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
What is rounded to the nearest hundredth? 48/27
- A. 1.7
- B. 1.77
- C. 1.78
- D. 1.8
Correct Answer & Rationale
Correct Answer: C
To find the value of \( \frac{48}{27} \), we perform the division, resulting in approximately 1.7778. Rounding this number to the nearest hundredth involves looking at the third decimal place (7) to determine whether to round up or down. Since 7 is 5 or greater, we round up, resulting in 1.78. - Option A (1.7) is too low, as it does not reflect the precise value. - Option B (1.77) rounds down incorrectly, failing to account for the third decimal. - Option D (1.8) rounds up too far, exceeding the correct value. Thus, 1.78 accurately represents the rounded result.
To find the value of \( \frac{48}{27} \), we perform the division, resulting in approximately 1.7778. Rounding this number to the nearest hundredth involves looking at the third decimal place (7) to determine whether to round up or down. Since 7 is 5 or greater, we round up, resulting in 1.78. - Option A (1.7) is too low, as it does not reflect the precise value. - Option B (1.77) rounds down incorrectly, failing to account for the third decimal. - Option D (1.8) rounds up too far, exceeding the correct value. Thus, 1.78 accurately represents the rounded result.
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.
If 40 is 20 percent of a number, then the number is what percent of 40?
- A. 500%
- B. 200%
- C. 80%
- D. 20%
Correct Answer & Rationale
Correct Answer: A
To determine what percent a number (let's call it X) is of 40, we first establish that 40 is 20% of X. This can be represented as the equation: 40 = 0.2X. Solving for X gives us X = 200. Now, to find out what percent 200 is of 40, we use the formula (part/whole) × 100, which results in (200/40) × 100 = 500%. Option B (200%) is incorrect as it mistakenly uses X instead of calculating the percentage of 40. Option C (80%) and Option D (20%) are also incorrect for similar reasons; they do not accurately reflect the relationship between 200 and 40.
To determine what percent a number (let's call it X) is of 40, we first establish that 40 is 20% of X. This can be represented as the equation: 40 = 0.2X. Solving for X gives us X = 200. Now, to find out what percent 200 is of 40, we use the formula (part/whole) × 100, which results in (200/40) × 100 = 500%. Option B (200%) is incorrect as it mistakenly uses X instead of calculating the percentage of 40. Option C (80%) and Option D (20%) are also incorrect for similar reasons; they do not accurately reflect the relationship between 200 and 40.
0.4/0.04 =
- A. 100
- B. 10
- C. 0.1
- D. 0.01
Correct Answer & Rationale
Correct Answer: B
To solve 0.4 divided by 0.04, it’s helpful to convert both numbers to whole numbers for easier calculation. Multiplying both by 100 gives us 40 divided by 4. This simplifies to 10, confirming option B as the solution. Option A (100) results from miscalculating the division, possibly by incorrectly interpreting the decimal places. Option C (0.1) and Option D (0.01) suggest a misunderstanding of division, as they reflect values far smaller than the actual quotient. Thus, only option B accurately represents the result of the division.
To solve 0.4 divided by 0.04, it’s helpful to convert both numbers to whole numbers for easier calculation. Multiplying both by 100 gives us 40 divided by 4. This simplifies to 10, confirming option B as the solution. Option A (100) results from miscalculating the division, possibly by incorrectly interpreting the decimal places. Option C (0.1) and Option D (0.01) suggest a misunderstanding of division, as they reflect values far smaller than the actual quotient. Thus, only option B accurately represents the result of the division.