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 solve (2, 12/15 - 1/10) ÷ (16/6), first, convert the mixed number 2, 12/15 to an improper fraction: 2 = 30/15, so 2, 12/15 = 30/15 + 12/15 = 42/15. Next, simplify 12/15 - 1/10. Finding a common denominator (30), we have 24/30 - 3/30 = 21/30, which simplifies to 7/10. Thus, we compute (42/15 - 7/10) = (28/10 - 21/30) = (84/30 - 21/30) = 63/30 = 21/10. Dividing by (16/6) equals (21/10) ÷ (8/3) = (21/10) × (3/8) = 63/80, which is closest to 1. Options C and D (2 and 3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result of the division.
To solve (2, 12/15 - 1/10) ÷ (16/6), first, convert the mixed number 2, 12/15 to an improper fraction: 2 = 30/15, so 2, 12/15 = 30/15 + 12/15 = 42/15. Next, simplify 12/15 - 1/10. Finding a common denominator (30), we have 24/30 - 3/30 = 21/30, which simplifies to 7/10. Thus, we compute (42/15 - 7/10) = (28/10 - 21/30) = (84/30 - 21/30) = 63/30 = 21/10. Dividing by (16/6) equals (21/10) ÷ (8/3) = (21/10) × (3/8) = 63/80, which is closest to 1. Options C and D (2 and 3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result of the division.
Other Related Questions
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.
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.
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.
Kayla has a stack of photographs that is 20 centimeters high. If each photograph is 0.04 cm thick, how many photos are there in the stack?
- A. 8
- B. 50
- C. 80
- D. 500
Correct Answer & Rationale
Correct Answer: D
To determine the number of photographs in the stack, divide the total height of the stack by the thickness of each photograph. The stack is 20 cm high and each photograph is 0.04 cm thick. Calculating this gives: 20 cm ÷ 0.04 cm = 500 photographs. Option A (8) is incorrect as it underestimates the total by not accounting for the thickness appropriately. Option B (50) also miscalculates the total, suggesting a much smaller number of photographs. Option C (80) is an overestimation, failing to consider the correct division of height by thickness. Only option D (500) accurately reflects the calculation, confirming the total number of photographs in the stack.
To determine the number of photographs in the stack, divide the total height of the stack by the thickness of each photograph. The stack is 20 cm high and each photograph is 0.04 cm thick. Calculating this gives: 20 cm ÷ 0.04 cm = 500 photographs. Option A (8) is incorrect as it underestimates the total by not accounting for the thickness appropriately. Option B (50) also miscalculates the total, suggesting a much smaller number of photographs. Option C (80) is an overestimation, failing to consider the correct division of height by thickness. Only option D (500) accurately reflects the calculation, confirming the total number of photographs in the stack.