Question

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

Answer 1

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**.