Question 1: Convert the fraction 3/4 to a percentage. Show your working.

Answer: 75%

Question 2: A student incorrectly converts 2/5 to 50% by dividing numerator by denominator and then multiplying by 100. Identify and correct the mistake.

Answer: Correct method: (2 ÷ 5) × 100 = 40%. The mistake was using 2 ÷ 5 = 0.2 and then multiplying by 100 to get 20%, which is incorrect. It should be 40%.

Question 3: Express 7/20 as a percentage. Show all steps.

Answer: 35%

Question 4: Simplify the common mistake: Converting 1/8 directly to 12.5% by dividing numerator by denominator.

Answer: Incorrect. 1/8 as a decimal is 0.125, which is 12.5%. The mistake is assuming dividing numerator by denominator directly gives percentage; actually, convert to decimal first then to percentage.

Question 5: If a recipe requires 2/3 of a cup of sugar, what percentage of a full cup does this represent? Show your working.

Answer: 66.67%

Question 6: A common misconception is that converting 5/8 to a percentage is 50%. Explain why this is incorrect and provide the correct percentage.

Answer: Incorrect because 5/8 as a decimal is 0.625, which is 62.5%. The wrong assumption likely comes from incorrectly approximating 5/8 as 0.5.

Question 7: Plot the point representing 3/5 as a percentage on the provided grid.

Answer: 60%

Question 8: Construct a triangle with angles corresponding to the percentages 25%, 50%, and 25%. Use the grid for drawing.

Answer: Correctly draw a triangle with angles of 90°, 180° - 50° - 25° = 105°, and 25°.

Question 9: Convert 9/16 into a percentage. Show detailed steps.

Answer: 56.25%

Question 10: A student mistakenly converts 4/5 to 80% by dividing numerator by 100. Correct this approach and find the right percentage.

Answer: Incorrect method. Correct way: (4 ÷ 5) × 100 = 80%. The mistake was dividing numerator by 100 instead of numerator divided by denominator, then multiply by 100.

Question 11: Express 11/40 as a percentage and explain why some students might get this wrong.

Answer: 27.5%. Some students might incorrectly think 11/40 is 25% because they approximate or wrongly divide 11 by 40 to get 0.275 directly.