Question

what rational number should be substract from the sumof3÷14and -4÷7to get 13÷21

Answer 1

Let the rational number be $\frac{a}{b}$. 
Then, 
$( \frac{3}{14} + \frac{-4}{7} ) - \frac{a}{b} = \frac{13}{21}$
$( \frac{3+(-8)}{14} ) - \frac{a}{b} = \frac{13}{21}$
$\frac{-5}{14} - \frac{a}{b} = \frac{13}{21}$
$\frac{a}{b} = \frac{13}{21} + \frac{5}{14}$
$\frac{a}{b} = \frac{41}{42}$

Hence, the required rational number is $\frac{41}{42}$.