Question

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

6/10 and 4/9
6/10 and 4/9

2/11 and 5/7
2/11 and 5/7

2/7 and 3/10
2/7 and 3/10

4/9 and 11/20
4/9 and 11/20

5/2 and 1/13

Answer 1

To determine which fraction pairs are useful to compare using the benchmarks of 0, 1/2, and 1, we look for pairs of fractions that can be easily understood in relation to these benchmarks. Here are the comparisons for each pair:

1. **6/10 and 4/9**:
- 6/10 is equivalent to 0.6 (greater than 1/2).
- 4/9 is approximately 0.444 (less than 1/2).
- Useful to compare because one is above 1/2, one is below.

2. **2/11 and 5/7**:
- 2/11 is approximately 0.182 (less than 1/2).
- 5/7 is approximately 0.714 (greater than 1/2).
- Useful to compare because one is below 1/2, one is above.

3. **2/7 and 3/10**:
- 2/7 is approximately 0.286 (less than 1/2).
- 3/10 is 0.3 (less than 1/2).
- Not useful for this benchmark because both are below 1/2.

4. **4/9 and 11/20**:
- 4/9 is approximately 0.444 (less than 1/2).
- 11/20 is 0.55 (greater than 1/2).
- Useful to compare because one is below 1/2, one is above.

5. **5/2 and 1/13**:
- 5/2 is 2.5 (greater than 1).
- 1/13 is approximately 0.077 (less than 1/2).
- Useful to compare because one is above 1, one is below.

### Conclusion
The three pairs that would be useful to compare using the benchmarks of 0, 1/2, and 1 are:

1. **6/10 and 4/9**
2. **2/11 and 5/7**
3. **4/9 and 11/20**
4. **5/2 and 1/13**

So the correct answer is:
- 6/10 and 4/9
- 2/11 and 5/7
- 4/9 and 11/20 OR 5/2 and 1/13

If you need to select three pairs, then stick with the first three listed here.