Rešite {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=

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

Ovrednoti

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

Koraki rešitve

Zmanjšajte ulomek \frac{5}{10} na najmanjši imenovalec tako, da izpeljete in okrajšate 5.

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

Zmanjšajte ulomek \frac{3}{9} na najmanjši imenovalec tako, da izpeljete in okrajšate 3.

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

Seštejte \frac{1}{2} in \frac{1}{3}, da dobite \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 potenco \frac{5}{6} števila 2, da dobite \frac{25}{36}.

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

Zmanjšajte ulomek \frac{15}{9} na najmanjši imenovalec tako, da izpeljete in okrajšate 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 potenco \frac{5}{3} števila 2, da dobite \frac{25}{9}.

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

Delite \frac{25}{36} s/z \frac{25}{9} tako, da pomnožite \frac{25}{36} z obratno vrednostjo \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} in \frac{9}{25}, da dobite \frac{1}{4}.

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

Delite \frac{7}{10} s/z \frac{84}{90} tako, da pomnožite \frac{7}{10} z obratno vrednostjo \frac{84}{90}.

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

Okrajšaj 3\times 7\times 10 v števcu in imenovalcu.

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

Delite \frac{24}{9} s/z \frac{4}{9} tako, da pomnožite \frac{24}{9} z obratno vrednostjo \frac{4}{9}.

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

Okrajšaj 3\times 3\times 4 v števcu in imenovalcu.

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

Pomnožite 2 in 3, da dobite 6.

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

Seštejte \frac{3}{4} in 6, da dobite \frac{27}{4}.

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

Pomnožite \frac{27}{4} in \frac{2}{27}, da dobite \frac{1}{2}.

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

Seštejte \frac{1}{2} in \frac{5}{12}, da dobite \frac{11}{12}.

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

Če 11 delite z 12, dobite 0 in ostanek 11. Spremenite zapis vrednosti \frac{11}{12} v 0+\frac{11}{12}.

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

Zgornja meja realnega števila a je najmanjše celo število, večje ali enako vrednosti a. Zgornja meja vrednosti 0+\frac{11}{12} je 1.

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

Seštejte \frac{1}{4} in 1, da dobite \frac{5}{4}.

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

Faktoriziraj

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