Question 1: Calculate: (3/4) ÷ (2/5).

Answer: 15/8

Question 2: Calculate: (5/6) ÷ (3/4).

Answer: 20/18 or 10/9

Question 3: Simplify: (7/8) ÷ (14/16).

Answer: 1

Question 4: In a recipe, if 2/3 of a cup of sugar is used for every 1/4 cup of flour, what is the ratio of sugar to flour?

Answer: 8/3 or 2 2/3

Question 5: A swimmer completes 3/5 of a lap in a pool. How many laps does the swimmer complete in total if they swim 2/3 of a lap each time?

Answer: 9/10

Question 6: Divide: 4/9 ÷ 2/3. Show your working.

Answer: 4/9 * 3/2 = 12/18 = 2/3

Question 7: A garden has 3/4 of an acre of roses and 2/3 of an acre of tulips. What is the ratio of roses to tulips?

Answer: 9/8 or 1 1/8

Question 8: Calculate: (9/10) ÷ (3/5).

Answer: 3/2

Question 9: If a car travels 5/8 of a mile every minute, how far does it travel in 3/4 of a minute?

Answer: 15/32 miles

Question 10: Challenge: Simplify (11/12) ÷ (7/8) and explain each step.

Answer: 11/12 * 8/7 = 88/84 = 22/21

Question 11: An artist mixes 2/3 of a liter of blue paint with 3/4 of a liter of yellow paint. What is the ratio of blue to yellow paint?

Answer: 8/9

Question 12: Error Analysis: A student calculates (2/3) ÷ (4/5) as 2/3 * 4/5 = 8/15. Identify the mistake and correct it.

Answer: The student incorrectly multiplied instead of dividing. Correct method: (2/3) ÷ (4/5) = (2/3) * (5/4) = 10/12 = 5/6.