Question

Add the following rational numbers:

(i) $\frac{12}{7}\mathrm{and}\frac{3}{7}$
(ii) $\frac{-2}{5}\mathrm{and}\frac{1}{5}$
(iii) $\frac{3}{-8}\mathrm{and}\frac{1}{8}$
(iv) $\frac{-5}{11}\mathrm{and}\frac{7}{-11}$
(v) $\frac{9}{-13}\mathrm{and}\frac{-11}{-13}$
(vi) $\frac{-2}{9}\mathrm{and}\frac{-5}{9}$
(vii) $\frac{-17}{9}\mathrm{and}\frac{-11}{9}$
(viii) $\frac{-3}{7}\mathrm{and}\frac{5}{-7}$

Answer 1

(i)
$\frac{12}{7}+\frac{3}{7}=\frac{12+3}{7}=\frac{15}{7}$

(ii)
$\frac{-2}{5}+\frac{1}{5}=\frac{-2+1}{5}=\frac{-1}{5}$

(iii)

$\frac{3}{-8}\times \frac{-1}{-1}=\frac{-3}{8}$

$\frac{-3}{8}+\frac{1}{8}=\frac{-3+1}{8}=\frac{-2}{8}$

(iv)

$$\begin{gathered} \frac{7}{-11}\times \frac{-1}{-1}=\frac{-7}{11} \\ \frac{-5}{11}+\frac{-7}{11}=\frac{-5+(-7)}{11}=\frac{-5-7}{11}=\frac{-12}{11} \end{gathered}$$


(v)

$\frac{-11}{-13}\times \frac{-1}{-1}=\frac{11}{13}$

=$\frac{-9}{13}+\frac{11}{13}=\frac{-9+11}{13}=\frac{2}{13}$

(vi)

$\frac{-2}{9}+\frac{-5}{9}=\frac{-2-5}{9}=\frac{-7}{9}$

(vii)

$\frac{(-17)}{9}+\frac{(-11)}{9}=\frac{-17-11}{9}=\frac{-28}{9}$

(viii)
$\frac{5}{-7}\times \frac{-1}{-1}=\frac{-5}{7}$


$\frac{-3}{7}+\frac{(-5)}{7}=\frac{-3-5}{7}=\frac{-8}{7}$