Let's go step by step to arrange the given numbers in order from least to greatest.

The numbers to compare are:

$\frac{1}{4}, \, -1, \, \sqrt{5}, \, -\frac{9}{2}, \, 4.4$

1. Convert all values to decimals:

   • $\frac{1}{4} = 0.25$
   • $-1$ remains $-1$
   • $\sqrt{5} \approx 2.236$
   • $-\frac{9}{2} = -4.5$
   • $4.4$ remains $4.4$

2. List the decimal values:

   • $-4.5$, $-1$, $0.25$, $2.236$, $4.4$

3. Order from least to greatest: $-4.5, \, -1, \, 0.25, \, 2.236, \, 4.4$

Now, we match this ordering with the multiple-choice options:

• Option A: $-1, \, -\frac{9}{2}, \, \frac{1}{4}, \, 4.4, \, \sqrt{5}$
• Option B: $\frac{1}{4}, \, -1, \, 4.4, \, \sqrt{5}, \, -\frac{9}{2}$
• Option C: $-\frac{9}{2}, \, -1, \, \frac{1}{4}, \, 4.4, \, \sqrt{5}$
• Option D: $-\frac{9}{2}, \, -1, \, \frac{1}{4}, \, \sqrt{5}, \, 4.4$

The correct option is D, as it matches the correct order: $-\frac{9}{2} \, (-4.5), \, -1, \, \frac{1}{4} \, (0.25), \, \sqrt{5} \, (2.236), \, 4.4$

Would you like more details, or do you have any further questions?

Here are 5 related questions:

1. How can you compare square roots with fractions quickly?
2. What are common mistakes in comparing negative and positive decimals?
3. How do you calculate square roots of non-perfect squares?
4. Why is converting to decimals useful for ordering?
5. How does the order of operations affect sorting of mixed numbers?

Tip: Converting all terms to a common form, like decimals, makes comparison easier.