Riješi {left(5/10+3/9right)}^2div{left(15/9right)}^2+lceil(7/10divfrac{84}{90}+frac{24}{9}divfrac{4}{9})*frac{2}{27}+frac{5}{12}rceil=

$${ \left( \frac{ 5 }{ 10 } + \frac{ 3 }{ 9 } \right) }^{ 2 } \div { \left( \frac{ 15 }{ 9 } \right) }^{ 2 } + \lceil ( \frac{ 7 }{ 10 } \div \frac{ 84 }{ 90 } + \frac{ 24 }{ 9 } \div \frac{ 4 }{ 9 } ) \times \frac{ 2 }{ 27 } + \frac{ 5 }{ 12 } \rceil =$$

Procijeni

$$\frac{5}{4}=1,25$$

Koraci za rješenje

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

$$\frac{\left(\frac{1}{2}+\frac{3}{9}\right)^{2}}{\left(\frac{15}{9}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

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

$$\frac{\left(\frac{1}{2}+\frac{1}{3}\right)^{2}}{\left(\frac{15}{9}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Saberite \frac{1}{2} i \frac{1}{3} da biste dobili \frac{5}{6}.

$$\frac{\left(\frac{5}{6}\right)^{2}}{\left(\frac{15}{9}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Izračunajte \frac{5}{6} stepen od 2 i dobijte \frac{25}{36}.

$$\frac{\frac{25}{36}}{\left(\frac{15}{9}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

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

$$\frac{\frac{25}{36}}{\left(\frac{5}{3}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

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

$$\frac{\frac{25}{36}}{\frac{25}{9}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Podijelite \frac{25}{36} sa \frac{25}{9} tako što ćete pomnožiti \frac{25}{36} recipročnom vrijednošću od \frac{25}{9}.

$$\frac{25}{36}\times \frac{9}{25}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Pomnožite \frac{25}{36} i \frac{9}{25} da biste dobili \frac{1}{4}.

$$\frac{1}{4}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Podijelite \frac{7}{10} sa \frac{84}{90} tako što ćete pomnožiti \frac{7}{10} recipročnom vrijednošću od \frac{84}{90}.

$$\frac{1}{4}+\lceil \left(\frac{7\times 90}{10\times 84}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

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

$$\frac{1}{4}+\lceil \left(\frac{3}{4}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

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

$$\frac{1}{4}+\lceil \left(\frac{3}{4}+\frac{24\times 9}{9\times 4}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

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

$$\frac{1}{4}+\lceil \left(\frac{3}{4}+2\times 3\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Pomnožite 2 i 3 da biste dobili 6.

$$\frac{1}{4}+\lceil \left(\frac{3}{4}+6\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Saberite \frac{3}{4} i 6 da biste dobili \frac{27}{4}.

$$\frac{1}{4}+\lceil \frac{27}{4}\times \frac{2}{27}+\frac{5}{12}\rceil$$

Pomnožite \frac{27}{4} i \frac{2}{27} da biste dobili \frac{1}{2}.

$$\frac{1}{4}+\lceil \frac{1}{2}+\frac{5}{12}\rceil$$

Saberite \frac{1}{2} i \frac{5}{12} da biste dobili \frac{11}{12}.

$$\frac{1}{4}+\lceil \frac{11}{12}\rceil$$

Dijeljenje 11 sa 12 daje 0 i ostatak 11. Ponovo napišite \frac{11}{12} kao 0+\frac{11}{12}.

$$\frac{1}{4}+\lceil 0+\frac{11}{12}\rceil$$

Maksimalna vrijednost realnog broja a je najmanji cijeli broj veći od ili jednak a. Maksimalna vrijednost od 0+\frac{11}{12} je 1.

$$\frac{1}{4}+1$$

Saberite \frac{1}{4} i 1 da biste dobili \frac{5}{4}.

$$\frac{5}{4}$$

Faktor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1,25$$