Løs {3/2+1-3/2*[(1/6*3/5+frac{7}{5}*frac{1}{7})*frac{5}{2}]}*frac{4}{33}+(1-frac{1}{2})^2:3+(frac{2}{3})^2

$$\{ \frac { 3 } { 2 } + 1 - \frac { 3 } { 2 } \times [ ( \frac { 1 } { 6 } \times \frac { 3 } { 5 } + \frac { 7 } { 5 } \times \frac { 1 } { 7 } ) \times \frac { 5 } { 2 } ] \} \times \frac { 4 } { 33 } + ( 1 - \frac { 1 } { 2 } ) ^ { 2 } : 3 + ( \frac { 2 } { 3 } ) ^ { 2 }$$

Evaluer

$$\frac{25}{36}\approx 0,694444444$$

Løsningsvejledning

Tilføj \frac{3}{2} og 1 for at få \frac{5}{2}.

$$\left(\frac{5}{2}-\frac{3}{2}\left(\frac{1}{6}\times \frac{3}{5}+\frac{7}{5}\times \frac{1}{7}\right)\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}$$

Multiplicer \frac{1}{6} og \frac{3}{5} for at få \frac{1}{10}.

$$\left(\frac{5}{2}-\frac{3}{2}\left(\frac{1}{10}+\frac{7}{5}\times \frac{1}{7}\right)\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}$$

Multiplicer \frac{7}{5} og \frac{1}{7} for at få \frac{1}{5}.

$$\left(\frac{5}{2}-\frac{3}{2}\left(\frac{1}{10}+\frac{1}{5}\right)\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}$$

Tilføj \frac{1}{10} og \frac{1}{5} for at få \frac{3}{10}.

$$\left(\frac{5}{2}-\frac{3}{2}\times \frac{3}{10}\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}$$

Multiplicer \frac{3}{2} og \frac{3}{10} for at få \frac{9}{20}.

$$\left(\frac{5}{2}-\frac{9}{20}\times \frac{5}{2}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}$$

Multiplicer \frac{9}{20} og \frac{5}{2} for at få \frac{9}{8}.

$$\left(\frac{5}{2}-\frac{9}{8}\right)\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}$$

Subtraher \frac{9}{8} fra \frac{5}{2} for at få \frac{11}{8}.

$$\frac{11}{8}\times \frac{4}{33}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}$$

Multiplicer \frac{11}{8} og \frac{4}{33} for at få \frac{1}{6}.

$$\frac{1}{6}+\frac{\left(1-\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}$$

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

$$\frac{1}{6}+\frac{\left(\frac{1}{2}\right)^{2}}{3}+\left(\frac{2}{3}\right)^{2}$$

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

$$\frac{1}{6}+\frac{\frac{1}{4}}{3}+\left(\frac{2}{3}\right)^{2}$$

Udtryk \frac{\frac{1}{4}}{3} som en enkelt brøk.

$$\frac{1}{6}+\frac{1}{4\times 3}+\left(\frac{2}{3}\right)^{2}$$

Multiplicer 4 og 3 for at få 12.

$$\frac{1}{6}+\frac{1}{12}+\left(\frac{2}{3}\right)^{2}$$

Tilføj \frac{1}{6} og \frac{1}{12} for at få \frac{1}{4}.

$$\frac{1}{4}+\left(\frac{2}{3}\right)^{2}$$

Beregn \frac{2}{3} til potensen af 2, og få \frac{4}{9}.

$$\frac{1}{4}+\frac{4}{9}$$

Tilføj \frac{1}{4} og \frac{4}{9} for at få \frac{25}{36}.

$$\frac{25}{36}$$

Faktoriser

$$\frac{5 ^ {2}}{2 ^ {2} \cdot 3 ^ {2}} = 0,6944444444444444$$