Question 1: When dividing fractions, what is the correct first step before multiplying? Briefly explain.

Answer: Keep the first fraction as is and flip the second fraction.

Question 2: A student mistakenly multiplies instead of dividing. What is the common misconception, and how does it affect the answer?

Answer: They think dividing is the same as multiplying, which leads to incorrect results because they do not flip the second fraction.

Question 3: Calculate: 3/4 ÷ 2/5 using the correct method. Show your working.

Answer: 3/4 * 5/2 = (3*5)/(4*2) = 15/8

Question 4: Identify the error in the following solution: 5/6 ÷ 1/3 = 5/6 * 3/1 = 15/6 = 5/2.

Answer: No error; the solution is correct.

Question 1: A recipe calls for 2/3 cup of sugar. If you want to make only half the recipe, how much sugar do you need? Show your work.

Answer: 1/3 cup

Question 2: A cyclist traveled 3/4 of a mile in 1/2 hour. What is their average speed in miles per hour? Show your calculation.

Answer: (3/4) ÷ (1/2) = (3/4)*(2/1) = 6/4 = 3/2 = 1.5 mph

Question 3: A student mistakenly divides instead of multiplying: 7/8 ÷ 2/3 = ? Identify the mistake and compute the correct answer.

Answer: They should flip 2/3 to 3/2 and then multiply: 7/8 * 3/2 = 21/16

Question 4: Calculate: 4/5 ÷ 3/10. Show your working.

Answer: 4/5 * 10/3 = (4*10)/(5*3) = 40/15 = 8/3

Question 5: A common mistake when dividing fractions is to forget to flip the second fraction. Explain why this mistake leads to incorrect answers.

Answer: Because dividing fractions requires multiplying by the reciprocal; forgetting to flip results in addition or multiplication errors.

Question 1: Incorrect solution: 5/8 ÷ 1/4 = 5/8 * 1/4 = 5/32. What's wrong with this? Correct the mistake.

Answer: They didn't flip 1/4 to 4/1 before multiplying. Correct: 5/8 * 4/1 = 20/8 = 5/2

Question 2: A student multiplies instead of dividing: 2/3 ÷ 4/5 = ?. Correct their error and give the correct answer.

Answer: They should flip 4/5 to 5/4 and multiply: 2/3 * 5/4 = 10/12 = 5/6

Question 1: A worker uses 3/4 of a liter of paint for one coat. If they need to paint 5 walls, each requiring 2/3 liter, how many coats can they complete? Show your reasoning.

Answer: Total paint needed = 5 * 2/3 = 10/3 liters. Number of coats = (3/4) ÷ (2/3) = (3/4)*(3/2) = 9/8 = 1.125 coats

Question 2: Construct a diagram on the grid to represent dividing a circle (representing a pizza) into 8 equal slices, then determine how much pizza each slice represents in fraction form.

Answer: Each slice = 1/8 of the pizza.

Question 1: Solve: If you divide 9/10 by 3/5, what is the result? Show your working.

Answer: 9/10 ÷ 3/5 = 9/10 * 5/3 = (9*5)/(10*3) = 45/30 = 3/2

Question 2: Explain why flipping the second fraction is essential in dividing fractions, using an example.

Answer: Because dividing is the same as multiplying by the reciprocal, flipping ensures the correct multiplication.