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 gives (7/2) × (7/3) = 49/6. Converting 49/6 back to a mixed number results in 8 1/6, which matches option A. Option B (7 5/6) is incorrect as it suggests a lower product. Option C (6 1/6) underestimates the multiplication result. Option D (5 5/6) is also too low, indicating a misunderstanding of fraction multiplication. Thus, only option A accurately reflects the product of the two mixed numbers.
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 gives (7/2) × (7/3) = 49/6. Converting 49/6 back to a mixed number results in 8 1/6, which matches option A. Option B (7 5/6) is incorrect as it suggests a lower product. Option C (6 1/6) underestimates the multiplication result. Option D (5 5/6) is also too low, indicating a misunderstanding of fraction multiplication. Thus, only option A accurately reflects the product of the two mixed numbers.
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, start by recognizing that she has 5 times the number of books Jerry has. Since Jerry has 15 books, you multiply 15 by 5: 15 × 5 = 75. Thus, Marisol has 75 books. Option A (10) is incorrect as it suggests Marisol has fewer books than Jerry. Option B (20) also underestimates her total, as it does not account for the multiplication factor of 5. Option D (225) overestimates the total by incorrectly multiplying the number of Jerry's books. Only option C accurately reflects the calculation based on the relationship between Marisol's and Jerry's books.
To determine how many books Marisol has, start by recognizing that she has 5 times the number of books Jerry has. Since Jerry has 15 books, you multiply 15 by 5: 15 × 5 = 75. Thus, Marisol has 75 books. Option A (10) is incorrect as it suggests Marisol has fewer books than Jerry. Option B (20) also underestimates her total, as it does not account for the multiplication factor of 5. Option D (225) overestimates the total by incorrectly multiplying the number of Jerry's books. Only option C accurately reflects the calculation based on the relationship between Marisol's and Jerry's books.
2 + (2 × 2) + 2 =
- A. 8
- B. 10
- C. 12
- D. 16
Correct Answer & Rationale
Correct Answer: A
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
Of the following, which is closest to 17/6 + 6/17 ?
- A. 1
- B. 2
- C. 3
- D. 23
Correct Answer & Rationale
Correct Answer: C
To solve 17/6 + 6/17, we first find a common denominator, which is 102. Rewriting the fractions gives us (17*17)/(6*17) + (6*6)/(17*6) = 289/102 + 36/102 = 325/102. Dividing 325 by 102 yields approximately 3.19, which is closest to 3. Option A (1) is too low, as it does not account for the combined value of the fractions. Option B (2) is still below the calculated sum. Option D (23) is excessively high and not feasible given the values involved. Thus, option C (3) is the most accurate approximation.
To solve 17/6 + 6/17, we first find a common denominator, which is 102. Rewriting the fractions gives us (17*17)/(6*17) + (6*6)/(17*6) = 289/102 + 36/102 = 325/102. Dividing 325 by 102 yields approximately 3.19, which is closest to 3. Option A (1) is too low, as it does not account for the combined value of the fractions. Option B (2) is still below the calculated sum. Option D (23) is excessively high and not feasible given the values involved. Thus, option C (3) is the most accurate approximation.
The chart above shows the store's cost and list price for three models of stoves sold by an appliance store.
During a 20 percent off sale, Gene bought a Model Y stove from this store. How much profit did the store
make on Gene's purchase? (Profit = Price paid - Store's cost)
- A. $260
- B. $380
- C. $590
- D. $760
Correct Answer & Rationale
Correct Answer: D
To determine the profit made by the store on Gene's purchase of Model Y, first calculate the sale price. If the list price is $950, a 20% discount reduces it by $190, resulting in a sale price of $760. Next, subtract the store's cost of $0 from the sale price, yielding a profit of $760. Option A ($260) incorrectly assumes a lower sale price or higher cost. Option B ($380) miscalculates by not accurately applying the discount or cost. Option C ($590) likely reflects a misunderstanding of the profit calculation. Only option D correctly reflects the profit based on the sale price and cost.
To determine the profit made by the store on Gene's purchase of Model Y, first calculate the sale price. If the list price is $950, a 20% discount reduces it by $190, resulting in a sale price of $760. Next, subtract the store's cost of $0 from the sale price, yielding a profit of $760. Option A ($260) incorrectly assumes a lower sale price or higher cost. Option B ($380) miscalculates by not accurately applying the discount or cost. Option C ($590) likely reflects a misunderstanding of the profit calculation. Only option D correctly reflects the profit based on the sale price and cost.