Question

\(\dfrac{1}{5}-\dfrac{3}{7}+\dfrac{5}{9}-\dfrac{2}{11}+\dfrac{7}{13}-\dfrac{9}{16}-\dfrac{7}{13}+\dfrac{2}{11}-\dfrac{5}{9}+\dfrac{3}{7}-\dfrac{1}{5}\)

Answer 1

\(=\left(\dfrac{1}{5}-\dfrac{1}{5}\right)+\left(\dfrac{-3}{7}+\dfrac{3}{7}\right)+\left(\dfrac{5}{9}-\dfrac{5}{9}\right)+\left(\dfrac{-2}{11}+\dfrac{2}{11}\right)+\left(\dfrac{7}{13}-\dfrac{7}{13}\right)-\dfrac{9}{16}\)

=-9/16

Answer 2

` 1/5 - 3/7 + 5/9 - 2/11 + 7/13 - 9/16 - 7/13 + 2/11 - 5/9 + 3/7 - 1/5`

` = ( 1/5 - 1/5) + ( -3/7 + 3/7) + ( 5/9 - 5/9) + ( -2/11 + 2/11) + (7/13 - 7/13) - 9/16`

` = 0 + 0 + 0 + 0 + 0 -  9/16`

` = -9/16`

Answer 3

\(=\left(\dfrac{1}{5}-\dfrac{1}{5}\right)+\left(\dfrac{3}{7}-\dfrac{3}{7}\right)+\left(\dfrac{5}{9}-\dfrac{5}{9}\right)+\left(\dfrac{2}{11}-\dfrac{2}{11}\right)+\left(\dfrac{7}{13}-\dfrac{7}{13}\right)-\dfrac{9}{16}\)

\(=0+0+0+0+0-\dfrac{9}{16}=-\dfrac{9}{16}\)

Answer 4

=(1/5 -1/5) +(-3/7 +3/7)+(5/9 -5/9)+(-2/11 +2/11)+(7/13 -7/13)+9/16 =9/16