Add the following rational numbers:
(i) $ \frac{-5}{7} $ and $ \frac{3}{7} $
(ii) $ \frac{-15}{4} $ and $ \frac{7}{4} $
(iii) $ \frac{-8}{11} $ and $ \frac{-4}{11} $
(iv) $ \frac{6}{13} $ and $ \frac{-9}{13} $

To do:

We have to add the given rational numbers. 

Solution:

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

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

$=\frac{-2}{7}$

Therefore, $\frac{-5}{7}+\frac{3}{7}=\frac{-2}{7}$.

(ii) $\frac{-15}{4}+\frac{7}{4}=\frac{-15+7}{4}$ 

$=\frac{-(15-7)}{4}$

$=\frac{-8}{4}$

$=-2$

Therefore, $\frac{-15}{4}+\frac{7}{4}=-2$. 

(iii) $\frac{-8}{11}+\frac{-4}{11}=\frac{-8+(-4)}{11}$ 

$=\frac{-(8+4)}{11}$

$=\frac{-12}{11}$

Therefore, $\frac{-8}{11}+\frac{-4}{11}=\frac{-12}{11}$.  

(iv) $\frac{6}{13}+\frac{-9}{13}=\frac{6+(-9)}{13}$ 

$=\frac{-(9-6)}{13}$

$=\frac{-3}{13}$

Therefore, $\frac{6}{13}+\frac{-9}{13}=\frac{-3}{13}$.   

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Updated on: 10-Oct-2022

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