Lutasin ang {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=

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

I-evaluate

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

Mga Hakbang ng Solution

Bawasan ang fraction \frac{5}{10} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 5.

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

Bawasan ang fraction \frac{3}{9} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 3.

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

Idagdag ang \frac{1}{2} at \frac{1}{3} para makuha ang \frac{5}{6}.

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

Kalkulahin ang \frac{5}{6} sa power ng 2 at kunin ang \frac{25}{36}.

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

Bawasan ang fraction \frac{15}{9} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 3.

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

Kalkulahin ang \frac{5}{3} sa power ng 2 at kunin ang \frac{25}{9}.

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

I-divide ang \frac{25}{36} gamit ang \frac{25}{9} sa pamamagitan ng pagmu-multiply sa \frac{25}{36} gamit ang reciprocal ng \frac{25}{9}.

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

I-multiply ang \frac{25}{36} at \frac{9}{25} para makuha ang \frac{1}{4}.

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

I-divide ang \frac{7}{10} gamit ang \frac{84}{90} sa pamamagitan ng pagmu-multiply sa \frac{7}{10} gamit ang reciprocal ng \frac{84}{90}.

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

I-cancel out ang 3\times 7\times 10 sa parehong numerator at denominator.

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

I-divide ang \frac{24}{9} gamit ang \frac{4}{9} sa pamamagitan ng pagmu-multiply sa \frac{24}{9} gamit ang reciprocal ng \frac{4}{9}.

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

I-cancel out ang 3\times 3\times 4 sa parehong numerator at denominator.

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

I-multiply ang 2 at 3 para makuha ang 6.

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

Idagdag ang \frac{3}{4} at 6 para makuha ang \frac{27}{4}.

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

I-multiply ang \frac{27}{4} at \frac{2}{27} para makuha ang \frac{1}{2}.

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

Idagdag ang \frac{1}{2} at \frac{5}{12} para makuha ang \frac{11}{12}.

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

Kapag na-divide ang 11 gamit ang 12, ang resulta ay 0 at ang remainder ay 11. Isulat ang \frac{11}{12} bilang 0+\frac{11}{12}.

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

Ang ceiling ng isang real number na a ay ang pinakamaliit na integer na numero nang mas malaki o katumbas ng a. Ang ceiling ng 0+\frac{11}{12} ay 1.

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

Idagdag ang \frac{1}{4} at 1 para makuha ang \frac{5}{4}.

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

I-factor

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