Question

\(\left(-\dfrac{5}{11}:\dfrac{13}{8}-\dfrac{5}{11}:\dfrac{13}{5}\right)\) + \(-\dfrac{1}{33}\)

 

Answer 1

\(\left(-\dfrac{5}{11}:\dfrac{13}{8}-\dfrac{5}{11}:\dfrac{13}{5}\right)+\left(-\dfrac{1}{33}\right)\\ =\left(-\dfrac{5}{11}\cdot\dfrac{8}{13}-\dfrac{5}{11}.\dfrac{5}{13}\right)-\dfrac{1}{33}\\ =-\dfrac{5}{11}.\left(\dfrac{8}{13}+\dfrac{5}{13}\right)-\dfrac{1}{33}\\ =-\dfrac{5}{11}\cdot1-\dfrac{1}{33}\\ =-\dfrac{5}{11}-\dfrac{1}{33}\\ =-\dfrac{15}{33}-\dfrac{1}{33}\\ =-\dfrac{16}{33}\)

Answer 2

`(-5/11 : 13/8 - 5/11 : 13/5) + -1/33`

`= (-5/11 * 8/13 - 5/11 * 5/13) + -1/33`

`= (5/11 * -8/13 - 5/13 * 5/11) + -1/33`

`= 5/11 * (-8/13 - 5/13) + -1/33`

`= 5/11 * (-1) + -1/33`

`= -5/11 + -1/33`

`= -16/33`