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)
2/11 and 5/7
2/7 and 3/10
4/9 and 11/20
5/2 and 1 1/3
6/10 and 4/9

Answer 1

To determine which fraction pairs would benefit from comparing to the benchmarks of 0, 1/2, and 1, we want to look for pairs of fractions that straddle these benchmarks or that are near them. Here are the fraction pairs:

1. **2/11 and 5/7**:
- 2/11 is much less than 1/2 (approximately 0.18).
- 5/7 is greater than 1/2 (approximately 0.71).
- This pair can be compared using the benchmarks.

2. **2/7 and 3/10**:
- 2/7 is approximately 0.29 (less than 1/2).
- 3/10 is 0.3 (also less than 1/2).
- This pair does not effectively use the benchmarks of 0 and 1/2.

3. **4/9 and 11/20**:
- 4/9 is approximately 0.44 (less than 1/2).
- 11/20 is 0.55 (greater than 1/2).
- This pair can be compared using the benchmarks.

4. **5/2 and 1 1/3**:
- 5/2 is 2.5 (greater than 1).
- 1 1/3 is approximately 1.33 (also greater than 1).
- This pair does not effectively use the 0, 1/2, and 1 benchmarks.

5. **6/10 and 4/9**:
- 6/10 is 0.6 (greater than 1/2).
- 4/9 is approximately 0.44 (less than 1/2).
- This pair can be compared using the benchmarks.

Based on this analysis, the three pairs that would be useful to compare using the benchmarks 0, 1/2, and 1 are:

- **2/11 and 5/7**
- **4/9 and 11/20**
- **6/10 and 4/9**