First, let's convert the mixed numbers and fractions you provided into improper fractions or decimals to facilitate ordering them from least to greatest.
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11 is \(11\).
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6 is \(6\).
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2 and 3 can be expressed as: \[ 2\frac{3}{6} = \frac{12 + 3}{6} = \frac{15}{6} \] Decimal: \( \frac{15}{6} = 2.5 \)
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11 and 2 can be expressed similarly: \[ 11\frac{2}{6} = \frac{66 + 2}{6} = \frac{68}{6} \] Decimal: \( \frac{68}{6} \approx 11.33 \)
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5 and 6 can be expressed as: \[ 5\frac{6}{6} = \frac{30 + 6}{6} = \frac{36}{6} \] Decimal: \( \frac{36}{6} = 6 \)
So, ordering those, we have:
- 6 (which is 6)
- 2\(\frac{3}{6}\) (which is 2.5)
- 11\(\frac{2}{6}\) (which is approximately 11.33)
- 11 (which is 11)
The ordered numbers from least to greatest are:
- 2\(\frac{3}{6}\) (2.5)
- 6
- 11
- 11\(\frac{2}{6}\) (approximately 11.33)
Now, let’s analyze the fractions and mixed numbers listed:
- Two-thirds as a decimal is \( \frac{2}{3} \approx 0.67\).
- StartFraction 5 Over 6 EndFraction or \( \frac{5}{6} \approx 0.83\).
- 1 and one-sixth is \( 1\frac{1}{6} = \frac{6+1}{6} = \frac{7}{6} \approx 1.17\).
- 1 and one-half is \( 1\frac{1}{2} = \frac{3}{2} = 1.5\).
Now, let's order these from least to greatest utilizing decimals:
- Two-thirds: \( \approx 0.67\)
- StartFraction 5 Over 6: \( \approx 0.83\)
- 1 and one-sixth: \( \approx 1.17\)
- 1 and one-half: \( \approx 1.5\)
Thus, the ordered list from least to greatest is:
- Two-thirds
- StartFraction 5 Over 6 EndFraction
- 1 and one-sixth
- 1 and one-half
The only option that matches this order is: Two-thirds, StartFraction 5 Over 6 EndFraction, 1 and one-sixth, 1 and one-half.