To simplify the expression [tex]\(-4 \frac{3}{4} - 8 \frac{4}{5}\)[/tex], we will break it down into smaller steps.
### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert [tex]\(-4 \frac{3}{4}\)[/tex] to an improper fraction:
- [tex]\(-4 \frac{3}{4}\)[/tex] can be rewritten as:
[tex]\[
-4 - \frac{3}{4}
\][/tex]
- Convert [tex]\(-4\)[/tex] to a fraction with a common denominator:
[tex]\[
-4 = - \frac{16}{4}
\][/tex]
- Combine with [tex]\(-\frac{3}{4}\)[/tex]:
[tex]\[
-4 - \frac{3}{4} = - \frac{16}{4} - \frac{3}{4} = - \frac{19}{4}
\][/tex]
2. Convert [tex]\(-8 \frac{4}{5}\)[/tex] to an improper fraction:
- [tex]\(-8 \frac{4}{5}\)[/tex] can be rewritten as:
[tex]\[
-8 - \frac{4}{5}
\][/tex]
- Convert [tex]\(-8\)[/tex] to a fraction with a common denominator:
[tex]\[
-8 = - \frac{40}{5}
\][/tex]
- Combine with [tex]\(-\frac{4}{5}\)[/tex]:
[tex]\[
-8 - \frac{4}{5} = - \frac{40}{5} - \frac{4}{5} = - \frac{44}{5}
\][/tex]
### Step 2: Add the Improper Fractions
To add the fractions [tex]\(- \frac{19}{4}\)[/tex] and [tex]\(- \frac{44}{5}\)[/tex], we need a common denominator. The least common multiple of [tex]\(4\)[/tex] and [tex]\(5\)[/tex] is [tex]\(20\)[/tex].
1. Convert [tex]\(-\frac{19}{4}\)[/tex] to a denominator of 20:
[tex]\[
- \frac{19}{4} = - \frac{19 \times 5}{4 \times 5} = - \frac{95}{20}
\][/tex]
2. Convert [tex]\(-\frac{44}{5}\)[/tex] to a denominator of 20:
[tex]\[
- \frac{44}{5} = - \frac{44 \times 4}{5 \times 4} = - \frac{176}{20}
\][/tex]
3. Add the fractions with the common denominator:
[tex]\[
- \frac{95}{20} + - \frac{176}{20} = - \frac{95 + 176}{20} = - \frac{271}{20}
\][/tex]
### Step 3: Simplify the Result
The resulting fraction is [tex]\(- \frac{271}{20}\)[/tex], which is already in its simplest form.
The final simplified result of [tex]\( -4 \frac{3}{4} - 8 \frac{4}{5} \)[/tex] is:
[tex]\[
-\frac{271}{20}
\][/tex]
Thus, the correct choice is:
[tex]\(\frac{271}{20}\)[/tex]
