Evaluate: 4 7 +0+-8 9 +-13 7 +17 9 - Vidyadip

Question

Evaluate: $\frac{4}{7}+0+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{9}$

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Answer

$\frac{4}{7}+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{9}$
$ =\left[\frac{4}{7}+\left(\frac{-13}{7}\right)\right]+\left(\frac{-8}{9}+\frac{17}{9}\right)$
$ =\left(\frac{4}{7}\right)-\frac{13}{7}+\frac{-8}{9}+\frac{17}{9}$
$ =\frac{-9}{7}+\frac{9}{9}=\frac{-9}{7}+1$
$ =\frac{-9 \times 1}{7 \times 1}+\frac{1 \times 7}{1 \times 7}$
$(\text{LCM}$ of $1$ and $7=7 )$
$=\frac{-9}{7}+\frac{7}{7}=\frac{-2}{7}$

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