Reciprocal of $\frac{-26}{12}$ is $\frac{-12}{26}$.

$\frac{2}{13}+\frac{-12}{26}$      [Taking LCM]
$=\frac{4}{26}-\frac{12}{26}=\frac{4-12}{26}=\frac{-8}{26}=\frac{-4}{13}$

$\frac{-7}{19}+\frac{-2}{57}=\frac{(-7\times 3)}{(19\times 3)}+\frac{-2}{57}$

$=\frac{-21}{57}+\frac{-2}{57}=\frac{-23}{57}$

Any positive number is greater than 0. 

$\frac{10}{2}=\frac{2\times 5}{2}$

$=5$

A negative number cannot be greater than a positive number.

so,$\frac{-4}{3}<\frac{24}{36}$

$\text{Let the unknown number be}x.$

$\frac{-1}{5}=\frac{3}{10}+\frac{-2}{5}+xx=\frac{-1}{5}-\frac{3}{10}+\frac{2}{5}$
$\text{Taking LCM, we get,}x=\frac{-2}{10}-\frac{3}{10}+\frac{4}{10}x=\frac{-1}{10}$

$\text{Let}\frac{p}{q}\text{be a non-zero rational number.}\text{Then}p,q\ne 0.$
$\text{Its additive inverse is}\frac{-p}{q}.$
$\text{That is,}\frac{p}{q}+\frac{-p}{q}=\frac{-p}{q}+\frac{p}{q}=0$
$\text{On dividing}\frac{p}{q}\text{by}\frac{-p}{q},\text{we get -1.}$

Let the number be $x.$

$\frac{1}{4}-x=\frac{1}{2}$

$x=\frac{1}{4}-\frac{1}{2}=-\frac{1}{4}$

Converting all the lengths into centimetre.

Total length of the rope = 4050 cm,
Length of each piece 
$=\frac{9}{4}\times 100=\frac{900}{4}$
Number of Pieces
$=\frac{Totallength}{Lengthofeachpiece}$ 

Number Of  Pieces Cut
$=\frac{4050}{\frac{(9\times 100)}{4}}=18$ 
$=\frac{4050\times 4}{(9\times 100)}=18$ 

Number of pieces cut = 18.