Solve 6[2/3*(2/7-5/4-3/8)^2-(frac{7}{3}-frac{8}{4})^2:frac{27}{9}]:frac{3}{7}}

$$6 [ \frac { 2 } { 3 } \times ( \frac { 2 } { 7 } - \frac { 5 } { 4 } - \frac { 3 } { 8 } ) ^ { 2 } - ( \frac { 7 } { 3 } - \frac { 8 } { 4 } ) ^ { 2 } : \frac { 27 } { 9 } ] : \frac { 3 } { 7 } \}$$

Evaluate

$$\frac{49057}{3024}\approx 16.22255291$$

Solution Steps

Subtract \frac{5}{4} from \frac{2}{7} to get -\frac{27}{28}.

$$\frac{6\left(\frac{2}{3}\left(-\frac{27}{28}-\frac{3}{8}\right)^{2}-\frac{\left(\frac{7}{3}-\frac{8}{4}\right)^{2}}{\frac{27}{9}}\right)}{\frac{3}{7}}$$

Subtract \frac{3}{8} from -\frac{27}{28} to get -\frac{75}{56}.

$$\frac{6\left(\frac{2}{3}\left(-\frac{75}{56}\right)^{2}-\frac{\left(\frac{7}{3}-\frac{8}{4}\right)^{2}}{\frac{27}{9}}\right)}{\frac{3}{7}}$$

Calculate -\frac{75}{56} to the power of 2 and get \frac{5625}{3136}.

$$\frac{6\left(\frac{2}{3}\times \frac{5625}{3136}-\frac{\left(\frac{7}{3}-\frac{8}{4}\right)^{2}}{\frac{27}{9}}\right)}{\frac{3}{7}}$$

Multiply \frac{2}{3} and \frac{5625}{3136} to get \frac{1875}{1568}.

$$\frac{6\left(\frac{1875}{1568}-\frac{\left(\frac{7}{3}-\frac{8}{4}\right)^{2}}{\frac{27}{9}}\right)}{\frac{3}{7}}$$

Divide 8 by 4 to get 2.

$$\frac{6\left(\frac{1875}{1568}-\frac{\left(\frac{7}{3}-2\right)^{2}}{\frac{27}{9}}\right)}{\frac{3}{7}}$$

Subtract 2 from \frac{7}{3} to get \frac{1}{3}.

$$\frac{6\left(\frac{1875}{1568}-\frac{\left(\frac{1}{3}\right)^{2}}{\frac{27}{9}}\right)}{\frac{3}{7}}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{6\left(\frac{1875}{1568}-\frac{\frac{1}{9}}{\frac{27}{9}}\right)}{\frac{3}{7}}$$

Divide 27 by 9 to get 3.

$$\frac{6\left(\frac{1875}{1568}-\frac{\frac{1}{9}}{3}\right)}{\frac{3}{7}}$$

Express \frac{\frac{1}{9}}{3} as a single fraction.

$$\frac{6\left(\frac{1875}{1568}-\frac{1}{9\times 3}\right)}{\frac{3}{7}}$$

Multiply 9 and 3 to get 27.

$$\frac{6\left(\frac{1875}{1568}-\frac{1}{27}\right)}{\frac{3}{7}}$$

Subtract \frac{1}{27} from \frac{1875}{1568} to get \frac{49057}{42336}.

$$\frac{6\times \frac{49057}{42336}}{\frac{3}{7}}$$

Multiply 6 and \frac{49057}{42336} to get \frac{49057}{7056}.

$$\frac{\frac{49057}{7056}}{\frac{3}{7}}$$

Divide \frac{49057}{7056} by \frac{3}{7} by multiplying \frac{49057}{7056} by the reciprocal of \frac{3}{7}.

$$\frac{49057}{7056}\times \frac{7}{3}$$

Multiply \frac{49057}{7056} and \frac{7}{3} to get \frac{49057}{3024}.

$$\frac{49057}{3024}$$

Factor

$$\frac{49057}{2 ^ {4} \cdot 3 ^ {3} \cdot 7} = 16\frac{673}{3024} = 16.22255291005291$$