Question

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:
$\frac{3}{5} + \frac{ - 7}{6} + \frac{2}{5} + \frac{ - 5}{6}$
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Answer 1

$\huge\underline{\underline\frak{AnSwEr: -}}$

Re-arranging and grouping the numbers in pairs in such a way that each group contains a pair of rational numbers with equal denominators, we have,

$\frac{3}{5} + \frac{ - 7}{6} + \frac{2}{5} + \frac{ - 5}{6}$

$\frac{3}{5} + \frac{2}{5} = \frac{ - 7}{6} + \frac{ - 5}{6 }$

$= \frac{3 + 2}{5} = \frac{( - 7) + (- 5)}{6} \\ \\ = \frac{5}{5} + \frac{( - 12)}{6} \\ \\ = (1 + ( - 2) = 1 - 2 = - 1)$