Réitigh (1-1/2)^2(-2)^3-3/2+|-(-1/6)^2+frac{1/4-frac{1}{5}}{(1-frac{2}{5})^2}|-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}=

$$( 1 - \frac { 1 } { 2 } ) ^ { 2 } ( - 2 ) ^ { 3 } - \frac { 3 } { 2 } + | - ( - \frac { 1 } { 6 } ) ^ { 2 } + \frac { \frac { 1 } { 4 } - \frac { 1 } { 5 } } { ( 1 - \frac { 2 } { 5 } ) ^ { 2 } } | - \frac { \frac { 1 } { 3 } - \frac { 2 } { 9 } } { \frac { 1 } { 8 } - \frac { 15 } { 8 } } =$$

Luacháil

$$-\frac{419}{126}\approx -3.325396825$$

Céimeanna Réitigh

Dealaigh \frac{1}{2} ó 1 chun \frac{1}{2} a fháil.

$$\left(\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Ríomh cumhacht \frac{1}{2} de 2 agus faigh \frac{1}{4}.

$$\frac{1}{4}\left(-2\right)^{3}-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Ríomh cumhacht -2 de 3 agus faigh -8.

$$\frac{1}{4}\left(-8\right)-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Méadaigh \frac{1}{4} agus -8 chun -2 a fháil.

$$-2-\frac{3}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Dealaigh \frac{3}{2} ó -2 chun -\frac{7}{2} a fháil.

$$-\frac{7}{2}+|-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Ríomh cumhacht -\frac{1}{6} de 2 agus faigh \frac{1}{36}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Dealaigh \frac{1}{5} ó \frac{1}{4} chun \frac{1}{20} a fháil.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Dealaigh \frac{2}{5} ó 1 chun \frac{3}{5} a fháil.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Ríomh cumhacht \frac{3}{5} de 2 agus faigh \frac{9}{25}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Roinn \frac{1}{20} faoi \frac{9}{25} trí \frac{1}{20} a mhéadú faoi dheilín \frac{9}{25}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{1}{20}\times \frac{25}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Méadaigh \frac{1}{20} agus \frac{25}{9} chun \frac{5}{36} a fháil.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{5}{36}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Suimigh -\frac{1}{36} agus \frac{5}{36} chun \frac{1}{9} a fháil.

$$-\frac{7}{2}+|\frac{1}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Is é luach uimhriúil réaduimhir a ná a nuair is a\geq 0, nó -a nuair is a<0. Is é \frac{1}{9} luach uimhriúil \frac{1}{9}.

$$-\frac{7}{2}+\frac{1}{9}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Suimigh -\frac{7}{2} agus \frac{1}{9} chun -\frac{61}{18} a fháil.

$$-\frac{61}{18}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Dealaigh \frac{2}{9} ó \frac{1}{3} chun \frac{1}{9} a fháil.

$$-\frac{61}{18}-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Dealaigh \frac{15}{8} ó \frac{1}{8} chun -\frac{7}{4} a fháil.

$$-\frac{61}{18}-\frac{\frac{1}{9}}{-\frac{7}{4}}$$

Roinn \frac{1}{9} faoi -\frac{7}{4} trí \frac{1}{9} a mhéadú faoi dheilín -\frac{7}{4}.

$$-\frac{61}{18}-\frac{1}{9}\left(-\frac{4}{7}\right)$$

Méadaigh \frac{1}{9} agus -\frac{4}{7} chun -\frac{4}{63} a fháil.

$$-\frac{61}{18}-\left(-\frac{4}{63}\right)$$

Tá \frac{4}{63} urchomhairleach le -\frac{4}{63}.

$$-\frac{61}{18}+\frac{4}{63}$$

Suimigh -\frac{61}{18} agus \frac{4}{63} chun -\frac{419}{126} a fháil.

$$-\frac{419}{126}$$

Fachtóirigh

$$-\frac{419}{126} = -3\frac{41}{126} = -3.3253968253968256$$