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:
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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.
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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.
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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.
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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.
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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