To solve this problem, let's go through the steps of adding the mixed numbers [tex]\(-1 \frac{1}{3}\)[/tex] and [tex]\(-4 \frac{2}{3}\)[/tex].
### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number to an improper fraction.
For [tex]\(-1 \frac{1}{3}\)[/tex]:
1. Separate the whole number part (-1) and the fractional part ([tex]\(\frac{1}{3}\)[/tex]).
2. Combine these parts: [tex]\[-1 \frac{1}{3} = -1 - \frac{1}{3}\][/tex]
[tex]\[-1 = -\frac{3}{3}\][/tex]
[tex]\[-1 \frac{1}{3} = -\frac{3}{3} - \frac{1}{3} = -\frac{4}{3}\][/tex]
So, [tex]\(-1 \frac{1}{3}\)[/tex] is equivalent to [tex]\(-\frac{4}{3}\)[/tex].
For [tex]\(-4 \frac{2}{3}\)[/tex]:
1. Separate the whole number part (-4) and the fractional part ([tex]\(\frac{2}{3}\)[/tex]).
2. Combine these parts: [tex]\[-4 \frac{2}{3} = -4 - \frac{2}{3}\][/tex]
[tex]\[-4 = -\frac{12}{3}\][/tex]
[tex]\[-4 \frac{2}{3} = -\frac{12}{3} - \frac{2}{3} = -\frac{14}{3}\][/tex]
So, [tex]\(-4 \frac{2}{3}\)[/tex] is equivalent to [tex]\(-\frac{14}{3}\)[/tex].
### Step 2: Add the Improper Fractions
Now, we need to add the two improper fractions:
[tex]\[
-\frac{4}{3} + \left(-\frac{14}{3}\right)
\][/tex]
Since the fractions have the same denominator (3), we can directly add the numerators:
[tex]\[
-\frac{4 + 14}{3} = -\frac{18}{3}
\][/tex]
### Step 3: Simplify the Result
Simplify [tex]\(-\frac{18}{3}\)[/tex]:
[tex]\[
-\frac{18}{3} = -6
\][/tex]
Thus, the result of adding [tex]\(-1 \frac{1}{3}\)[/tex] and [tex]\(-4 \frac{2}{3}\)[/tex] is [tex]\(-6\)[/tex].
So,
[tex]\[
-1 \frac{1}{3} + \left(-4 \frac{2}{3}\right) = -6
\][/tex]
