Question

using the rearrangement property find the sum

Answer 1

Question:

Using the rearrangement property, find the sum :

• (i) $\dfrac{ - 13}{20} + \dfrac{11}{14} + \dfrac{ - 5}{7} + \dfrac{7}{10}$

Solution :

Using commutative law :

$\implies \dfrac{ - 13}{20} + \dfrac{7}{10} + \dfrac{ - 5}{7} + \dfrac{11}{14} \\ \\ \implies (\dfrac{ - 13}{20} + \dfrac{7}{10} ) + ( \dfrac{- 5}{7} + \dfrac{11}{14} ) \\ \\ \implies(\dfrac{ - 13+ (2\times 7)}{20} ) + (\dfrac{ (- 5\times 2) + 11}{14} ) \\ \\ \implies(\dfrac{ - 13+ 14}{20} ) + (\dfrac{ - 10 + 11}{14} ) \\ \\ \implies \dfrac{1}{20} + \dfrac{1}{14} \\ \\ \implies \dfrac{(1\times 7) + (1\times 10)}{140} \\ \\ \implies \dfrac{7 + 10}{140} \\ \\ \implies \dfrac{17}{140}$

$\green{\tt{\therefore {The\:sum\:is\:\dfrac{17}{140}.}}}$