Question 1: Calculate the product of 3/4 and 2/5. Show your working.

Answer: 6/20 or 3/10

Question 2: Divide 5/8 by 2/3. Show your working.

Answer: 5/8 ÷ 2/3 = 5/8 × 3/2 = 15/16

Question 3: Simplify the fraction resulting from multiplying 4/7 by 14/12.

Answer: 4/7 × 14/12 = (4×14)/(7×12) = 56/84 = 2/3

Question 4: What is the result of dividing 9/10 by 3/5? Show your working.

Answer: 9/10 ÷ 3/5 = 9/10 × 5/3 = 45/30 = 3/2

Question 1: A scientist mixes 2/3 of a liter of chemical A with 3/4 of a liter of chemical B. If the mixture is then divided into portions each containing 1/5 of a liter, how many such portions can be made?

Answer: Total volume = 2/3 + 3/4 = 8/12 + 9/12 = 17/12 liters; number of portions = (17/12) ÷ (1/5) = (17/12) × 5 = 85/12 ≈ 7.08, so 7 full portions.

Question 2: A solution is prepared by diluting a concentrated chemical so that the amount of chemical in 1/2 liter is 3/4 of the original. If the original solution had 1 liter of chemical, what volume of the diluted solution contains the same amount of chemical?

Answer: Original amount = 1 liter; amount in 1/2 liter after dilution = (3/4) × 1 liter = 3/4 liter; to find volume V where amount is 3/4, V = (3/4) ÷ (amount per liter) = (3/4) ÷ 1 = 3/4 liter.

Question 1: In an experiment, a researcher uses 3/8 of a liter of a reagent. If the reagent is to be diluted by adding an equal amount of water to make a total of 1/2 liter, how much water should be added? Show your working.

Answer: Total volume after dilution = 1/2 liter; reagent used = 3/8 liter; water to add = 1/2 - 3/8 = 4/8 - 3/8 = 1/8 liter.

Question 2: A solution's concentration is reduced by dividing it into 1/4 of its original volume. If the original volume was 2 liters, what is the volume after reduction?

Answer: Volume after reduction = 2 liters ÷ 4 = 0.5 liters.

Question 1: A scientist mixes 5/6 of a liter of solution A with 2/3 of a liter of solution B. If they then divide the mixture into small portions each containing 1/10 of a liter, how many portions can be made? Show all steps.

Answer: Total volume = 5/6 + 2/3 = 5/6 + 4/6 = 9/6 = 3/2 liters; number of portions = (3/2) ÷ (1/10) = (3/2) × 10 = 15 portions.

Question 2: How would the process differ if the division was into portions of 1/15 liter instead of 1/10 liter? Calculate the number of portions.

Answer: Number of portions = (3/2) ÷ (1/15) = (3/2) × 15 = 45.

Question 1: Calculate: (2/3) × (3/4).

Answer: 1/2

Question 2: Divide 7/8 by 1/2.

Answer: 7/8 ÷ 1/2 = 7/8 × 2/1 = 14/8 = 7/4

Question 3: Construct a triangle on the grid with sides measuring 1/2, 1/3, and 1/4, using the grid for measurement.

Answer: Students draw a triangle with sides proportionally scaled to these fractional lengths; specific measurements on grid depend on scale.

Question 1: A student attempted to multiply 2/3 by 4/5 and concluded the answer was 8/15, but made a mistake. The student's work was: (2/3) × (4/5) = (2×4)/(3×5) = 8/15. Is the student's answer correct? If not, what mistake did they make?

Answer: Yes, the answer is correct. The student's method is correct; no mistake.

Question 2: A student divided 3/4 by 2/3 and obtained 3/8. Identify the mistake and provide the correct answer.

Answer: Mistake: They might have done 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8, not 3/8. Correct answer: 9/8.