(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 .

Answer 1

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.

Answer 2

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 3

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.

Answer 4

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

Answer 5

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