Question

Simplify 3/7 + 5/7 + (- 3)/7 + (- 5)/7 .​

Answer 1

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Question:

$\sf {Simplify,\:\dfrac{3}{7} + \dfrac{5}{7} + \dfrac{-3}{7} + \dfrac{-5}{7} }$

To find the sum of three or more rational numbers, we may arrange them in any order we like. The arrangement does not alter the sum.

Explanation:

First Method:

$\sf {\dfrac{3}{7} + \dfrac{5}{7} + \dfrac{-3}{7} + \dfrac{-5}{7} }$

$\longrightarrow \sf {\bigg(\dfrac{3}{7} + \dfrac{-3}{7}\bigg) + \bigg(\dfrac{5}{7} + \dfrac{-5}{7}\bigg) }$

$\longrightarrow \sf {0 + 0 = 0}$

Sum of a number and it's additive inverse is zero.

Second Method:

$\sf {\bigg(\dfrac{3}{7} + \dfrac{5}{7}\bigg) + \bigg(\dfrac{-3}{7} + \dfrac{-5}{7}\bigg) }$

$\longrightarrow \sf {\bigg(\dfrac{3 + 5}{7}\bigg) + \bigg(\dfrac{-3 + (-5)}{7}\bigg) }$

$\longrightarrow \sf {\dfrac{8}{7} + \bigg(\dfrac{-3 - 5}{7} \bigg) }$

$\longrightarrow \sf {\dfrac{8}{7} + \bigg(\dfrac{-8}{7} \bigg) = 0}$