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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)
Responses

6/10 and 4/9
6/10 and 4/9

2/11 and 5/7
2/11 and 5/7

2/7 and 3/10
2/7 and 3/10

4/9 and 11/20
4/9 and 11/20

5/2 and 1/13

1 answer

To determine which fraction pairs are useful to compare using the benchmarks of 0, 1/2, and 1, we look for pairs of fractions that can be easily understood in relation to these benchmarks. Here are the comparisons for each pair:

  1. 6/10 and 4/9:

    • 6/10 is equivalent to 0.6 (greater than 1/2).
    • 4/9 is approximately 0.444 (less than 1/2).
    • Useful to compare because one is above 1/2, one is below.

  2. 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).
    • Useful to compare because one is below 1/2, one is above.

  3. 2/7 and 3/10:

    • 2/7 is approximately 0.286 (less than 1/2).
    • 3/10 is 0.3 (less than 1/2).
    • Not useful for this benchmark because both are below 1/2.

  4. 4/9 and 11/20:

    • 4/9 is approximately 0.444 (less than 1/2).
    • 11/20 is 0.55 (greater than 1/2).
    • Useful to compare because one is below 1/2, one is above.

  5. 5/2 and 1/13:

    • 5/2 is 2.5 (greater than 1).
    • 1/13 is approximately 0.077 (less than 1/2).
    • Useful to compare because one is above 1, one is below.

Conclusion

The three pairs that would be useful to compare using the benchmarks of 0, 1/2, and 1 are:

  1. 6/10 and 4/9
  2. 2/11 and 5/7
  3. 4/9 and 11/20
  4. 5/2 and 1/13

So the correct answer is:

  • 6/10 and 4/9
  • 2/11 and 5/7
  • 4/9 and 11/20 OR 5/2 and 1/13

If you need to select three pairs, then stick with the first three listed here.