Riješi (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}]

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

Procijeni

$$\frac{20387}{2700}\approx 7,550740741$$

Koraci za rješenje

Podijelite 3 sa 3 da biste dobili 1.

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

Svedite razlomak \frac{5}{10} na najprostije elemente rastavlјanjem i kraćenjem 5.

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

Saberite \frac{1}{2} i 1 da biste dobili \frac{3}{2}.

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

Izračunajte \frac{3}{2} stepen od 2 i dobijte \frac{9}{4}.

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

Svedite razlomak \frac{15}{9} na najprostije elemente rastavlјanjem i kraćenjem 3.

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

Izračunajte \frac{5}{3} stepen od 2 i dobijte \frac{25}{9}.

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

Podijelite \frac{9}{4} sa \frac{25}{9} tako što ćete pomnožiti \frac{9}{4} recipročnom vrijednošću od \frac{25}{9}.

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

Pomnožite \frac{9}{4} i \frac{9}{25} da biste dobili \frac{81}{100}.

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

Podijelite \frac{7}{10} sa \frac{84}{30} tako što ćete pomnožiti \frac{7}{10} recipročnom vrijednošću od \frac{84}{30}.

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

Otkaži 3\times 7\times 10 u brojiocu i imeniocu.

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

Saberite \frac{81}{100} i \frac{1}{4} da biste dobili \frac{53}{50}.

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

Podijelite \frac{24}{9} sa \frac{4}{9} tako što ćete pomnožiti \frac{24}{9} recipročnom vrijednošću od \frac{4}{9}.

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

Otkaži 3\times 3\times 4 u brojiocu i imeniocu.

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

Pomnožite 2 i 3 da biste dobili 6.

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

Saberite \frac{53}{50} i 6 da biste dobili \frac{353}{50}.

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

Saberite \frac{353}{50} i \frac{2}{27} da biste dobili \frac{9631}{1350}.

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

Saberite \frac{9631}{1350} i \frac{5}{12} da biste dobili \frac{20387}{2700}.

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

Faktor

$$\frac{19 \cdot 29 \cdot 37}{2 ^ {2} \cdot 3 ^ {3} \cdot 5 ^ {2}} = 7\frac{1487}{2700} = 7,550740740740741$$