To determine which fraction pairs would be useful to use the benchmarks 0, 1/2, and 1 for comparison, we need to identify fraction pairs that straddle the benchmark values or are clearly on different sides of them.
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6/10 and 4/9:
- 6/10 is equivalent to 3/5, which is greater than 1/2.
- 4/9 is less than 1/2.
- These fractions straddle 1/2, so they are useful for comparison.
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2/11 and 5/7:
- 2/11 is less than 1/2.
- 5/7 is greater than 1/2 but less than 1.
- These fractions straddle 1/2, so they are useful for comparison.
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2/7 and 3/10:
- Both 2/7 and 3/10 are less than 1/2.
- They do not straddle any of the benchmark values, so they are not useful for comparison.
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4/9 and 11/20:
- 4/9 is less than 1/2.
- 11/20 is also less than 1/2.
- These fractions do not straddle any of the benchmark values, so they are not useful for comparison.
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5/2 and 1 1/13:
- 5/2 is greater than 1 and 1 1/13 is also greater than 1 but less than 2.
- They do not straddle any of the benchmark values; both are above 1, so they are not useful for comparison.
The three pairs that would be useful to use the benchmarks 0, 1/2, and 1 are:
- 6/10 and 4/9
- 2/11 and 5/7
You only need to identify three pairs, but we only found two pairs that work in this instance. The third response, based on the list provided, does not seem applicable as none of the other pairs straddle the benchmarks significantly.
Thus, the two correct pairs are:
- 6/10 and 4/9
- 2/11 and 5/7
1 answer