Find the sum:
`(-3)/(-11) + (5)/(9)`

Answer

To find the sum of the rational numbers \(-\frac{3}{-11} + \frac{5}{9}\), we can follow these steps:

### Step 1: Simplify the first term
The first term is \(-\frac{3}{-11}\). Since both the numerator and denominator are negative, we can simplify it:
\[ -\frac{3}{-11} = \frac{3}{11} \]

### Step 2: Write the expression with the simplified term
Now we can rewrite the expression:
\[ \frac{3}{11} + \frac{5}{9} \]

### Step 3: Find the least common denominator (LCD)
To add the fractions, we need a common denominator. The denominators are 11 and 9. The least common multiple (LCM) of 11 and 9 is:
\[ 11 \times 9 = 99 \]
So, the common denominator is 99.

### Step 4: Convert each fraction to have the common denominator
Now, we will convert both fractions to have a denominator of 99.

For \(\frac{3}{11}\):
\[ \frac{3}{11} \times \frac{9}{9} = \frac{27}{99} \]

For \(\frac{5}{9}\):
\[ \frac{5}{9} \times \frac{11}{11} = \frac{55}{99} \]

### Step 5: Add the fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{27}{99} + \frac{55}{99} = \frac{27 + 55}{99} = \frac{82}{99} \]

### Final Answer
Thus, the sum of \(-\frac{3}{-11} + \frac{5}{9}\) is:
\[ \frac{82}{99} \]

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