Question

Вычислите: (2 1/6+5 1/6:4 2/15)*3/82

Answer 1

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

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

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