Add the following rational numbers:
`{:((i) (-2)/(5) and (4)/(5),(ii) (-6)/(11) and (-4)/(11) , (iii) (-11)/(8) and (5)/(8)), ((iv) (-7)/(3) and (1)/(3),(v) (5)/(6) and (-1)/(6),(vi) (-17)/(15) and (-1)/(15)):}`

Answer

Let's solve the given question step by step.

### Question:
Add the following rational numbers:
1. \(-\frac{2}{5}\) and \(\frac{4}{5}\)
2. \(-\frac{6}{11}\) and \(-\frac{4}{11}\)
3. \(-\frac{11}{8}\) and \(\frac{5}{8}\)
4. \(-\frac{7}{3}\) and \(\frac{1}{3}\)
5. \(\frac{5}{6}\) and \(-\frac{1}{6}\)
6. \(-\frac{17}{15}\) and \(-\frac{1}{15}\)

### Step-by-Step Solutions:

#### (i) Adding \(-\frac{2}{5}\) and \(\frac{4}{5}\):
1. **Identify the denominators**: Both denominators are 5.
2. **Combine the numerators**:
\[ -2 + 4 = 2 \]
3. **Write the result**:
\[ \frac{2}{5} \]

#### (ii) Adding \(-\frac{6}{11}\) and \(-\frac{4}{11}\):
1. **Identify the denominators**: Both denominators are 11.
2. **Combine the numerators**:
\[ -6 + (-4) = -10 \]
3. **Write the result**:
\[ -\frac{10}{11} \]

#### (iii) Adding \(-\frac{11}{8}\) and \(\frac{5}{8}\):
1. **Identify the denominators**: Both denominators are 8.
2. **Combine the numerators**:
\[ -11 + 5 = -6 \]
3. **Write the result**:
\[ -\frac{6}{8} = -\frac{3}{4} \quad (\text{after simplification}) \]

#### (iv) Adding \(-\frac{7}{3}\) and \(\frac{1}{3}\):
1. **Identify the denominators**: Both denominators are 3.
2. **Combine the numerators**:
\[ -7 + 1 = -6 \]
3. **Write the result**:
\[ -\frac{6}{3} = -2 \quad (\text{after simplification}) \]

#### (v) Adding \(\frac{5}{6}\) and \(-\frac{1}{6}\):
1. **Identify the denominators**: Both denominators are 6.
2. **Combine the numerators**:
\[ 5 + (-1) = 4 \]
3. **Write the result**:
\[ \frac{4}{6} = \frac{2}{3} \quad (\text{after simplification}) \]

#### (vi) Adding \(-\frac{17}{15}\) and \(-\frac{1}{15}\):
1. **Identify the denominators**: Both denominators are 15.
2. **Combine the numerators**:
\[ -17 + (-1) = -18 \]
3. **Write the result**:
\[ -\frac{18}{15} = -\frac{6}{5} \quad (\text{after simplification}) \]

### Final Results:
1. \(\frac{2}{5}\)
2. \(-\frac{10}{11}\)
3. \(-\frac{3}{4}\)
4. \(-2\)
5. \(\frac{2}{3}\)
6. \(-\frac{6}{5}\)