Question 1: Simplify the expression: \( \frac{2}{3} \times \frac{3}{4} \).

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

Question 2: Calculate \( \frac{4}{5} \div \frac{2}{3} \).

Answer: \( \frac{6}{5} \)

Question 3: Add \( \frac{1}{4} \) and \( \frac{3}{8} \).

Answer: \( \frac{5}{8} \)

Question 4: A student multiplies \( \frac{2}{3} \) by \( \frac{3}{4} \) and gets \( \frac{6}{7} \). Identify and correct the mistake.

Answer: Incorrect multiplication; the correct answer is \( \frac{1}{2} \).

Question 5: Subtract \( \frac{5}{6} \) from \( \frac{3}{4} \).

Answer: \( -\frac{1}{12} \)

Question 6: A teacher adds \( \frac{2}{5} \) and \( \frac{3}{7} \). They write the answer as \( \frac{29}{35} \). Is this correct? Explain.

Answer: Yes, because \( \frac{2}{5} + \frac{3}{7} = \frac{14}{35} + \frac{15}{35} = \frac{29}{35} \).

Question 7: Construct an algebraic expression representing multiplying \( \frac{a}{b} \) by \( \frac{c}{d} \).

Answer: \( \frac{a \times c}{b \times d} \)

Question 8: A student incorrectly adds \( \frac{1}{2} \) and \( \frac{1}{3} \) and gets \( \frac{2}{5} \). Identify the mistake and correct it.

Answer: Incorrect addition; common denominator is 6, so sum is \( \frac{3}{6} + \( \frac{2}{6} = \frac{5}{6} \).

Question 9: Evaluate: \( \frac{7}{8} - \frac{3}{4} \).

Answer: \( \frac{1}{8} \)

Question 10: Challenge: Simplify \( \frac{6}{9} \times \frac{3}{4} + \frac{1}{3} \).

Answer: \( \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \)

Question 11: Plot the graph of \( y = 2x \) on the grid.

Answer: Student plots points like (0,0), (1,2), (2,4), etc., and draws the line accordingly.

Question 12: Identify the common mistake: A student tries to add \( \frac{2}{3} \) and \( \frac{4}{7} \) by adding numerators and denominators separately. Why is this wrong?

Answer: Adding numerators and denominators separately is incorrect; fractions must have common denominators before addition.