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.

A. 2/11 and 5/7
B. 6/10 and 4/9
C. 4/9 and 11/20
D. 5/2 and 1 1/3
E. 2/7 and 3/10

Answer 1

To determine which fraction pairs would be useful to use the benchmarks 0, 1/2, and 1 to compare, we can analyze each pair to see if they contain fractions that fall around these benchmarks:

A. 2/11 and 5/7
- 2/11 is less than 1/2, and 5/7 is greater than 1/2. Useful to compare.

B. 6/10 and 4/9
- 6/10 is exactly 1/2, while 4/9 is slightly less than 1/2. Useful to compare.

C. 4/9 and 11/20
- 4/9 is slightly less than 1/2, and 11/20 is also slightly less than 1/2. Comparisons to the benchmark 1/2 may not be particularly useful.

D. 5/2 and 1 1/3
- 5/2 is greater than 1 and 1 1/3 is also greater than 1. Useful to compare.

E. 2/7 and 3/10
- 2/7 is less than 1/2 and 3/10 is also less than 1/2. Comparisons to 1/2 may not provide much insight.

Based on the analysis, the three pairs where benchmarks 0, 1/2, and 1 would be useful for comparison are:

- A. 2/11 and 5/7
- B. 6/10 and 4/9
- D. 5/2 and 1 1/3