Simplify the following.
`(1)/(3) + ((2)/(5) + ((-11)/(15)))`

Answer

To simplify the expression \(\frac{1}{3} + \left(\frac{2}{5} + \left(-\frac{11}{15}\right)\right)\), we will follow these steps:

### Step 1: Rewrite the expression
We can rewrite the expression as:
\[ \frac{1}{3} + \frac{2}{5} - \frac{11}{15} \]

### Step 2: Find a common denominator
The denominators we have are 3, 5, and 15. The least common multiple (LCM) of these numbers is 15. We will convert each fraction to have a denominator of 15.

### Step 3: Convert \(\frac{1}{3}\) to a denominator of 15
To convert \(\frac{1}{3}\) to a denominator of 15, we multiply the numerator and denominator by 5:
\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \]

### Step 4: Convert \(\frac{2}{5}\) to a denominator of 15
To convert \(\frac{2}{5}\) to a denominator of 15, we multiply the numerator and denominator by 3:
\[ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \]

### Step 5: Rewrite the expression with the new fractions
Now we can rewrite the entire expression using the common denominator:
\[ \frac{5}{15} + \frac{6}{15} - \frac{11}{15} \]

### Step 6: Combine the fractions
Now that all fractions have the same denominator, we can combine them:
\[ \frac{5 + 6 - 11}{15} \]

### Step 7: Simplify the numerator
Calculating the numerator:
\[ 5 + 6 = 11 \]
Now substituting back:
\[ \frac{11 - 11}{15} = \frac{0}{15} \]

### Step 8: Final result
Since the numerator is 0, the final result is:
\[ 0 \]