Solve (1/2)^2+7/5:(-3-4/15)*(-frac{14/9)+frac{5}{24}}{-frac{3}{2}*(frac{5}{4}+frac{1}{12}-1-frac{1}{5}*frac{10}{3})^2}

$$\frac { ( \frac { 1 } { 2 } ) ^ { 2 } + \frac { 7 } { 5 } : ( - 3 - \frac { 4 } { 15 } ) \cdot ( - \frac { 14 } { 9 } ) + \frac { 5 } { 24 } } { - \frac { 3 } { 2 } \cdot ( \frac { 5 } { 4 } + \frac { 1 } { 12 } - 1 - \frac { 1 } { 5 } \cdot \frac { 10 } { 3 } ) ^ { 2 } }$$

Evaluate

$$-\frac{27}{4}=-6.75$$

Solution Steps

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}+\frac{\frac{7}{5}}{-3-\frac{4}{15}}\left(-\frac{14}{9}\right)+\frac{5}{24}}{-\frac{3}{2}\left(\frac{5}{4}+\frac{1}{12}-1-\frac{1}{5}\times \frac{10}{3}\right)^{2}}$$

Subtract \frac{4}{15} from -3 to get -\frac{49}{15}.

$$\frac{\frac{1}{4}+\frac{\frac{7}{5}}{-\frac{49}{15}}\left(-\frac{14}{9}\right)+\frac{5}{24}}{-\frac{3}{2}\left(\frac{5}{4}+\frac{1}{12}-1-\frac{1}{5}\times \frac{10}{3}\right)^{2}}$$

Divide \frac{7}{5} by -\frac{49}{15} by multiplying \frac{7}{5} by the reciprocal of -\frac{49}{15}.

$$\frac{\frac{1}{4}+\frac{7}{5}\left(-\frac{15}{49}\right)\left(-\frac{14}{9}\right)+\frac{5}{24}}{-\frac{3}{2}\left(\frac{5}{4}+\frac{1}{12}-1-\frac{1}{5}\times \frac{10}{3}\right)^{2}}$$

Multiply \frac{7}{5} and -\frac{15}{49} to get -\frac{3}{7}.

$$\frac{\frac{1}{4}-\frac{3}{7}\left(-\frac{14}{9}\right)+\frac{5}{24}}{-\frac{3}{2}\left(\frac{5}{4}+\frac{1}{12}-1-\frac{1}{5}\times \frac{10}{3}\right)^{2}}$$

Multiply -\frac{3}{7} and -\frac{14}{9} to get \frac{2}{3}.

$$\frac{\frac{1}{4}+\frac{2}{3}+\frac{5}{24}}{-\frac{3}{2}\left(\frac{5}{4}+\frac{1}{12}-1-\frac{1}{5}\times \frac{10}{3}\right)^{2}}$$

Add \frac{1}{4} and \frac{2}{3} to get \frac{11}{12}.

$$\frac{\frac{11}{12}+\frac{5}{24}}{-\frac{3}{2}\left(\frac{5}{4}+\frac{1}{12}-1-\frac{1}{5}\times \frac{10}{3}\right)^{2}}$$

Add \frac{11}{12} and \frac{5}{24} to get \frac{9}{8}.

$$\frac{\frac{9}{8}}{-\frac{3}{2}\left(\frac{5}{4}+\frac{1}{12}-1-\frac{1}{5}\times \frac{10}{3}\right)^{2}}$$

Add \frac{5}{4} and \frac{1}{12} to get \frac{4}{3}.

$$\frac{\frac{9}{8}}{-\frac{3}{2}\left(\frac{4}{3}-1-\frac{1}{5}\times \frac{10}{3}\right)^{2}}$$

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

$$\frac{\frac{9}{8}}{-\frac{3}{2}\left(\frac{1}{3}-\frac{1}{5}\times \frac{10}{3}\right)^{2}}$$

Multiply \frac{1}{5} and \frac{10}{3} to get \frac{2}{3}.

$$\frac{\frac{9}{8}}{-\frac{3}{2}\left(\frac{1}{3}-\frac{2}{3}\right)^{2}}$$

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

$$\frac{\frac{9}{8}}{-\frac{3}{2}\left(-\frac{1}{3}\right)^{2}}$$

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

$$\frac{\frac{9}{8}}{-\frac{3}{2}\times \frac{1}{9}}$$

Multiply -\frac{3}{2} and \frac{1}{9} to get -\frac{1}{6}.

$$\frac{\frac{9}{8}}{-\frac{1}{6}}$$

Divide \frac{9}{8} by -\frac{1}{6} by multiplying \frac{9}{8} by the reciprocal of -\frac{1}{6}.

$$\frac{9}{8}\left(-6\right)$$

Multiply \frac{9}{8} and -6 to get -\frac{27}{4}.

$$-\frac{27}{4}$$

Factor

$$-\frac{27}{4} = -6\frac{3}{4} = -6.75$$