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.
Other Related Questions
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.
Which of the following integers, when rounded to the nearest thousand, results in 2,000?
- A. 2,567
- B. 1,499
- C. 1,097
- D. 1,601
Correct Answer & Rationale
Correct Answer: d
When rounding to the nearest thousand, we look at the hundreds digit. If it is 5 or higher, we round up; if it is 4 or lower, we round down. Option D (1,601) rounds to 2,000 because the hundreds digit (6) is greater than 5, leading to an increase in the thousands place. Option A (2,567) rounds to 3,000, as the hundreds digit (5) prompts rounding up. Option B (1,499) rounds to 1,000 since the hundreds digit (4) indicates rounding down. Option C (1,097) also rounds to 1,000 for the same reason as B. Thus, only D rounds to 2,000.
When rounding to the nearest thousand, we look at the hundreds digit. If it is 5 or higher, we round up; if it is 4 or lower, we round down. Option D (1,601) rounds to 2,000 because the hundreds digit (6) is greater than 5, leading to an increase in the thousands place. Option A (2,567) rounds to 3,000, as the hundreds digit (5) prompts rounding up. Option B (1,499) rounds to 1,000 since the hundreds digit (4) indicates rounding down. Option C (1,097) also rounds to 1,000 for the same reason as B. Thus, only D rounds to 2,000.
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 inside the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division, 1,500 ÷ 20 equals 75, making option A the correct choice. Option B (130) results from incorrect calculations, possibly misapplying the division. Option C (315) may stem from an error in interpreting the division or addition. Option D (400) could arise from mistakenly multiplying instead of dividing. Thus, only option A accurately reflects the correct computation.
To solve the expression 1,500 ÷ (15 + 5), first calculate the sum inside the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division, 1,500 ÷ 20 equals 75, making option A the correct choice. Option B (130) results from incorrect calculations, possibly misapplying the division. Option C (315) may stem from an error in interpreting the division or addition. Option D (400) could arise from mistakenly multiplying instead of dividing. Thus, only option A accurately reflects the correct computation.
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.