Question 1: Simplify the expression: (3/x) + (2/x).

Answer: 5/x

Question 2: Calculate: (4/5) ÷ (2/3).

Answer: 12/5

Question 3: Add: (x/4) + (3x/4).

Answer: x

Question 4: Simplify: (2x/3) - (x/3).

Answer: x/3

Question 5: Express as a single fraction: (x/2) + (3/x).

Answer: (x^2 + 6)/2x

Question 6: Solve for x: (x/3) + (2/3) = 7/3.

Answer: x=5

Question 7: Construct a simplified algebraic fraction equivalent to (2x^2 + 4x) / (2x).

Answer: x + 2

Question 8: Evaluate: (x/4) ÷ (x/2) when x ≠ 0.

Answer: 1/2

Question 9: If (a/b) × (c/d) = 6/8, find the value of (a×c)/(b×d).

Answer: 3/4

Question 10: A student makes the mistake of adding numerators and denominators separately: (x/3 + 2/3) = (x+2)/3. Correct this error in a brief explanation.

Answer: They should combine over a common denominator, so addition is (x+2)/3, which is correct. The mistake is assuming addition of fractions is just numerator plus numerator over denominator plus denominator, which is incorrect.

Question 11: Challenge: Simplify (x^2/4) - (x/2) + 1, expressing as a single fraction in simplest form.

Answer: (x-2)^2/4

Question 12: Plot the graph of y = 2x + 1 on the grid.

Answer: Student draws the line passing through (0,1) with slope 2.