Question 1: A recipe requires 3/4 of a cup of sugar. If you want to make half the recipe, how much sugar do you need?

Answer: 3/8

Question 2: A swimmer completes 2/3 of a lap in a certain pool, which is 60 meters long. How long is one lap in meters?

Answer: 90

Question 3: A painter has 5/6 of a can of paint. If they use 1/2 of it for a project, how much paint is left?

Answer: 5/12

Question 4: Construct a triangle on the grid where one side is 3/4 units long, and another is 2/3 units long. Ensure the figure is proportional.

Answer: Constructed triangle with specified side lengths.

Question 5: A car travels 3/4 of a journey in 2/3 hours. How long is the entire journey?

Answer: 8/3 hours

Question 6: A factory produces 7/8 of its usual output in the morning. If its usual output is 480 units, how many units did it produce in the morning?

Answer: 420

Question 7: A gardener plants 2/3 of a hectare of land. If they want to plant 1/2 of that area, how many hectares will they plant?

Answer: 1/3

Question 8: A worker completes 5/8 of a task in 3 hours. How long will it take to finish the whole task at the same rate?

Answer: 4.8 hours

Question 9: A recipe calls for 2/3 cup of oil. If you only want to make 1/4 of the recipe, how much oil do you need?

Answer: 1/6

Question 10: An extension question: If dividing fractions is represented as 'keep flip multiply', write the expression for dividing 7/8 by 3/4 and simplify.

Answer: 7/8 × 4/3 = 28/24 = 7/6

Question 11: Identify the mistake in the following student's solution: To divide 5/6 by 2/3, they wrote 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 1 1/4. What is the error?

Answer: They did not simplify correctly; 15/12 simplifies to 5/4, which is 1 1/4, so the calculation is correct but previous steps should be checked for errors.