Question

Вычислите: (2 1/6+5 1/6:4 2/15)*3/82

Answer 1

$\boldsymbol{\boxed{(2\dfrac{1}{6}+5\dfrac{1}{6}:4 \dfrac{2}{15}) \cdot \dfrac{3}{82}=\dfrac{1}{8}}}\\\\\\1) 5\dfrac{1}{6} : 4\dfrac{2}{15} \ = \ \dfrac{6\cdot5+1}{6} : \dfrac{15\cdot4+2}{15} \ = \ \dfrac{31}{6}:\dfrac{62}{15} \ = \ \dfrac{31}{6}\cdot\dfrac{15}{62} \ = \ \dfrac{31\cdot15}{6\cdot62} \ = \dfrac{465^{:93}}{372^{:93}} \ = \ \dfrac{5}{4}.$

$2) \ 2\dfrac{1}{6} + \dfrac{5}{4} \ = \ \dfrac{6\cdot2+1}{6} + \dfrac{5}{4} \ = \ \dfrac{13^{*2}}{6^{*2}} + \dfrac{5^{*3}}{4^{*3}} \ = \ \dfrac{26+15}{12} \ = \ \dfrac{41}{12}. \\ \\ \\ 3) \ \dfrac{41}{12} \cdot \dfrac{3}{82} \ = \ \dfrac{41 \cdot 3}{12 \cdot 82} \ = \ \dfrac{123}{984} \ = \ \dfrac{1}{8}.$

$\boldsymbol{\boxed{OTBET: \dfrac{1}{8} } }$