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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

2/11 and 5/7

2/7 and 3/10

4/9 and 11/20

5/2 and 1 1/13

1 answer

To determine which fraction pairs would benefit from using the benchmarks 0, 1/2, and 1 for comparison, we can look at the values of the fractions involved to see where they lie relative to these benchmarks.

  1. 6/10 and 4/9:

    • 6/10 = 0.6 (greater than 1/2)
    • 4/9 ≈ 0.444 (less than 1/2)
    • Useful for comparison

  2. 2/11 and 5/7:

    • 2/11 ≈ 0.182 (less than 1/2)
    • 5/7 ≈ 0.714 (greater than 1/2)
    • Useful for comparison

  3. 2/7 and 3/10:

    • 2/7 ≈ 0.286 (less than 1/2)
    • 3/10 = 0.3 (less than 1/2)
    • Not useful for comparison since both are less than 1/2

  4. 4/9 and 11/20:

    • 4/9 ≈ 0.444 (less than 1/2)
    • 11/20 = 0.55 (greater than 1/2)
    • Useful for comparison

  5. 5/2 and 1 1/13:

    • 5/2 = 2.5 (greater than 1)
    • 1 1/13 ≈ 1.077 (greater than 1)
    • Not useful for comparison since both are greater than 1

Based on this analysis, the three pairs that would be useful to compare using the benchmarks 0, 1/2, and 1 are:

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