Choose the best answer. If necessary, use the paper you were given.
3(1/2) * 2(1/3) =
- A. 8(1/6)
- B. 7(5/6)
- C. 6(1/6)
- D. 5(5/6)
Correct Answer & Rationale
Correct Answer: A
To solve 3(1/2) * 2(1/3), first convert the mixed numbers to improper fractions: 3(1/2) becomes 7/2 and 2(1/3) becomes 7/3. Multiplying these fractions yields (7/2) * (7/3) = 49/6. Converting 49/6 back to a mixed number gives 8(1/6). Option B, 7(5/6), results from incorrect multiplication. Option C, 6(1/6), miscalculates the product as well. Option D, 5(5/6), reflects a misunderstanding of fraction multiplication. The proper method confirms that 8(1/6) is indeed the accurate result.
To solve 3(1/2) * 2(1/3), first convert the mixed numbers to improper fractions: 3(1/2) becomes 7/2 and 2(1/3) becomes 7/3. Multiplying these fractions yields (7/2) * (7/3) = 49/6. Converting 49/6 back to a mixed number gives 8(1/6). Option B, 7(5/6), results from incorrect multiplication. Option C, 6(1/6), miscalculates the product as well. Option D, 5(5/6), reflects a misunderstanding of fraction multiplication. The proper method confirms that 8(1/6) is indeed the accurate result.
Other Related Questions
Marisol has 5 times as many books as Jerry. Jerry has 15 books. How many books does Marisol have?
- A. 10
- B. 20
- C. 75
- D. 225
Correct Answer & Rationale
Correct Answer: C
To determine how many books Marisol has, multiply the number of books Jerry has (15) by 5, since Marisol has 5 times as many. This calculation yields 15 x 5 = 75. Option A (10) is incorrect as it underestimates the multiplication factor. Option B (20) also miscalculates, suggesting a much lower total. Option D (225) overestimates the number of books, resulting from an incorrect multiplication. Thus, the only accurate answer is 75, reflecting Marisol's total based on Jerry's count.
To determine how many books Marisol has, multiply the number of books Jerry has (15) by 5, since Marisol has 5 times as many. This calculation yields 15 x 5 = 75. Option A (10) is incorrect as it underestimates the multiplication factor. Option B (20) also miscalculates, suggesting a much lower total. Option D (225) overestimates the number of books, resulting from an incorrect multiplication. Thus, the only accurate answer is 75, reflecting Marisol's total based on Jerry's count.
If 32% of n is 20.8, what is n?
- A. 64
- B. 65
- C. 66
- D. 154
Correct Answer & Rationale
Correct Answer: B
To find n, we start with the equation derived from the problem: \(0.32n = 20.8\). Dividing both sides by 0.32 gives \(n = \frac{20.8}{0.32}\), which simplifies to 65. This confirms that option B is accurate. Option A (64) results from an incorrect calculation of \(0.32n\). Option C (66) overestimates n, suggesting a misunderstanding of the percentage relationship. Option D (154) is far too high, indicating a significant miscalculation. Thus, only option B aligns correctly with the mathematical solution.
To find n, we start with the equation derived from the problem: \(0.32n = 20.8\). Dividing both sides by 0.32 gives \(n = \frac{20.8}{0.32}\), which simplifies to 65. This confirms that option B is accurate. Option A (64) results from an incorrect calculation of \(0.32n\). Option C (66) overestimates n, suggesting a misunderstanding of the percentage relationship. Option D (154) is far too high, indicating a significant miscalculation. Thus, only option B aligns correctly with the mathematical solution.
Maria worked 2 weeks, earning $435.50 the first week and $278.38 the second week. If she paid one-half of her two-week earnings for tuition, how much did she pay for tuition?
- A. $713.88
- B. $356.94
- C. $217.75
- D. $139.19
Correct Answer & Rationale
Correct Answer: B
To find the amount Maria paid for tuition, first calculate her total earnings for the two weeks. Adding her earnings from both weeks: $435.50 + $278.38 = $713.88. Since she paid one-half of her total earnings for tuition, divide this amount by 2: $713.88 / 2 = $356.94. Option A ($713.88) represents her total earnings, not the tuition amount. Option C ($217.75) and Option D ($139.19) do not correctly reflect half of her total earnings. Therefore, $356.94 accurately represents the amount she paid for tuition.
To find the amount Maria paid for tuition, first calculate her total earnings for the two weeks. Adding her earnings from both weeks: $435.50 + $278.38 = $713.88. Since she paid one-half of her total earnings for tuition, divide this amount by 2: $713.88 / 2 = $356.94. Option A ($713.88) represents her total earnings, not the tuition amount. Option C ($217.75) and Option D ($139.19) do not correctly reflect half of her total earnings. Therefore, $356.94 accurately represents the amount she paid for tuition.
2(1/2 + 1/3) =
- A. 1(2/3)
- B. 1(5/6)
- C. 2(1/6)
- D. 2(5/6)
Correct Answer & Rationale
Correct Answer: A
To solve 2(1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. Rewrite the fractions: 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding these gives 5/6. Now, multiply by 2: 2 * 5/6 equals 10/6, which simplifies to 1(2/3). Option B, 1(5/6), results from miscalculating the addition. Option C, 2(1/6), misinterprets the multiplication step. Option D, 2(5/6), incorrectly applies the multiplication to the wrong sum. Each incorrect option reflects a misunderstanding of the operations involved.
To solve 2(1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. Rewrite the fractions: 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding these gives 5/6. Now, multiply by 2: 2 * 5/6 equals 10/6, which simplifies to 1(2/3). Option B, 1(5/6), results from miscalculating the addition. Option C, 2(1/6), misinterprets the multiplication step. Option D, 2(5/6), incorrectly applies the multiplication to the wrong sum. Each incorrect option reflects a misunderstanding of the operations involved.