Question

Rearrange & simplify:
1 4/13-2 5/8+(-8/39)+9/16

Answer 1

$1\frac{4}{13} - 2\frac{5}{8} + \big(\frac{-8}{39}\big) + \frac{9}{16}\\ = \frac{17}{13} - \frac{21}{8} - \frac{8}{39} + \frac{9}{16}$

/* Rearranging the terms , we get */

$= \frac{17}{13} - \frac{8}{39} + \frac{9}{16} - \frac{21}{8} \\= \frac{3\times 17-8}{39} + \frac{9-42}{16}\\= \frac{51 - 8}{39} - \frac{33}{16}\\= \frac{43}{39} - \frac{33}{16}\\= \frac{688-1287}{624}\\= \frac{-599}{624}$

Therefore.,

$red{ 1\frac{4}{13} - 2\frac{5}{8} + \big(\frac{-8}{39}\big) + \frac{9}{16}}$

$\green {= \frac{-599}{624}}$

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