4).

Answer: 1/2

Question 2: Calculate and simplify: (5/6) × (2/3).

Answer: 5/9

Question 3: Calculate and simplify: (7/8) × (4/5).

Answer: 7/10

Question 4: Calculate and simplify: (3/4) × (2/5).

Answer: 3/10

Question 5: Calculate and simplify: (4/9) × (3/4).

Answer: 1/3

Question 6: A recipe requires 2/3 cup of sugar. If you want to make half the recipe, how much sugar do you need? (Express as a simplified fraction).

Answer: 1/3

Question 7: A painter mixes 3/4 litre of blue paint with 2/3 litre of yellow paint. How much paint is mixed in total? Simplify your answer.

Answer: 17/12 litres

Question 8: Construct a rectangle on the grid with a length of 3/4 units and width of 2/3 units. Calculate the area and simplify your answer.

Answer: 1/2

Question 9: A fabric pattern repeats every 2/5 metre. How far will 3/4 metre cover in terms of pattern repetitions? Simplify your answer.

Answer: 3/10

Question 10: Identify and correct the mistake: Calculate (2/3) × (3/4) = 6/12 = 1/2. Is this correct? If not, explain and give the correct simplified answer.

Answer: No, the mistake is simplifying 6/12 directly to 1/2 without considering the initial fractions. The correct calculation is (2/3)×(3/4)= (2×3)/(3×4)=6/12=1/2, which is correct. So, the original work is correct.

Question 11: Challenge: A garden bed is 3/4 metre long and 2/5 metre wide. If the gardener decides to double the length and keep the width the same, what is the new area? Simplify your answer.

Answer: 3/5