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

2/7 and 3/10

4/9 and 11/20

6/10 and 4/9

5/2 and 1 1/3

2/11 and 5/7

1 answer

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:

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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:

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