Question

Sa se efectueze [4 + 6 2/3 - 9/4 x ( 1/3 + 1/9)] :4 5/6 -2
( "/" inseamna supra)

Answer 1

 

$\displaystyle\\\hbox{Sa se calculeze:}\\\\\left[4+6\frac{2}{3}-\frac{9}{4}\times\left(\frac{1}{3}+\frac{1}{9}\right)\right]:4\frac{5}{6}-2=\\\\\\=\left[4+\frac{6\times3+2}{3}-\frac{9}{4}\times\left(\frac{1}{3}+\frac{1}{9}\right)\right]:\frac{4\times6+5}{6}-2=\\\\\\=\left[4+\frac{20}{3}-\frac{9}{4}\times\left(\frac{1}{3}+\frac{1}{9}\right)\right]:\frac{29}{6}-2=\\\\\\=\left[4+\frac{20}{3}-\frac{9}{4}\times\left(\frac{3}{9}+\frac{1}{9}\right)\right]:\frac{29}{6}-2=$

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$\displaystyle\\=\left[4+\frac{20}{3}-\frac{9}{4}\times\frac{3+1}{9}\right]:\frac{29}{6}-2=\\\\\\=\left[4+\frac{20}{3}-\frac{9}{4}\times\frac{4}{9}\right]:\frac{29}{6}-2=\\\\\\=\left[4+\frac{20}{3}-\frac{9\times4}{4\times9}\right]:\frac{29}{6}-2=\\\\\\=\left[4+\frac{20}{3}-1\right]:\frac{29}{6}-2=\\\\\\=\left[3+\frac{20}{3}\right]:\frac{29}{6}-2=\\\\\\=\left[\frac{9}{3} +\frac{20}{3}\right]:\frac{29}{6}-2=\\\\\\=\frac{9+20}{3}:\frac{29}{6}-2=$

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$\displaystyle\\=\frac{29}{3}\times\frac{6}{29}-2=\\\\\\=\frac{29\times6}{3\times29}-2=\\\\\\=\frac{1\times2}{1\times1}-2=\\\\=2-2=\boxed{\bf0}$

 

Answer 2

$\it \Big[4+6\dfrac{2}{3}-\dfrac{9}{4}\cdot\Big(\dfrac{^{3)}1}{\ 3}+\dfrac{1}{9}\Big)\Big]:4\dfrac{5}{6}-2=\Big(4+\dfrac{20}{3}-\dfrac{9}{4}\cdot\dfrac{4}{9}\Big):\dfrac{29}{6}-2=\\ \\ \\ = \Big(4+\dfrac{20}{3}-1\Big):\dfrac{29}{6}-2=\Big(^{3)}3+\dfrac{20}{3}\Big)\cdot\dfrac{6}{29}-2 =\dfrac{29}{3}\cdot\dfrac{6}{29}-2=2-2=0$