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Add the following rational numbers: {:...

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)):}`

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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. \(-\frac{6}{5}\)
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