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
1,500 / (15 + 5) =
- A. 75
- B. 130
- C. 315
- D. 400
Correct Answer & Rationale
Correct Answer: A
To solve the expression 1,500 / (15 + 5), first calculate the sum in the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division gives 1,500 รท 20 = 75, confirming option A as the correct answer. Option B (130) results from an incorrect division or miscalculation. Option C (315) likely stems from misunderstanding the order of operations, possibly miscalculating the sum before division. Option D (400) may arise from mistakenly multiplying instead of dividing. Understanding the correct order of operations is crucial for accurate calculations.
To solve the expression 1,500 / (15 + 5), first calculate the sum in the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division gives 1,500 รท 20 = 75, confirming option A as the correct answer. Option B (130) results from an incorrect division or miscalculation. Option C (315) likely stems from misunderstanding the order of operations, possibly miscalculating the sum before division. Option D (400) may arise from mistakenly multiplying instead of dividing. Understanding the correct order of operations is crucial for accurate calculations.
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.
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.
Which of the following is equivalent to 1.04?
- A. 52/51
- B. 51/50
- C. 27/25
- D. 26/25
Correct Answer & Rationale
Correct Answer: D
To determine which option is equivalent to 1.04, we convert each fraction to a decimal. A: 52/51 equals approximately 1.0196, which is less than 1.04. B: 51/50 equals 1.02, also below 1.04. C: 27/25 equals 1.08, exceeding 1.04. D: 26/25 calculates to 1.04 exactly, matching the target value. Thus, option D accurately represents 1.04, while the other options do not meet the requirement.
To determine which option is equivalent to 1.04, we convert each fraction to a decimal. A: 52/51 equals approximately 1.0196, which is less than 1.04. B: 51/50 equals 1.02, also below 1.04. C: 27/25 equals 1.08, exceeding 1.04. D: 26/25 calculates to 1.04 exactly, matching the target value. Thus, option D accurately represents 1.04, while the other options do not meet the requirement.