Question 1: Calculate 1/2 of 36.

Answer: 18

Question 2: Calculate 1/4 of 64.

Answer: 16

Question 3: A student mistakenly calculates 1/2 of 50 as 25 by dividing 50 by 2. Is this correct? Explain your reasoning.

Answer: Yes, dividing by 2 gives 1/2 of 50, which is correct.

Question 4: A common mistake is to multiply instead of divide when finding 1/4 of a number. Identify the error in calculating 1/4 of 48 if someone multiplies 48 by 4 instead of dividing.

Answer: The error is multiplying instead of dividing; 48×4=192, which is incorrect for 1/4 of 48.

Question 5: Construct a rectangle on the grid such that its length is 8 units and its width is 1/2 of that. Show your drawing.

Answer: Rectangle with length 8 units and width 4 units.

Question 6: Explain why multiplying by 1/2 or 1/4 does not give the same result as dividing by 2 or 4.

Answer: Multiplying by 1/2 or 1/4 scales down the number, similar to division, but the operation differs mathematically. Dividing is the inverse of multiplication, so to find a fraction of a number, you divide by the denominator.

Question 7: If someone incorrectly finds 1/2 of 24 by subtracting 12, what misconception might they have?

Answer: They might think 1/2 means subtracting half, not dividing.

Question 8: A calculator gives 6 for 1/4 of 24. Is this correct? Why or why not?

Answer: Yes, because 24 divided by 4 equals 6.

Question 9: A student mistakenly finds 1/2 of 20 as 10 by dividing 20 by 2. Is this correct? Explain the mistake if any.

Answer: Yes, dividing by 2 correctly finds 1/2 of 20. The student’s method is correct.

Question 10: Calculate 1/2 of 80 and 1/4 of 32, then compare the two results.

Answer: 1/2 of 80 = 40; 1/4 of 32 = 8; comparison: 40 is five times 8.

Question 11: Identify and correct the mistake: Someone calculates 1/2 of 50 as 25 by dividing 50 by 5.

Answer: The mistake is dividing by 5 instead of 2; 1/2 of 50 is 25 because 50 divided by 2 equals 25.

Question 12: A challenging problem: Find a number such that when you take 1/2 of it and then 1/4 of the result, you get 6. What is the original number?

Answer: Original number is 48. Calculation: Let x be the number. (1/2)x = y; (1/4)y = 6. So, y=4×6=24; (1/2)x=24; x=24×2=48.