Which of the following inequalities is correct?
- A. 2/3 < 3/5 < 5/7
- B. 2/3 < 5/7 < 3/5
- C. 3/5 < 2/3 < 5/7
- D. 3/5 < 5/7 < 2/3
Correct Answer & Rationale
Correct Answer: C
To determine the order of the fractions, we can convert them to decimals or find a common denominator. - **Option A (2/3 < 3/5 < 5/7)** is incorrect because 2/3 (approximately 0.67) is greater than 3/5 (0.6), violating the first inequality. - **Option B (2/3 < 5/7 < 3/5)** is also incorrect, as 5/7 (approximately 0.71) is greater than 2/3, making the first inequality false. - **Option D (3/5 < 5/7 < 2/3)** is incorrect because, while 3/5 is less than 5/7, 5/7 is greater than 2/3, contradicting the second inequality. - **Option C (3/5 < 2/3 < 5/7)** is accurate; 3/5 is indeed less than 2/3, and 2/3 is less than 5/7, maintaining the correct order.
To determine the order of the fractions, we can convert them to decimals or find a common denominator. - **Option A (2/3 < 3/5 < 5/7)** is incorrect because 2/3 (approximately 0.67) is greater than 3/5 (0.6), violating the first inequality. - **Option B (2/3 < 5/7 < 3/5)** is also incorrect, as 5/7 (approximately 0.71) is greater than 2/3, making the first inequality false. - **Option D (3/5 < 5/7 < 2/3)** is incorrect because, while 3/5 is less than 5/7, 5/7 is greater than 2/3, contradicting the second inequality. - **Option C (3/5 < 2/3 < 5/7)** is accurate; 3/5 is indeed less than 2/3, and 2/3 is less than 5/7, maintaining the correct order.
Other Related Questions
50.50 ÷ 0.25
- A. 202
- B. 2.2
- C. 2.02
- D. 0.22
Correct Answer & Rationale
Correct Answer: A
To solve 50.50 ÷ 0.25, converting the division into a simpler form is helpful. Dividing both numbers by 0.25 effectively transforms the problem into 50.50 ÷ 0.25 = 50.50 × 4, which equals 202. Option B (2.2) is incorrect as it misrepresents the scale of the division, resulting from a misunderstanding of decimal placement. Option C (2.02) also miscalculates the division, likely stemming from incorrect multiplication or division steps. Option D (0.22) is far too low, indicating a significant error in understanding the relationship between the dividend and divisor.
To solve 50.50 ÷ 0.25, converting the division into a simpler form is helpful. Dividing both numbers by 0.25 effectively transforms the problem into 50.50 ÷ 0.25 = 50.50 × 4, which equals 202. Option B (2.2) is incorrect as it misrepresents the scale of the division, resulting from a misunderstanding of decimal placement. Option C (2.02) also miscalculates the division, likely stemming from incorrect multiplication or division steps. Option D (0.22) is far too low, indicating a significant error in understanding the relationship between the dividend and divisor.
What is 0.3 percent of 90?
- A. 0.027
- B. 0.27
- C. 0.3
- D. 2.7
Correct Answer & Rationale
Correct Answer: B
To find 0.3 percent of 90, convert the percentage to a decimal by dividing by 100, resulting in 0.003. Then, multiply 0.003 by 90, yielding 0.27. Option A (0.027) is too small, as it miscalculates the multiplication. Option C (0.3) represents the percentage itself, not the calculated value of 0.3 percent of 90. Option D (2.7) is ten times larger than the correct answer, indicating a misunderstanding of the percent calculation. Thus, B (0.27) accurately represents 0.3 percent of 90.
To find 0.3 percent of 90, convert the percentage to a decimal by dividing by 100, resulting in 0.003. Then, multiply 0.003 by 90, yielding 0.27. Option A (0.027) is too small, as it miscalculates the multiplication. Option C (0.3) represents the percentage itself, not the calculated value of 0.3 percent of 90. Option D (2.7) is ten times larger than the correct answer, indicating a misunderstanding of the percent calculation. Thus, B (0.27) accurately represents 0.3 percent of 90.
Harriet took 48 minutes to ride her bike the distance from her house to the town library. If she rode at a constant rate, what fraction of the total distance did she ride in the first 12 minutes?
- A. 1/4
- B. 1/3
- C. 1/2
- D. 3/4
Correct Answer & Rationale
Correct Answer: A
To determine the fraction of the total distance Harriet rode in the first 12 minutes, we start by recognizing that she took 48 minutes for the entire trip. Riding at a constant rate means that her distance covered is proportional to the time spent riding. In 12 minutes, which is one-fourth of the total 48 minutes, she would have covered one-fourth of the total distance. Thus, the fraction of the total distance she rode in the first 12 minutes is 1/4. Options B (1/3), C (1/2), and D (3/4) misrepresent the proportion of time to total time. Each suggests a greater fraction than what corresponds to 12 minutes relative to 48 minutes, leading to incorrect conclusions about the distance covered.
To determine the fraction of the total distance Harriet rode in the first 12 minutes, we start by recognizing that she took 48 minutes for the entire trip. Riding at a constant rate means that her distance covered is proportional to the time spent riding. In 12 minutes, which is one-fourth of the total 48 minutes, she would have covered one-fourth of the total distance. Thus, the fraction of the total distance she rode in the first 12 minutes is 1/4. Options B (1/3), C (1/2), and D (3/4) misrepresent the proportion of time to total time. Each suggests a greater fraction than what corresponds to 12 minutes relative to 48 minutes, leading to incorrect conclusions about the distance covered.
4/9 (3/16 - 1/12) =
- A. 5/108
- B. 5/48
- C. 2/9
- D. 20/48
Correct Answer & Rationale
Correct Answer: A
To solve \( \frac{4}{9} \left( \frac{3}{16} - \frac{1}{12} \right) \), first calculate \( \frac{3}{16} - \frac{1}{12} \). Finding a common denominator (48), we convert the fractions: \( \frac{3}{16} = \frac{9}{48} \) and \( \frac{1}{12} = \frac{4}{48} \). Thus, \( \frac{9}{48} - \frac{4}{48} = \frac{5}{48} \). Next, multiply \( \frac{4}{9} \) by \( \frac{5}{48} \): \[ \frac{4 \times 5}{9 \times 48} = \frac{20}{432} = \frac{5}{108} \] Option B (5/48) is incorrect as it misrepresents the multiplication step. Option C (2/9) ignores the subtraction and multiplication entirely. Option D (20/48) fails to simplify the fraction correctly.
To solve \( \frac{4}{9} \left( \frac{3}{16} - \frac{1}{12} \right) \), first calculate \( \frac{3}{16} - \frac{1}{12} \). Finding a common denominator (48), we convert the fractions: \( \frac{3}{16} = \frac{9}{48} \) and \( \frac{1}{12} = \frac{4}{48} \). Thus, \( \frac{9}{48} - \frac{4}{48} = \frac{5}{48} \). Next, multiply \( \frac{4}{9} \) by \( \frac{5}{48} \): \[ \frac{4 \times 5}{9 \times 48} = \frac{20}{432} = \frac{5}{108} \] Option B (5/48) is incorrect as it misrepresents the multiplication step. Option C (2/9) ignores the subtraction and multiplication entirely. Option D (20/48) fails to simplify the fraction correctly.