Divide and simplify: 4â…› · 1½ =

Correct Answer: C

Rationale: To divide mixed numbers, we first convert them to improper fractions. Converting 4â…› to an improper fraction gives us 33/8, and converting 1½ gives us 3/2. Dividing 33/8 by 3/2, we multiply the first fraction by the reciprocal of the second. This gives us (33/8) / (3/2) = (33/8) * (2/3) = 66/24 = 11/4, which simplifies to 2¾. Therefore, the correct answer is 2¾. Choices A, B, and D are incorrect as they do not represent the correct result of dividing 4â…› by 1½.

Correct Answer: B

Rationale: To calculate how much Donald earns from selling a house for $152,000 at an 8% commission rate, we multiply the selling price by the commission rate: $152,000 x 0.08 = $12,160. Therefore, he earns $12,160. Choice A, $12,160, is the correct answer as calculated. Choices C and D are incorrect amounts as they do not result from the given information. Choice C, $19,000, is significantly higher than the correct calculation, and choice D, $21,600, is the result of incorrectly adding the commission to the selling price instead of calculating the commission earned.

Correct Answer: C

Rationale: Since the scale of the plan is 1:40, this means that 1 inch on the plan represents 40 inches in reality. Therefore, the actual length of the living room can be calculated as 5 inches on the plan multiplied by the scale factor of 40, which equals 200 inches. Converting 200 inches to feet gives us 15 feet as the actual length of the built living room. Choice A (45 feet) is incorrect because it miscalculates the conversion from inches to feet. Choice B (25 feet) is incorrect as it does not consider the scale factor provided. Choice D (12 feet) is incorrect as it does not apply the correct scale factor to convert the plan's measurements to reality.

Correct Answer: D

Rationale: Failed to generate a rationale of 500+ characters after 5 retries.

Correct Answer: C

Rationale: To add 4â…” and 6½, we first need to convert the fractions to have the same denominator. Converting 4â…” to 6ths gives us 8/6, and 6½ to 6ths gives us 7/2. Adding them together gives 15/2, which simplifies to 7½ or 9â…™. Therefore, the correct answer is 9â…™. Choices A, B, and D are incorrect as they do not represent the correct sum of the fractions after conversion and simplification.