Choose the best answer. If necessary, use the paper you were given.
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.
Other Related Questions
Of the following, which is closest to (2(12/15) - 1/10) / (16/6)?
- B. 1
- C. 2
- D. 3
Correct Answer & Rationale
Correct Answer: B
To evaluate the expression (2(12/15) - 1/10) / (16/6), we first simplify the numerator. Calculating 2(12/15) gives us 16/15. Next, we convert 1/10 to a common denominator of 30, resulting in 3/30. Thus, the numerator becomes (16/15 - 3/30). Converting 16/15 to a denominator of 30 yields 32/30, leading to (32/30 - 3/30) = 29/30. Now, simplifying the denominator, 16/6 reduces to 8/3. Dividing (29/30) by (8/3) is equivalent to multiplying by its reciprocal: (29/30) * (3/8) = 87/240, which approximates to 0.36, closest to 1. Options C (2) and D (3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result.
To evaluate the expression (2(12/15) - 1/10) / (16/6), we first simplify the numerator. Calculating 2(12/15) gives us 16/15. Next, we convert 1/10 to a common denominator of 30, resulting in 3/30. Thus, the numerator becomes (16/15 - 3/30). Converting 16/15 to a denominator of 30 yields 32/30, leading to (32/30 - 3/30) = 29/30. Now, simplifying the denominator, 16/6 reduces to 8/3. Dividing (29/30) by (8/3) is equivalent to multiplying by its reciprocal: (29/30) * (3/8) = 87/240, which approximates to 0.36, closest to 1. Options C (2) and D (3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result.
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.
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.
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.