Løs (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}}

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

Evaluer

$$-\frac{7981}{2268}\approx -3,518959436$$

Løsningsvejledning

Subtraher \frac{1}{2} fra 1 for at få \frac{1}{2}.

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

Beregn \frac{1}{2} til potensen af 2, og få \frac{1}{4}.

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

Beregn -2 til potensen af 3, og få -8.

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

Multiplicer \frac{1}{4} og -8 for at få -2.

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

Subtraher \frac{3}{2} fra -2 for at få -\frac{7}{2}.

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

Beregn -\frac{1}{6} til potensen af 2, og få \frac{1}{36}.

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

Subtraher \frac{1}{36} fra -\frac{7}{2} for at få -\frac{127}{36}.

$$-\frac{127}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Subtraher \frac{1}{5} fra \frac{1}{4} for at få \frac{1}{20}.

$$-\frac{127}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Subtraher \frac{2}{5} fra 1 for at få \frac{3}{5}.

$$-\frac{127}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Beregn \frac{3}{5} til potensen af 2, og få \frac{9}{25}.

$$-\frac{127}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Divider \frac{1}{20} med \frac{9}{25} ved at multiplicere \frac{1}{20} med den reciprokke værdi af \frac{9}{25}.

$$-\frac{127}{36}+\frac{1}{20}\times \frac{25}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Multiplicer \frac{1}{20} og \frac{25}{9} for at få \frac{5}{36}.

$$-\frac{127}{36}+\frac{5}{36}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Subtraher \frac{2}{9} fra \frac{1}{3} for at få \frac{1}{9}.

$$-\frac{127}{36}+\frac{5}{36}|-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Subtraher \frac{15}{8} fra \frac{1}{8} for at få -\frac{7}{4}.

$$-\frac{127}{36}+\frac{5}{36}|-\frac{\frac{1}{9}}{-\frac{7}{4}}|$$

Divider \frac{1}{9} med -\frac{7}{4} ved at multiplicere \frac{1}{9} med den reciprokke værdi af -\frac{7}{4}.

$$-\frac{127}{36}+\frac{5}{36}|-\frac{1}{9}\left(-\frac{4}{7}\right)|$$

Multiplicer \frac{1}{9} og -\frac{4}{7} for at få -\frac{4}{63}.

$$-\frac{127}{36}+\frac{5}{36}|-\left(-\frac{4}{63}\right)|$$

Det modsatte af -\frac{4}{63} er \frac{4}{63}.

$$-\frac{127}{36}+\frac{5}{36}|\frac{4}{63}|$$

Den absolutte værdi af et reelt tal a er a, når a\geq 0, eller -a, når a<0. Den absolutte værdi af \frac{4}{63} er \frac{4}{63}.

$$-\frac{127}{36}+\frac{5}{36}\times \frac{4}{63}$$

Multiplicer \frac{5}{36} og \frac{4}{63} for at få \frac{5}{567}.

$$-\frac{127}{36}+\frac{5}{567}$$

Tilføj -\frac{127}{36} og \frac{5}{567} for at få -\frac{7981}{2268}.

$$-\frac{7981}{2268}$$

Faktoriser

$$-\frac{7981}{2268} = -3\frac{1177}{2268} = -3,5189594356261025$$