To solve the problem of adding \( \frac{4}{11} \) and \( -\frac{8}{11} \), we can follow these steps:
### Step 1: Write the expression
We start by writing the expression for the addition of the two rational numbers:
\[
\frac{4}{11} + \left(-\frac{8}{11}\right)
\]
### Step 2: Identify the common denominator
Since both fractions have the same denominator (11), we can directly add the numerators. The common denominator is:
\[
11
\]
### Step 3: Add the numerators
Now we will add the numerators:
\[
4 + (-8) = 4 - 8
\]
### Step 4: Perform the subtraction
Now we perform the subtraction:
\[
4 - 8 = -4
\]
### Step 5: Write the result as a fraction
Now we can write the result as a fraction with the common denominator:
\[
\frac{-4}{11}
\]
### Final Answer
Thus, the sum of \( \frac{4}{11} \) and \( -\frac{8}{11} \) is:
\[
\frac{-4}{11}
\]
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