Order from least to greatest: 11

6
, 2
3
, 11
2
, 5
6
.

A number line contains the numbers 0, 1, 2. There are 6 equal spaces between each number.
Which list shows the fractions ordered from least to greatest?
Two-thirds, StartFraction 5 Over 6 EndFraction, 1 and one-sixth, 1 and one-half
StartFraction 5 Over 6 EndFraction, two-thirds, 1 and one-sixth, 1 and one-half
1 and one-sixth, two-thirds, 1 and one-half, StartFraction 5 Over 6 EndFraction
1 and one-sixth, 1 and one-half, two-thirds, StartFraction 5 Over 6 EndFraction

1 answer

First, let's convert the mixed numbers and fractions you provided into improper fractions or decimals to facilitate ordering them from least to greatest.

  1. 11 is \(11\).

  2. 6 is \(6\).

  3. 2 and 3 can be expressed as: \[ 2\frac{3}{6} = \frac{12 + 3}{6} = \frac{15}{6} \] Decimal: \( \frac{15}{6} = 2.5 \)

  4. 11 and 2 can be expressed similarly: \[ 11\frac{2}{6} = \frac{66 + 2}{6} = \frac{68}{6} \] Decimal: \( \frac{68}{6} \approx 11.33 \)

  5. 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:

  1. Two-thirds as a decimal is \( \frac{2}{3} \approx 0.67\).
  2. StartFraction 5 Over 6 EndFraction or \( \frac{5}{6} \approx 0.83\).
  3. 1 and one-sixth is \( 1\frac{1}{6} = \frac{6+1}{6} = \frac{7}{6} \approx 1.17\).
  4. 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.