Question 1: Calculate: \( \frac{3}{4} \times \frac{2}{5} \)

Answer: 3/10

Question 2: Divide: \( \frac{5}{8} \div \frac{1}{4} \)

Answer: 5/2

Question 3: Construct a fraction equivalent to \( \frac{2}{3} \) by multiplying numerator and denominator by 4.

Answer: 8/12

Question 4: Simplify: \( \frac{6}{9} \div \frac{2}{3} \)

Answer: 1

Question 5: A recipe calls for \( \frac{3}{4} \) cup of sugar. If you want to make half the recipe, how much sugar do you need? (Divide the amount by 2)

Answer: 3/8

Question 6: Calculate: \( \left( \frac{7}{10} \times \frac{2}{3} \right) \div \frac{1}{5} \)

Answer: 14/6 or 7/3

Question 7: Plot the graph of \( y=2x \) on the provided grid. (Draw a straight line passing through the origin with slope 2.)

Answer:

Question 8: Construct a triangle with sides \( \frac{3}{4} \), \( \frac{1}{2} \), and \( \frac{5}{4} \). Show your construction on the grid. Are these sides capable of forming a triangle?

Answer: Yes, because the sum of any two sides is greater than the third.

Question 9: A worker completes \( \frac{4}{7} \) of a task each day. How much of the task remains after 3 days?

Answer: 1/7

Question 10: Identify the mistake in this calculation: \( \frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2} \).

Answer: Correct calculation; no mistake.

Question 11: Challenge: Find a fraction that is greater than \( \frac{3}{4} \) but less than \( 1 \), and can be obtained by multiplying \( \frac{3}{4} \) by a number less than 1.

Answer: Any fraction like 9/16 (multiplied by 4/3) or similar, but requires explanation.