For which fraction pairs would it be useful to use the benchmarks 0, 12, and 1

Question

to compare? Check the THREE that apply.(3 points)
Responses

49 and 1120
49 and 1120

52 and 113
52 and 113

610 and 49
610 and 49

27 and 310
27 and 310

211 and 57

Answer 1

To determine which pairs of fractions would be useful to compare using the benchmarks 0, 1/2, and 1, we should convert each pair of fractions into decimal form or simply assess their relative size and proximity to the benchmarks.

Let's analyze the given pairs:

1. 49 and 1120:

   • \( \frac{49}{1120} = 0.04375 \) (less than 1/2, close to 0)

2. 52 and 113:

   • \( \frac{52}{113} \approx 0.4602 \) (less than 1/2, close to 0)

3. 610 and 49:

   • \( \frac{610}{49} \approx 12.4489 \) (greater than 1)

4. 27 and 310:

   • \( \frac{27}{310} \approx 0.0871 \) (less than 1/2, close to 0)

5. 211 and 57:

   • \( \frac{211}{57} \approx 3.7018 \) (greater than 1)

Useful Benchmarks:

• To use benchmarks of 0, 1/2, and 1, it would be helpful to compare fractions that are close to these values:
  • Fractions that are less than 1/2 (like the first, second, and fourth pairs).
  • Fractions greater than 1/2 but less than 1 will also be beneficial to determine if they are exactly in the middle.
  • Fractions greater than 1 can also be compared against 1 to understand their relative size.

Selected Pairs:

The three pairs that would be useful to compare using the benchmarks would be:

1. 49 and 1120
2. 52 and 113
3. 27 and 310

The pair 610 and 49 and 211 and 57 do not fit well with just 0, 1/2, and 1 benchmarks as they are significantly above 1.