Question

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

Answer 1

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**