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
At the factory where he works, Mr. Lopez must make a minimum of 48 circuit boards per day. On Wednesday, he made 60 circuit boards. What percent of the required minimum did he make?
- A. 125%
- B. 112%
- C. 80%
- D. 25%
Correct Answer & Rationale
Correct Answer: A
To find the percentage of the required minimum that Mr. Lopez made, divide the number of circuit boards he produced (60) by the minimum required (48) and then multiply by 100. \[ \text{Percentage} = \left(\frac{60}{48}\right) \times 100 = 125\% \] Option A is correct as it reflects that he made 125% of the minimum requirement. Option B (112%) is incorrect because it underestimates his production relative to the minimum. Option C (80%) is also wrong, as it suggests he produced only a fraction of the required amount. Option D (25%) is far too low, indicating a misunderstanding of the basic calculation.
To find the percentage of the required minimum that Mr. Lopez made, divide the number of circuit boards he produced (60) by the minimum required (48) and then multiply by 100. \[ \text{Percentage} = \left(\frac{60}{48}\right) \times 100 = 125\% \] Option A is correct as it reflects that he made 125% of the minimum requirement. Option B (112%) is incorrect because it underestimates his production relative to the minimum. Option C (80%) is also wrong, as it suggests he produced only a fraction of the required amount. Option D (25%) is far too low, indicating a misunderstanding of the basic calculation.
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.
Charlotte is drilling three holes of different sizes in a bird house that she is making. The diameters of the holes are 1(1/2) inches, 1(3/4) inches, and 1(3/8) inches. Which of the following gives the diameters, in inches, in order from least to greatest?
- A. 1(1/2), 1(3/4), 1(3/8)
- B. 1(1/2), 1(3/8), 1(3/4)
- C. 1(3/8), 1(3/4), 1(1/2)
- D. 1(3/8), 1(1/2), 1(3/4)
Correct Answer & Rationale
Correct Answer: D
To determine the correct order of the hole diameters from least to greatest, we first convert the mixed numbers to improper fractions for easier comparison. - 1(1/2) = 3/2 - 1(3/4) = 7/4 - 1(3/8) = 11/8 By comparing these values, we find that 11/8 (1(3/8)) is the smallest, followed by 3/2 (1(1/2)), and finally 7/4 (1(3/4)). Option A incorrectly lists 1(1/2) as the smallest. Option B misplaces 1(3/8) and 1(3/4). Option C arranges the sizes incorrectly, placing the largest first. Therefore, the correct order is D: 1(3/8), 1(1/2), 1(3/4).
To determine the correct order of the hole diameters from least to greatest, we first convert the mixed numbers to improper fractions for easier comparison. - 1(1/2) = 3/2 - 1(3/4) = 7/4 - 1(3/8) = 11/8 By comparing these values, we find that 11/8 (1(3/8)) is the smallest, followed by 3/2 (1(1/2)), and finally 7/4 (1(3/4)). Option A incorrectly lists 1(1/2) as the smallest. Option B misplaces 1(3/8) and 1(3/4). Option C arranges the sizes incorrectly, placing the largest first. Therefore, the correct order is D: 1(3/8), 1(1/2), 1(3/4).
Of the following, which is greatest?
- A. -0.75
- B. 5/-2
- C. -3
- D. -2
Correct Answer & Rationale
Correct Answer: A
Option A, -0.75, is the greatest value among the choices since it is the least negative number. Option B, 5/-2, simplifies to -2.5, which is less than -0.75. Option C, -3, is clearly more negative than both -0.75 and -2. Option D, -2, is greater than -3 but still less than -0.75. In summary, -0.75 is the highest value among negative numbers, making it the greatest option in this comparison.
Option A, -0.75, is the greatest value among the choices since it is the least negative number. Option B, 5/-2, simplifies to -2.5, which is less than -0.75. Option C, -3, is clearly more negative than both -0.75 and -2. Option D, -2, is greater than -3 but still less than -0.75. In summary, -0.75 is the highest value among negative numbers, making it the greatest option in this comparison.