Solve 3/5+(4/5+8/15-1/6)^2:(frac{13}{3}-frac{11}{4}-1)+frac{8}{3}-frac{2}{3}*(+frac{18}{5})

$$\frac { 3 } { 5 } + ( \frac { 4 } { 5 } + \frac { 8 } { 15 } - \frac { 1 } { 6 } ) ^ { 2 } : ( \frac { 13 } { 3 } - \frac { 11 } { 4 } - 1 ) + \frac { 8 } { 3 } - \frac { 2 } { 3 } \cdot ( + \frac { 18 } { 5 } )$$

Evaluate

$$\frac{16}{5}=3.2$$

Solution Steps

Add \frac{4}{5} and \frac{8}{15} to get \frac{4}{3}.

$$\frac{3}{5}+\frac{\left(\frac{4}{3}-\frac{1}{6}\right)^{2}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Subtract \frac{1}{6} from \frac{4}{3} to get \frac{7}{6}.

$$\frac{3}{5}+\frac{\left(\frac{7}{6}\right)^{2}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Calculate \frac{7}{6} to the power of 2 and get \frac{49}{36}.

$$\frac{3}{5}+\frac{\frac{49}{36}}{\frac{13}{3}-\frac{11}{4}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Subtract \frac{11}{4} from \frac{13}{3} to get \frac{19}{12}.

$$\frac{3}{5}+\frac{\frac{49}{36}}{\frac{19}{12}-1}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Subtract 1 from \frac{19}{12} to get \frac{7}{12}.

$$\frac{3}{5}+\frac{\frac{49}{36}}{\frac{7}{12}}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Divide \frac{49}{36} by \frac{7}{12} by multiplying \frac{49}{36} by the reciprocal of \frac{7}{12}.

$$\frac{3}{5}+\frac{49}{36}\times \frac{12}{7}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Multiply \frac{49}{36} and \frac{12}{7} to get \frac{7}{3}.

$$\frac{3}{5}+\frac{7}{3}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Add \frac{3}{5} and \frac{7}{3} to get \frac{44}{15}.

$$\frac{44}{15}+\frac{8}{3}-\frac{2}{3}\times \frac{18}{5}$$

Add \frac{44}{15} and \frac{8}{3} to get \frac{28}{5}.

$$\frac{28}{5}-\frac{2}{3}\times \frac{18}{5}$$

Multiply \frac{2}{3} and \frac{18}{5} to get \frac{12}{5}.

$$\frac{28}{5}-\frac{12}{5}$$

Subtract \frac{12}{5} from \frac{28}{5} to get \frac{16}{5}.

$$\frac{16}{5}$$

Factor

$$\frac{2 ^ {4}}{5} = 3\frac{1}{5} = 3.2$$