Question

Simplify:

$4\frac{1}{10}-[2\frac{1}{2}-\{\frac{5}{6}-(\frac{2}{5}+\frac{3}{10}-\frac{4}{15})\}]$

Answer 1

$4\frac{1}{10}–[2\frac{1}{2}-\{\frac{5}{6}-(\frac{2}{5}+\frac{3}{10}-\frac{4}{15})\}]$

$=\frac{41}{10}-[\frac{5}{2}-\{\frac{5}{6}-(\frac{2\times 6}{5\times 6}+\frac{3\times 3}{10\times 3}-\frac{4\times 4}{15\times 4})]$

$=\frac{41}{10}-[\frac{5}{2}-\{\frac{5}{6}-(\frac{12}{30}+\frac{9}{30}-\frac{16}{60})]$

$=\frac{41}{10}-[\frac{5}{2}-\{\frac{5}{6}-\left(\frac{12+9-16}{30}\right]$

$=\frac{41}{10}-[\frac{5}{2}-\{\frac{5}{6}-\left(\frac{5}{30}\right)\left\}\right]$

$=\frac{41}{10}-[\frac{5}{2}-\{\frac{5}{6}-\frac{1}{6}\left\}\right]$

$=\frac{41}{10}-[\frac{5}{2}-\{\frac{5-1}{6}\left\}\right]$

$=\frac{41}{10}-[\frac{5}{2}-\frac{2}{3}]$

$=\frac{41}{10}-[\frac{5\times 3}{2\times 3}-\frac{2\times 2}{3\times 2}]$

$=\frac{41}{10}-[\frac{15}{6}-\frac{4}{6}]$

$=\frac{41}{10}-\frac{11}{6}$

$=\frac{41\times 3}{10\times 3}-\frac{11\times 5}{6\times 5}$

$=\frac{123-55}{30}$

$=\frac{68}{30}$

$=\frac{34}{15}=2\frac{4}{15}$