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 the equivalence to 1.04, we can convert each fraction to a decimal. Option A, 52/51, equals approximately 1.0196, which is less than 1.04. Option B, 51/50, equals 1.02, also less than 1.04. Option C, 27/25, equals 1.08, exceeding 1.04. Option D, 26/25, simplifies to 1.04, matching the target value exactly. Thus, only option D accurately represents 1.04, while the others deviate from this value.
To determine the equivalence to 1.04, we can convert each fraction to a decimal. Option A, 52/51, equals approximately 1.0196, which is less than 1.04. Option B, 51/50, equals 1.02, also less than 1.04. Option C, 27/25, equals 1.08, exceeding 1.04. Option D, 26/25, simplifies to 1.04, matching the target value exactly. Thus, only option D accurately represents 1.04, while the others deviate from this value.
Other Related Questions
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.
A book is on sale for 25% off. If the original price of the book was D dollars, what is the sale price, in dollars, in terms of D?
- A. D - 25
- B. 7.5D
- C. 0.75D
- D. 0.25D
Correct Answer & Rationale
Correct Answer: C
To find the sale price of a book that is 25% off, we first calculate the discount amount, which is 25% of the original price D. This can be expressed as 0.25D. The sale price is then the original price minus the discount, or D - 0.25D, which simplifies to 0.75D. Option A (D - 25) incorrectly subtracts a fixed dollar amount rather than a percentage, making it irrelevant to the problem. Option B (7.5D) mistakenly applies the percentage in a way that inflates the price instead of reducing it. Option D (0.25D) represents only the discount amount, not the sale price. Thus, 0.75D accurately reflects the sale price after applying the discount.
To find the sale price of a book that is 25% off, we first calculate the discount amount, which is 25% of the original price D. This can be expressed as 0.25D. The sale price is then the original price minus the discount, or D - 0.25D, which simplifies to 0.75D. Option A (D - 25) incorrectly subtracts a fixed dollar amount rather than a percentage, making it irrelevant to the problem. Option B (7.5D) mistakenly applies the percentage in a way that inflates the price instead of reducing it. Option D (0.25D) represents only the discount amount, not the sale price. Thus, 0.75D accurately reflects the sale price after applying the discount.
Which of the labeled points on the number line above has coordinate closest to
- A. A
- B. B
- C. C
- D. D
Correct Answer & Rationale
Correct Answer: D
Point D is closest to zero on the number line, making its coordinate the nearest to the origin. Points A, B, and C are further away from zero, with A being negative and C being a larger positive number. Point B, while positive, is also farther from zero than D. Thus, D represents the coordinate that is numerically closest to zero, confirming its position as the nearest point on the number line. Understanding the proximity of these points to zero is essential for accurately determining their coordinates.
Point D is closest to zero on the number line, making its coordinate the nearest to the origin. Points A, B, and C are further away from zero, with A being negative and C being a larger positive number. Point B, while positive, is also farther from zero than D. Thus, D represents the coordinate that is numerically closest to zero, confirming its position as the nearest point on the number line. Understanding the proximity of these points to zero is essential for accurately determining their coordinates.
Which of the following is equivalent to 8,1/4?
- A. 0.0825
- B. 0.825
- C. 8.25
- D. 82.5
Correct Answer & Rationale
Correct Answer: c
To convert the mixed number 8 1/4 into an improper fraction, first multiply the whole number (8) by the denominator (4), resulting in 32. Then, add the numerator (1) to get 33, making the improper fraction 33/4. When you divide 33 by 4, you get 8.25. Option A (0.0825) is incorrect as it represents a much smaller value. Option B (0.825) is also incorrect, as it is less than 1. Option D (82.5) is incorrect, being ten times larger than the correct value. Thus, 8.25 accurately reflects the original mixed number.
To convert the mixed number 8 1/4 into an improper fraction, first multiply the whole number (8) by the denominator (4), resulting in 32. Then, add the numerator (1) to get 33, making the improper fraction 33/4. When you divide 33 by 4, you get 8.25. Option A (0.0825) is incorrect as it represents a much smaller value. Option B (0.825) is also incorrect, as it is less than 1. Option D (82.5) is incorrect, being ten times larger than the correct value. Thus, 8.25 accurately reflects the original mixed number.