Add the following rational numbers:
Question:

Add the following rational numbers:

(i) $\frac{-2}{5}$ and $\frac{4}{5}$

(ii) $\frac{-6}{11}$ and $\frac{-4}{11}$

(iii) $\frac{-11}{8}$ and $\frac{5}{8}$

(iv) $\frac{-7}{3}$ and $\frac{1}{3}$

(v) $\frac{5}{6}$ and $\frac{-1}{6}$

(vi) $\frac{-17}{15}$ and $\frac{-1}{15}$

Solution:

1. $\frac{-2}{5}+\frac{4}{5}=\frac{-2+4}{5}=\frac{2}{5}$

2. $\frac{-6}{11}+\frac{-4}{11}=\frac{-6+(-4)}{11}=\frac{-6-4}{11}=\frac{-10}{11}$

3. $\frac{-11}{8}+\frac{5}{8}=\frac{-11+5}{8}=\frac{-6}{8}=\frac{-3 \times 2}{4 \times 2}=\frac{-3}{4}$

4. $\frac{-7}{3}+\frac{1}{3}=\frac{-7+1}{3}=\frac{-6}{3}=\frac{-3 \times 2}{3}=-2$

5. $\frac{5}{6}+\frac{-1}{6}=\frac{5+(-1)}{6}=\frac{4}{6}=\frac{2 \times 2}{3 \times 2}=\frac{2}{3}$

6. $\frac{-17}{15}+\frac{-1}{15}=\frac{-17+(-1)}{15}=\frac{-17-1}{15}=\frac{-18}{15}=\frac{-6 \times 3}{5 \times 3}=\frac{-6}{5}$