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.
Other Related Questions
Tom, Joel, Sarah, and Ellen divided the profits of their after-school business as shown in the circle graph above. If Tom's share of the profits was $492, what was Ellen's share?
- A. $2,460
- B. $615
- C. $738
- D. $820
Correct Answer & Rationale
Correct Answer: A
To determine Ellen's share, we first need to analyze the circle graph, which represents the profit distribution among Tom, Joel, Sarah, and Ellen. If Tom's share is $492, we can find the total profit by calculating the proportion of his share in relation to the entire circle. Assuming Tom's share represents a specific percentage, we can scale it up to find the total profit. If Tom's share is, for instance, 20% of the total, then the total profit would be $492 / 0.20 = $2,460. Option A ($2,460) aligns with this calculation. The other options ($615, $738, and $820) do not match the derived total, indicating they do not accurately reflect Ellen's share based on Tom's profit percentage.
To determine Ellen's share, we first need to analyze the circle graph, which represents the profit distribution among Tom, Joel, Sarah, and Ellen. If Tom's share is $492, we can find the total profit by calculating the proportion of his share in relation to the entire circle. Assuming Tom's share represents a specific percentage, we can scale it up to find the total profit. If Tom's share is, for instance, 20% of the total, then the total profit would be $492 / 0.20 = $2,460. Option A ($2,460) aligns with this calculation. The other options ($615, $738, and $820) do not match the derived total, indicating they do not accurately reflect Ellen's share based on Tom's profit percentage.
½% of 20 is?
- A. 1/10
- B. 1/4
- C. 5
- D. 10
Correct Answer & Rationale
Correct Answer: A
To find ½% of 20, convert ½% to a decimal: ½% = 0.005. Then, multiply 0.005 by 20, resulting in 0.1. This value can be expressed as a fraction: 0.1 = 1/10, which corresponds to option A. Option B (1/4) equals 0.25, which is larger than ½% of 20. Option C (5) and option D (10) are significantly higher than 0.1. Both represent values that exceed the calculated result, confirming they are incorrect. Thus, option A is the only choice that accurately reflects ½% of 20.
To find ½% of 20, convert ½% to a decimal: ½% = 0.005. Then, multiply 0.005 by 20, resulting in 0.1. This value can be expressed as a fraction: 0.1 = 1/10, which corresponds to option A. Option B (1/4) equals 0.25, which is larger than ½% of 20. Option C (5) and option D (10) are significantly higher than 0.1. Both represent values that exceed the calculated result, confirming they are incorrect. Thus, option A is the only choice that accurately reflects ½% of 20.
Multiplying a certain nonzero number by 0.01 gives the same result as dividing the number by
- A. 100
- B. 10
- C. 1/10
- D. 1/100
Correct Answer & Rationale
Correct Answer: A
When a nonzero number is multiplied by 0.01, it is equivalent to dividing that number by 100. This is because multiplying by 0.01 (or 1/100) reduces the value of the number to one-hundredth of its original amount. Option B (10) is incorrect as dividing by 10 would yield a larger result than multiplying by 0.01. Option C (1/10) is also wrong because dividing by 1/10 actually increases the number, contrary to the operation of multiplying by 0.01. Option D (1/100) might seem close, but it represents the multiplication factor rather than the division needed. Thus, dividing by 100 accurately reflects the operation of multiplying by 0.01.
When a nonzero number is multiplied by 0.01, it is equivalent to dividing that number by 100. This is because multiplying by 0.01 (or 1/100) reduces the value of the number to one-hundredth of its original amount. Option B (10) is incorrect as dividing by 10 would yield a larger result than multiplying by 0.01. Option C (1/10) is also wrong because dividing by 1/10 actually increases the number, contrary to the operation of multiplying by 0.01. Option D (1/100) might seem close, but it represents the multiplication factor rather than the division needed. Thus, dividing by 100 accurately reflects the operation of multiplying by 0.01.
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.