Question

Use benchmarks:
Compare two fractions using _.
Order _ using benchmarks.

Answer 1

To compare two fractions using benchmarks, you can use commonly known reference fractions such as 0, 1/2, and 1. Here’s how you can do it step by step:

1. **Identify the fractions you want to compare.**
For example, let's say the fractions are \( \frac{3}{8} \) and \( \frac{5}{12} \).

2. **Convert the fractions to decimals or compare them to benchmark fractions.**
- \( \frac{3}{8} = 0.375 \) (compare to 1/2, which is 0.5)
- \( \frac{5}{12} \approx 0.4167 \) (also compare to 1/2)

3. **Use the benchmark of 1/2 to order the fractions.**
Since both \( \frac{3}{8} \) and \( \frac{5}{12} \) are less than 1/2, we know they are both less than 0.5.

4. **Compare their decimal values directly.**
\( 0.375 < 0.4167 \) tells us that \( \frac{3}{8} < \frac{5}{12} \).

5. **Order the fractions.**
Therefore, when ordering the two fractions, we have:
\( \frac{3}{8} < \frac{5}{12} \).

In summary, you can compare fractions using benchmark fractions like 1/2, and then order them based on their relative values.

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