Question

Add the
following pairs of rational numbers

(i) $$\dfrac{3}{11},
\dfrac{-5}{11}$$

(ii) $$\dfrac{4}{9},
\dfrac{5}{-9}$$

(iii) $$\dfrac{5}{-7},
\dfrac{-2}{-7}$$

(iv) $$\dfrac{-2}{5},
\dfrac{3}{4}$$

Answer 1

$$(i) \dfrac{3}{11},
\dfrac{-5}{11}$$

$$=\dfrac{3}{11}+\dfrac{-5}{11}=\dfrac{3-5}{11}=\dfrac{-2}{11}$$

(ii) $$\dfrac{4}{9},
\dfrac{5}{-9}$$

$$ =\dfrac{4}{9}+\dfrac{5}{-9}=\dfrac{4}{9}+\dfrac{5
\times(-1)}{-9 \times(-1)} $$

$$=\dfrac{4}{9}-\dfrac{5}{9}=\dfrac{4-5}{9}=\dfrac{-1}{9} $$

(iii) $$\dfrac{5}{-7},
\dfrac{-2}{-7}$$

$$=\dfrac{5}{-7}+\dfrac{-2}{-7}=\dfrac{5
\times(-1)}{-7 \times(-1)}+\dfrac{2}{7}$$

$$=\dfrac{-5}{7}+\dfrac{2}{7}=\dfrac{-5+2}{7}=\dfrac{-3}{7}$$

$$(i v) \dfrac{-2}{5},
\dfrac{3}{4}$$

$$ =\dfrac{-2}{5}+\dfrac{3}{4}
$$

$$=\dfrac{(-2
\times 4)+(3 \times 5)}{20} $$

$$=\dfrac{-8+15}{20}
\quad(\mathrm{LCM} \text { of } 5,4=20) $$

$$=\dfrac{7}{20} $$