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

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

Evaluate

$$\frac{87}{760}\approx 0.114473684$$

Solution Steps

Multiply 1 and \frac{3}{5} to get \frac{3}{5}.

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

Subtract \frac{3}{5} from 2 to get \frac{7}{5}.

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

Calculate \frac{7}{5} to the power of 2 and get \frac{49}{25}.

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

Add \frac{49}{25} and \frac{5}{8} to get \frac{517}{200}.

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

Subtract \frac{3}{4} from \frac{517}{200} to get \frac{367}{200}.

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

Multiply \frac{6}{5} and \frac{1}{3} to get \frac{2}{5}.

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

Multiply \frac{2}{5} and 7 to get \frac{14}{5}.

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

Multiply \frac{14}{5} and \frac{1}{2} to get \frac{7}{5}.

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

Subtract \frac{7}{5} from \frac{367}{200} to get \frac{87}{200}.

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

Subtract \frac{6}{5} from 5 to get \frac{19}{5}.

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

Divide \frac{87}{200} by \frac{19}{5} by multiplying \frac{87}{200} by the reciprocal of \frac{19}{5}.

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

Multiply \frac{87}{200} and \frac{5}{19} to get \frac{87}{760}.

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

Factor

$$\frac{3 \cdot 29}{2 ^ {3} \cdot 5 \cdot 19} = 0.11447368421052631$$