To order the expressions from least to greatest, let's first convert them into improper fractions so we can easily compare them.
1. **-4 3/7** = -4 + (3/7) = -\(\frac{28}{7}\) - \(\frac{3}{7}\) = -\(\frac{31}{7}\)
2. **-4 6/7** = -4 + (6/7) = -\(\frac{28}{7}\) - \(\frac{6}{7}\) = -\(\frac{34}{7}\)
3. **-5 3/7** = -5 + (3/7) = -\(\frac{35}{7}\) - \(\frac{3}{7}\) = -\(\frac{38}{7}\)
4. **4 2/7** = 4 + (2/7) = \(\frac{28}{7}\) + \(\frac{2}{7}\) = \(\frac{30}{7}\)
5. **5 1/5** = 5 + (1/5) = \(\frac{25}{5}\) + \(\frac{1}{5}\) = \(\frac{26}{5}\) = \(\frac{78}{15}\) (this value is approximately 5.2)
Now, let's compare the values:
- **-5 3/7 (least)**: -\(\frac{38}{7}\) (approximately -5.43)
- **-4 6/7**: -\(\frac{34}{7}\) (approximately -4.86)
- **-4 3/7**: -\(\frac{31}{7}\) (approximately -4.43)
- **4 2/7**: \(\frac{30}{7}\) (approximately 4.29)
- **5 1/5 (greatest)**: \(\frac{26}{5}\) (approximately 5.2)
Now, let's arrange them from least to greatest:
1. **-5 3/7**
2. **-4 6/7**
3. **-4 3/7**
4. **4 2/7**
5. **5 1/5**
So the correct order from least to greatest is:
-5 3/7
-4 6/7
-4 3/7
4 2/7
5 1/5