Bot GPT 4-o mini To order the fractions \( \frac{3}{6} \), \( \frac{1}{6} \), \( \frac{5}{6} \), and \( \frac{2}{6} \) from smallest to largest, we can compare their values directly, or we can simplify and convert them if needed.
First, let's simplify the fractions where applicable:
- \( \frac{3}{6} = \frac{1}{2} \)
- \( \frac{1}{6} \) remains the same.
- \( \frac{5}{6} \) remains the same.
- \( \frac{2}{6} = \frac{1}{3} \)
Now, we can write the simplified fractions:
- \( \frac{1}{6} \)
- \( \frac{1}{3} \)
- \( \frac{1}{2} \)
- \( \frac{5}{6} \)
Next, let's convert these to a decimal form for easier comparison:
- \( \frac{1}{6} \approx 0.1667 \)
- \( \frac{1}{3} \approx 0.3333 \)
- \( \frac{1}{2} = 0.5 \)
- \( \frac{5}{6} \approx 0.8333 \)
Now, we can order the fractions based on their decimal values:
- \( \frac{1}{6} \) (approx. 0.1667)
- \( \frac{1}{3} \) (approx. 0.3333)
- \( \frac{1}{2} \) (0.5)
- \( \frac{5}{6} \) (approx. 0.8333)
Thus, the order of the fractions from smallest to largest is: \[ \frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{5}{6} \] (or \( \frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{5}{6} \) using the simplified forms).
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