To determine which fraction pairs would be useful to compare using the benchmarks 0, 1/2, and 1, we want to look for pairs that are distributed across this benchmark scale. Here's the analysis for each option:
A. 6/10 and 4/9
- 6/10 = 0.6 (greater than 1/2)
- 4/9 ≈ 0.444 (less than 1/2)
- This pair is useful for benchmarks.
B. 2/11 and 5/7
- 2/11 ≈ 0.182 (less than 1/2)
- 5/7 ≈ 0.714 (greater than 1/2)
- This pair is useful for benchmarks.
C. 2/7 and 3/10
- 2/7 ≈ 0.286 (less than 1/2)
- 3/10 = 0.3 (less than 1/2)
- This pair is not useful since both are less than 1/2.
D. 5/2 and 1 1/3 (which is 4/3)
- 5/2 = 2.5 (greater than 1)
- 4/3 ≈ 1.333 (greater than 1)
- This pair is not useful since both are greater than 1.
E. 4/9 and 11/20
- 4/9 ≈ 0.444 (less than 1/2)
- 11/20 = 0.55 (greater than 1/2)
- This pair is useful for benchmarks.
In summary, the pairs that are useful to compare using the benchmarks 0, 1/2, and 1 are:
- A. 6/10 and 4/9
- B. 2/11 and 5/7
- E. 4/9 and 11/20
1 answer