https://file.aiquickdraw.com/mathbot/file/17294531964413nqaaadn.jpg

The expression provided is:

\[
-4 \frac{3}{5} - 5 \frac{9}{10}
\]

First, let's convert these mixed numbers into improper fractions:

1. For \(-4 \frac{3}{5}\):
   \[
   -4 \frac{3}{5} = -\left(4 \times \frac{5}{5} + \frac{3}{5}\right) = -\frac{20}{5} - \frac{3}{5} = -\frac{23}{5}
   \]

2. For \(5 \frac{9}{10}\):
   \[
   5 \frac{9}{10} = 5 \times \frac{10}{10} + \frac{9}{10} = \frac{50}{10} + \frac{9}{10} = \frac{59}{10}
   \]

Now, the expression becomes:

\[
-\frac{23}{5} - \frac{59}{10}
\]

To subtract these fractions, we need a common denominator. The least common denominator (LCD) of 5 and 10 is 10. So, rewrite \(-\frac{23}{5}\) with a denominator of 10:

\[
-\frac{23}{5} = -\frac{46}{10}
\]

Now, the expression is:

\[
-\frac{46}{10} - \frac{59}{10}
\]

Since the denominators are the same, we can combine the numerators:

\[
-\frac{46}{10} - \frac{59}{10} = \frac{-46 - 59}{10} = \frac{-105}{10} = -10.5
\]

Thus, the final result is:

\[
-10.5
\]

Would you like further details on any part of the solution?

Here are 5 related questions for deeper understanding:
1. How do you convert a mixed number into an improper fraction?
2. Why is finding a common denominator necessary when subtracting fractions?
3. Can you explain how to simplify fractions after combining them?
4. What are the steps to convert a negative improper fraction into a decimal?
5. How would you solve a similar problem involving addition instead of subtraction?

**Tip:** When subtracting mixed numbers, always convert them to improper fractions first to avoid confusion with signs.

This step-by-step guide explains how to subtract mixed numbers such as -4 3/5 and 5 9/10 by converting them into improper fractions and finding a common denominator. Learn essential concepts like fraction operations and decimal conversion, suitable for Grades 5-7.

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