Løs [(2-1*3/5)^2+(5/8-3/4)-(6/5*frac{1}{3})(7*frac{1}{2})]div(5-frac{6}{5})

$$[ ( 2 - 1 \cdot \frac { 3 } { 5 } ) ^ { 2 } + ( \frac { 5 } { 8 } - \frac { 3 } { 4 } ) - ( \frac { 6 } { 5 } \cdot \frac { 1 } { 3 } ) ( 7 \cdot \frac { 1 } { 2 } ) ] \div ( 5 - \frac { 6 } { 5 } )$$

Evaluer

$$\frac{87}{760}\approx 0,114473684$$

Løsningsvejledning

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

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

Subtraher \frac{3}{5} fra 2 for at få \frac{7}{5}.

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

Beregn \frac{7}{5} til potensen af 2, og få \frac{49}{25}.

$$\frac{\frac{49}{25}+\frac{5}{8}-\frac{3}{4}-\frac{6}{5}\times \frac{1}{3}\times 7\times \frac{1}{2}}{5-\frac{6}{5}}$$

Tilføj \frac{49}{25} og \frac{5}{8} for at få \frac{517}{200}.

$$\frac{\frac{517}{200}-\frac{3}{4}-\frac{6}{5}\times \frac{1}{3}\times 7\times \frac{1}{2}}{5-\frac{6}{5}}$$

Subtraher \frac{3}{4} fra \frac{517}{200} for at få \frac{367}{200}.

$$\frac{\frac{367}{200}-\frac{6}{5}\times \frac{1}{3}\times 7\times \frac{1}{2}}{5-\frac{6}{5}}$$

Multiplicer \frac{6}{5} og \frac{1}{3} for at få \frac{2}{5}.

$$\frac{\frac{367}{200}-\frac{2}{5}\times 7\times \frac{1}{2}}{5-\frac{6}{5}}$$

Multiplicer \frac{2}{5} og 7 for at få \frac{14}{5}.

$$\frac{\frac{367}{200}-\frac{14}{5}\times \frac{1}{2}}{5-\frac{6}{5}}$$

Multiplicer \frac{14}{5} og \frac{1}{2} for at få \frac{7}{5}.

$$\frac{\frac{367}{200}-\frac{7}{5}}{5-\frac{6}{5}}$$

Subtraher \frac{7}{5} fra \frac{367}{200} for at få \frac{87}{200}.

$$\frac{\frac{87}{200}}{5-\frac{6}{5}}$$

Subtraher \frac{6}{5} fra 5 for at få \frac{19}{5}.

$$\frac{\frac{87}{200}}{\frac{19}{5}}$$

Divider \frac{87}{200} med \frac{19}{5} ved at multiplicere \frac{87}{200} med den reciprokke værdi af \frac{19}{5}.

$$\frac{87}{200}\times \frac{5}{19}$$

Multiplicer \frac{87}{200} og \frac{5}{19} for at få \frac{87}{760}.

$$\frac{87}{760}$$

Faktoriser

$$\frac{3 \cdot 29}{2 ^ {3} \cdot 5 \cdot 19} = 0,11447368421052631$$