To locate the fractions \( \frac{1}{6} \), \( \frac{1}{3} \), \( \frac{2}{3} \), and \( \frac{5}{6} \) on a number line from 0 to 1 in increments of \( \frac{1}{6} \), we can convert all fractions to have a common denominator, which in this case will be 6.
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Convert each fraction:
- \( \frac{1}{6} \) is already in the correct form.
- \( \frac{1}{3} = \frac{2}{6} \) (multiply both numerator and denominator by 2).
- \( \frac{2}{3} = \frac{4}{6} \) (multiply both numerator and denominator by 2).
- \( \frac{5}{6} \) is already in the correct form.
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Locate on the number line:
- \( 0 \)
- \( \frac{1}{6} \)
- \( \frac{2}{6} \) (which is \( \frac{1}{3} \))
- \( \frac{3}{6} \) (which is \( \frac{1}{2} \))
- \( \frac{4}{6} \) (which is \( \frac{2}{3} \))
- \( \frac{5}{6} \)
- \( 1 \)
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Comparison of the fractions: On the number line, the fractions, in order from smallest to largest, are:
- \( \frac{1}{6} \)
- \( \frac{1}{3} \)
- \( \frac{2}{3} \)
- \( \frac{5}{6} \)
Therefore, the greatest fraction among those listed is \( \frac{5}{6} \).