Réitigh (5/10+3/3)^2:(15/9)^2+[(7/10:frac{84}{30}+frac{24}{9}:frac{4}{9})+frac{2}{27}+frac{5}{12}]

$$( \frac { 5 } { 10 } + \frac { 3 } { 3 } ) ^ { 2 } : ( \frac { 15 } { 9 } ) ^ { 2 } + [ ( \frac { 7 } { 10 } : \frac { 84 } { 30 } + \frac { 24 } { 9 } : \frac { 4 } { 9 } ) + \frac { 2 } { 27 } + \frac { 5 } { 12 } ]$$

Luacháil

$$\frac{20387}{2700}\approx 7.550740741$$

Céimeanna Réitigh

Roinn 3 faoi 3 chun 1 a fháil.

$$\frac{\left(\frac{5}{10}+1\right)^{2}}{\left(\frac{15}{9}\right)^{2}}+\frac{\frac{7}{10}}{\frac{84}{30}}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Laghdaigh an codán \frac{5}{10} chuig na téarmaí is ísle trí 5 a bhaint agus a chealú.

$$\frac{\left(\frac{1}{2}+1\right)^{2}}{\left(\frac{15}{9}\right)^{2}}+\frac{\frac{7}{10}}{\frac{84}{30}}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Suimigh \frac{1}{2} agus 1 chun \frac{3}{2} a fháil.

$$\frac{\left(\frac{3}{2}\right)^{2}}{\left(\frac{15}{9}\right)^{2}}+\frac{\frac{7}{10}}{\frac{84}{30}}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Ríomh cumhacht \frac{3}{2} de 2 agus faigh \frac{9}{4}.

$$\frac{\frac{9}{4}}{\left(\frac{15}{9}\right)^{2}}+\frac{\frac{7}{10}}{\frac{84}{30}}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Laghdaigh an codán \frac{15}{9} chuig na téarmaí is ísle trí 3 a bhaint agus a chealú.

$$\frac{\frac{9}{4}}{\left(\frac{5}{3}\right)^{2}}+\frac{\frac{7}{10}}{\frac{84}{30}}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Ríomh cumhacht \frac{5}{3} de 2 agus faigh \frac{25}{9}.

$$\frac{\frac{9}{4}}{\frac{25}{9}}+\frac{\frac{7}{10}}{\frac{84}{30}}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Roinn \frac{9}{4} faoi \frac{25}{9} trí \frac{9}{4} a mhéadú faoi dheilín \frac{25}{9}.

$$\frac{9}{4}\times \frac{9}{25}+\frac{\frac{7}{10}}{\frac{84}{30}}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Méadaigh \frac{9}{4} agus \frac{9}{25} chun \frac{81}{100} a fháil.

$$\frac{81}{100}+\frac{\frac{7}{10}}{\frac{84}{30}}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Roinn \frac{7}{10} faoi \frac{84}{30} trí \frac{7}{10} a mhéadú faoi dheilín \frac{84}{30}.

$$\frac{81}{100}+\frac{7\times 30}{10\times 84}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Cealaigh 3\times 7\times 10 mar uimhreoir agus ainmneoir.

$$\frac{81}{100}+\frac{1}{4}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Suimigh \frac{81}{100} agus \frac{1}{4} chun \frac{53}{50} a fháil.

$$\frac{53}{50}+\frac{\frac{24}{9}}{\frac{4}{9}}+\frac{2}{27}+\frac{5}{12}$$

Roinn \frac{24}{9} faoi \frac{4}{9} trí \frac{24}{9} a mhéadú faoi dheilín \frac{4}{9}.

$$\frac{53}{50}+\frac{24\times 9}{9\times 4}+\frac{2}{27}+\frac{5}{12}$$

Cealaigh 3\times 3\times 4 mar uimhreoir agus ainmneoir.

$$\frac{53}{50}+2\times 3+\frac{2}{27}+\frac{5}{12}$$

Méadaigh 2 agus 3 chun 6 a fháil.

$$\frac{53}{50}+6+\frac{2}{27}+\frac{5}{12}$$

Suimigh \frac{53}{50} agus 6 chun \frac{353}{50} a fháil.

$$\frac{353}{50}+\frac{2}{27}+\frac{5}{12}$$

Suimigh \frac{353}{50} agus \frac{2}{27} chun \frac{9631}{1350} a fháil.

$$\frac{9631}{1350}+\frac{5}{12}$$

Suimigh \frac{9631}{1350} agus \frac{5}{12} chun \frac{20387}{2700} a fháil.

$$\frac{20387}{2700}$$

Fachtóirigh

$$\frac{19 \cdot 29 \cdot 37}{2 ^ {2} \cdot 3 ^ {3} \cdot 5 ^ {2}} = 7\frac{1487}{2700} = 7.550740740740741$$