To determine which fraction pairs would be useful to compare using benchmarks like 0, 1/2, and 1, we generally look for fractions that span a range that includes these benchmarks. Here are the comparisons for the given pairs:
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2/7 and 3/10:
- 2/7 is approximately 0.285 (less than 1/2).
- 3/10 is exactly 0.3 (less than 1/2).
- Both fractions are less than 1/2, so this pair could be useful for comparing with 0 and 1/2.
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4/9 and 11/20:
- 4/9 is approximately 0.444 (less than 1/2).
- 11/20 is 0.55 (greater than 1/2).
- This pair crosses the 1/2 benchmark, so it's useful for comparison.
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6/10 and 4/9:
- 6/10 (or 3/5) is 0.6 (greater than 1/2).
- 4/9 is approximately 0.444 (less than 1/2).
- This pair also crosses the 1/2 benchmark, making it useful.
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5/2 and 1 1/3:
- 5/2 is 2.5 (greater than 1).
- 1 1/3 is approximately 1.333 (greater than 1).
- Both are greater than 1, so this pair does not use the benchmarks 0 or 1/2 effectively.
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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).
- This pair crosses the 1/2 benchmark, so it's useful.
Based on this analysis, the three pairs that are useful to compare using the benchmarks 0, 1/2, and 1 are:
- 2/7 and 3/10
- 4/9 and 11/20
- 2/11 and 5/7