(i) Clearly,

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

(ii)

\(\frac{5}{-13}=\frac{5\times-1}{-13\times-1}=\frac{-5}{13}\)

\(\frac{-5}{13}\) and \(\frac{-35}{91}\)have different denominators.

Therefore, we take LCM of 13 and 91 that is 91. 

Now,

\(\frac{-5}{13}=\frac{-5\times7}{13\times7}=\frac{-35}{91}\)

And,

\(\frac{-35}{91}=\frac{-35\times1}{91\times1}=\frac{-35}{91}\)
Clearly,

\(\frac{-35}{91}=\frac{-35}{91}\)

Hence,

\(\frac{5}{-13}=\frac{-35}{91}\)

(iii) We can write \(-2=\frac{-2}{1}\)

\(\frac{-2}{1}\) and \(\frac{-13}{5}\) have different denominators.

Now,

\(\frac{-2}{1}=\frac{-2\times5}{1\times5}=\frac{-10}{5}\)
And,

\(\frac{-13}{5}=\frac{-13\times1}{5\times1}=\frac{-13}{5}\)

Since, -10 > -13

Therefore, \( \frac{-10}{5}>\frac{-13}{5}\)

Hence, \( -2>\frac{-13}{5}\)

(iv)  \(\frac{5}{-8}=\frac{5\times-1}{-8\times-1}=\frac{-5}{8}\)

 \(\frac{-2}{3}\) and \(\frac{-5}{8}\) have different denominators.

Therefore, we take LCM of 3 and 8 that is 24. 

Now,

\(\frac{2}{-3}=\frac{-2\times8}{3\times8}=\frac{-16}{24}\)
And,

\(\frac{-5}{8}=\frac{-5\times3}{8\times3}=\frac{-15}{24}\)
Since, -16 < -15

Therefore, \( \frac{-16}{24}<\frac{-15}{24}\)

Hence, \( \frac{-2}{3}<\frac{-5}{8}\)

(v)

\(\frac{-3}{-5}=\frac{-3\times-1}{-5\times-1}=\frac{3}{5}\)

\(\frac{3}{5}\)is a positive number and all positive numbers are greater than 0.

Therefore, \( 0<\frac{3}{5}\)

Hence, \( 0<\frac{-3}{-5}\)

(vi) 

 \(\frac{-8}{9}\) and \(\frac{-9}{10}\) have different denominators.

Therefore, we take LCM of 9 and 10 that is 90.

 Now,

\(\frac{-8}{9}=\frac{-8\times10}{9\times10}=\frac{-80}{90}\)

And,

\(\frac{-9}{10}=\frac{-9\times9}{10\times9}=\frac{-81}{90}\)

Since, -80 > -81

 Therefore, \( \frac{-80}{90}<\frac{-81}{90}\)

Hence, \( \frac{-8}{9}<\frac{-9}{10}\)