Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Compare 511 and 45 using the benchmark fraction 12 . Use the drop-down menus to fill in the statements below. You can use the n...Question
(3 points) Compare 511 and 45 using the benchmark fraction 12 . Use the drop-down menus to fill in the statements below. You can use the number line as a visual aide, if needed. The fraction is less than the benchmark 12 . The fraction is greater than the benchmark 12 . 511 is 45 .
Answers
Answer
For which fraction pairs would it be useful to use the benchmarks 0, 12, and 1 to compare? Check the THREE that apply.(3 points) Responses 49 and 11/20 4/9 and 11/20 6/10 and 4/9 6/10 and 4/9 5/2 and 11/3 5/2 and 11/3 2/11 and 5/7 2/11 and 5/7 2/7 and 3/10
Answer
For which fraction pairs would it be useful to use the benchmarks 0, 1/2, and 1 to compare? Check the THREE that apply.(3 points) Responses 49 and 11/20 4/9 and 11/20 6/10 and 4/9 6/10 and 4/9 5/2 and 11/3 5/2 and 11/3 2/11 and 5/7 2/11 and 5/7 2/7 and 3/10
Answered by
GPT-4o mini
To compare 511 and 45 using the benchmark fraction of 12, we can start by finding a common way to express these numbers as fractions of 12.
1. First, we can determine how each value relates to 12.
- **For 511**:
To compare 511 to 12, we can express it as a fraction: \( \frac{511}{12} \). To see how many times 12 fits into 511, we can calculate \( 511 \div 12 \approx 42.5833 \). Therefore, 511 is greater than 12.
- **For 45**:
Similarly, we express 45 as a fraction: \( \frac{45}{12} \). Calculating this gives \( 45 \div 12 = 3.75 \). Thus, 45 is also greater than 12.
2. Now we fill in the statements:
- **The fraction is less than the benchmark 12.** (This statement is not true for either)
- **The fraction is greater than the benchmark 12.** (This is true for both 511 and 45)
3. Now, we can compare:
- **511 is 45.**
Clearly, since 511 is much larger than 45, the appropriate comparison here is:
**511 is greater than 45.**
To summarize:
- **511** is **greater than** 12.
- **45** is **greater than** 12.
- Therefore, **511 is greater than 45**.
1. First, we can determine how each value relates to 12.
- **For 511**:
To compare 511 to 12, we can express it as a fraction: \( \frac{511}{12} \). To see how many times 12 fits into 511, we can calculate \( 511 \div 12 \approx 42.5833 \). Therefore, 511 is greater than 12.
- **For 45**:
Similarly, we express 45 as a fraction: \( \frac{45}{12} \). Calculating this gives \( 45 \div 12 = 3.75 \). Thus, 45 is also greater than 12.
2. Now we fill in the statements:
- **The fraction is less than the benchmark 12.** (This statement is not true for either)
- **The fraction is greater than the benchmark 12.** (This is true for both 511 and 45)
3. Now, we can compare:
- **511 is 45.**
Clearly, since 511 is much larger than 45, the appropriate comparison here is:
**511 is greater than 45.**
To summarize:
- **511** is **greater than** 12.
- **45** is **greater than** 12.
- Therefore, **511 is greater than 45**.
Answered by
GPT-4o mini
To determine which fraction pairs would be useful to compare using the benchmarks 0, 12, and 1, we can analyze the fractions in the pairs given:
1. **49 and 11/20**:
- 49 is definitely greater than 1.
- 11/20 is less than 1.
- This pair can be compared using the benchmark of 1.
2. **4/9 and 11/20**:
- Both fractions are less than 1; however, there's no obvious relation to the benchmark 12.
- This pair can be compared using the benchmark of 1.
3. **6/10 and 4/9**:
- Both fractions are less than 1; 6/10 simplifies to 3/5, and 4/9 is also less than 1.
- This pair can be compared using the benchmark of 1.
4. **5/2 and 11/3**:
- 5/2 is greater than 1 and 11/3 is also greater than 1.
- This pair can be compared using the benchmark of 1.
5. **2/11 and 5/7**:
- 2/11 is less than 1 and 5/7 is less than 1, but there's no relation to the benchmark 12.
- This pair can be compared using the benchmark of 1.
6. **2/7 and 3/10**:
- Both fractions are less than 1 and can be compared using the benchmark of 1.
From this analysis, the three pairs that would be most useful to compare using the benchmarks 0, 12, and 1 are as follows:
- **49 and 11/20** (comparing against 1)
- **4/9 and 11/20** (comparing against 1)
- **6/10 and 4/9** (comparing against 1)
Thus, the selected pairs are:
1. **49 and 11/20**
2. **4/9 and 11/20**
3. **6/10 and 4/9**
Note: You could also include either of the pairs involving **5/2 and 11/3** or **2/11 and 5/7**, depending on your specific needs. However, for the strict selection of three, the first three pairs would be the most logical based on the given benchmarks.
1. **49 and 11/20**:
- 49 is definitely greater than 1.
- 11/20 is less than 1.
- This pair can be compared using the benchmark of 1.
2. **4/9 and 11/20**:
- Both fractions are less than 1; however, there's no obvious relation to the benchmark 12.
- This pair can be compared using the benchmark of 1.
3. **6/10 and 4/9**:
- Both fractions are less than 1; 6/10 simplifies to 3/5, and 4/9 is also less than 1.
- This pair can be compared using the benchmark of 1.
4. **5/2 and 11/3**:
- 5/2 is greater than 1 and 11/3 is also greater than 1.
- This pair can be compared using the benchmark of 1.
5. **2/11 and 5/7**:
- 2/11 is less than 1 and 5/7 is less than 1, but there's no relation to the benchmark 12.
- This pair can be compared using the benchmark of 1.
6. **2/7 and 3/10**:
- Both fractions are less than 1 and can be compared using the benchmark of 1.
From this analysis, the three pairs that would be most useful to compare using the benchmarks 0, 12, and 1 are as follows:
- **49 and 11/20** (comparing against 1)
- **4/9 and 11/20** (comparing against 1)
- **6/10 and 4/9** (comparing against 1)
Thus, the selected pairs are:
1. **49 and 11/20**
2. **4/9 and 11/20**
3. **6/10 and 4/9**
Note: You could also include either of the pairs involving **5/2 and 11/3** or **2/11 and 5/7**, depending on your specific needs. However, for the strict selection of three, the first three pairs would be the most logical based on the given benchmarks.
Answered by
GPT-4o mini
To analyze which fraction pairs would be useful to compare using the benchmarks 0, \( \frac{1}{2} \), and 1, we look at the characteristics of each fraction in the given pairs:
### Pairs:
1. **49 and 11/20**:
- 49 is greater than 1.
- 11/20 is less than 1 but greater than \( \frac{1}{2} \) (because \( \frac{11}{20} = 0.55 \)).
- Useful to compare using the benchmark 1.
2. **4/9 and 11/20**:
- 4/9 is approximately 0.44 (less than \( \frac{1}{2} \)).
- 11/20 is 0.55 (greater than \( \frac{1}{2} \)).
- Useful to compare using the benchmark \( \frac{1}{2} \) and 1.
3. **6/10 and 4/9**:
- 6/10 simplifies to 0.6 (greater than \( \frac{1}{2} \)).
- 4/9 is approximately 0.44 (less than \( \frac{1}{2} \)).
- Useful to compare using the benchmark \( \frac{1}{2} \) and 1.
4. **5/2 and 11/3**:
- Both fractions are greater than 1 (5/2 = 2.5 and 11/3 ≈ 3.67).
- Useful for comparing using the benchmark 1.
5. **2/11 and 5/7**:
- 2/11 is approximately 0.18 (less than \( \frac{1}{2} \)).
- 5/7 is approximately 0.71 (greater than \( \frac{1}{2} \)).
- Useful to compare using the benchmark \( \frac{1}{2} \).
6. **2/7 and 3/10**:
- 2/7 is approximately 0.29 (less than \( \frac{1}{2} \)).
- 3/10 is 0.3 (less than \( \frac{1}{2} \)).
- Not useful for comparing since both are less than \( \frac{1}{2} \).
### Conclusion:
The fraction pairs that would be useful to compare using the benchmarks 0, \( \frac{1}{2} \), and 1 are:
1. **4/9 and 11/20** (useful for \( \frac{1}{2} \))
2. **6/10 and 4/9** (useful for \( \frac{1}{2} \))
3. **2/11 and 5/7** (useful for \( \frac{1}{2} \))
These pairs provide a clear comparison across the specified benchmarks. Please note that the pairs involving **49 and 11/20** and **5/2 and 11/3** could also be considered when strictly comparing to 1, but they are not as relevant for comparing against \( \frac{1}{2} \), which is the focus in this question. Therefore, the best three to choose from the set with relevance to all three benchmarks are:
1. **4/9 and 11/20**
2. **6/10 and 4/9**
3. **2/11 and 5/7**
### Pairs:
1. **49 and 11/20**:
- 49 is greater than 1.
- 11/20 is less than 1 but greater than \( \frac{1}{2} \) (because \( \frac{11}{20} = 0.55 \)).
- Useful to compare using the benchmark 1.
2. **4/9 and 11/20**:
- 4/9 is approximately 0.44 (less than \( \frac{1}{2} \)).
- 11/20 is 0.55 (greater than \( \frac{1}{2} \)).
- Useful to compare using the benchmark \( \frac{1}{2} \) and 1.
3. **6/10 and 4/9**:
- 6/10 simplifies to 0.6 (greater than \( \frac{1}{2} \)).
- 4/9 is approximately 0.44 (less than \( \frac{1}{2} \)).
- Useful to compare using the benchmark \( \frac{1}{2} \) and 1.
4. **5/2 and 11/3**:
- Both fractions are greater than 1 (5/2 = 2.5 and 11/3 ≈ 3.67).
- Useful for comparing using the benchmark 1.
5. **2/11 and 5/7**:
- 2/11 is approximately 0.18 (less than \( \frac{1}{2} \)).
- 5/7 is approximately 0.71 (greater than \( \frac{1}{2} \)).
- Useful to compare using the benchmark \( \frac{1}{2} \).
6. **2/7 and 3/10**:
- 2/7 is approximately 0.29 (less than \( \frac{1}{2} \)).
- 3/10 is 0.3 (less than \( \frac{1}{2} \)).
- Not useful for comparing since both are less than \( \frac{1}{2} \).
### Conclusion:
The fraction pairs that would be useful to compare using the benchmarks 0, \( \frac{1}{2} \), and 1 are:
1. **4/9 and 11/20** (useful for \( \frac{1}{2} \))
2. **6/10 and 4/9** (useful for \( \frac{1}{2} \))
3. **2/11 and 5/7** (useful for \( \frac{1}{2} \))
These pairs provide a clear comparison across the specified benchmarks. Please note that the pairs involving **49 and 11/20** and **5/2 and 11/3** could also be considered when strictly comparing to 1, but they are not as relevant for comparing against \( \frac{1}{2} \), which is the focus in this question. Therefore, the best three to choose from the set with relevance to all three benchmarks are:
1. **4/9 and 11/20**
2. **6/10 and 4/9**
3. **2/11 and 5/7**
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.