Question

5/13 +-5/7 + -20/41 +8/13 + -21/41

Answer 1

\(\dfrac{5}{13}+\left(-\dfrac{5}{7}\right)+\left(-\dfrac{20}{41}\right)+\dfrac{8}{13}+\left(-\dfrac{21}{41}\right)\)

\(=\dfrac{5}{13}-\dfrac{5}{7}-\dfrac{20}{41}+\dfrac{8}{13}-\dfrac{21}{41}\)

\(=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)-\left(\dfrac{20}{41}+\dfrac{21}{41}\right)-\dfrac{5}{7}\)

\(=\dfrac{13}{13}-\dfrac{41}{41}-\dfrac{5}{7}\)

\(=1-1-\dfrac{5}{7}\)

\(=0+\dfrac{5}{7}\)

\(=\dfrac{5}{7}\)

Answer 2

\(\dfrac{5}{13}+\dfrac{-5}{7}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{-21}{41}\)

\(=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(\dfrac{-20}{41}+\dfrac{-21}{41}\right)+\dfrac{-5}{7}\)

\(=1+\left(-1\right)+\dfrac{-5}{7}\)

\(=\dfrac{-5}{7}\)

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