Question

\(\dfrac{5}{13}\)+\(\dfrac{-5}{7}\)+\(\dfrac{-20}{41}\)+\(\dfrac{8}{13}\)+\(\dfrac{-12}{41}\)

Answer 1

\(=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(-\dfrac{5}{7}\right)+\left[\left(-\dfrac{20}{41}\right)+\left(-\dfrac{12}{41}\right)\right]\\ =1+\left(-\dfrac{5}{7}\right)+\left(-\dfrac{32}{41}\right)\\ =-\dfrac{142}{287}\)

Answer 2

`5/13 +(-5)/7+(-20)/41+8/13+(-12)/41`

`=(5/13+8/13)+(-5)/7`\(+\left(\dfrac{-20}{41}+\dfrac{-12}{41}\right)\)

`=1+(-5)/7+(-32)/41`

`=2/7+(-32)/41`

`=(-142)/287`

Answer 3

\(\dfrac{5}{13}+\dfrac{-5}{7}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{-12}{41}\)

\(=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(\dfrac{-20}{12}+\dfrac{-12}{41}\right)+\dfrac{-5}{7}\)

\(=1+\dfrac{-32}{41}+\dfrac{-5}{7}\)

\(=\dfrac{41}{41}+\dfrac{-32}{41}+\dfrac{-5}{7}\)

\(=\dfrac{9}{41}+\dfrac{-5}{7}\)

\(=\dfrac{-142}{287}\)

Answer 4

`5/13 + (-5)/7 + (-20)/41 + 8/13 + (-12)/41`

`  =(5/13 + 8/13) + ((-20)/41 + (-12)/41) + (-5)/7`

` = 13/13 + (-32)/41 + (-5)/7`

`  =1 + (-32)/41 + (-5)/7`

` = 9/41 + (-5)/7`

` = (-142)/287`