Resolver {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=

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

Calcular

$$\frac{5}{4}=1.25$$

Pasos da solución

Reduce a fracción \frac{5}{10} a termos máis baixos extraendo e cancelando 5.

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

Reduce a fracción \frac{3}{9} a termos máis baixos extraendo e cancelando 3.

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

Suma \frac{1}{2} e \frac{1}{3} para obter \frac{5}{6}.

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

Calcula \frac{5}{6} á potencia de 2 e obtén \frac{25}{36}.

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

Reduce a fracción \frac{15}{9} a termos máis baixos extraendo e cancelando 3.

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

Calcula \frac{5}{3} á potencia de 2 e obtén \frac{25}{9}.

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

Divide \frac{25}{36} entre \frac{25}{9} mediante a multiplicación de \frac{25}{36} polo recíproco de \frac{25}{9}.

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

Multiplica \frac{25}{36} e \frac{9}{25} para obter \frac{1}{4}.

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

Divide \frac{7}{10} entre \frac{84}{90} mediante a multiplicación de \frac{7}{10} polo recíproco de \frac{84}{90}.

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

Anula 3\times 7\times 10 no numerador e no denominador.

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

Divide \frac{24}{9} entre \frac{4}{9} mediante a multiplicación de \frac{24}{9} polo recíproco de \frac{4}{9}.

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

Anula 3\times 3\times 4 no numerador e no denominador.

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

Multiplica 2 e 3 para obter 6.

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

Suma \frac{3}{4} e 6 para obter \frac{27}{4}.

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

Multiplica \frac{27}{4} e \frac{2}{27} para obter \frac{1}{2}.

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

Suma \frac{1}{2} e \frac{5}{12} para obter \frac{11}{12}.

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

Dividir 11 entre 12 dá como resultado 0 e o resto 11. Reescribe \frac{11}{12} como 0+\frac{11}{12}.

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

O teito dun número real a é o número enteiro máis pequeno maior ou igual a a. O teito de 0+\frac{11}{12} é 1.

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

Suma \frac{1}{4} e 1 para obter \frac{5}{4}.

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

Factorizar

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$