Solve 36/5/{left(-frac{5{8}right)}^-1}+sqrt{27/16-1/8}-frac{13}{4}

$$\frac{ \frac{ 36 }{ 5 } }{ { \left(- \frac{ 5 }{ 8 } \right) }^{ -1 } } + \sqrt{ \frac{ 27 }{ 16 } - \frac{ 1 }{ 8 } } - \frac{ 13 }{ 4 }$$

Evaluate

$$-\frac{13}{2}=-6.5$$

Solution Steps

Calculate -\frac{5}{8} to the power of -1 and get -\frac{8}{5}.

$$\frac{\frac{36}{5}}{-\frac{8}{5}}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}$$

Divide \frac{36}{5} by -\frac{8}{5} by multiplying \frac{36}{5} by the reciprocal of -\frac{8}{5}.

$$\frac{36}{5}\left(-\frac{5}{8}\right)+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}$$

Multiply \frac{36}{5} and -\frac{5}{8} to get -\frac{9}{2}.

$$-\frac{9}{2}+\sqrt{\frac{27}{16}-\frac{1}{8}}-\frac{13}{4}$$

Subtract \frac{1}{8} from \frac{27}{16} to get \frac{25}{16}.

$$-\frac{9}{2}+\sqrt{\frac{25}{16}}-\frac{13}{4}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$-\frac{9}{2}+\frac{5}{4}-\frac{13}{4}$$

Add -\frac{9}{2} and \frac{5}{4} to get -\frac{13}{4}.

$$-\frac{13}{4}-\frac{13}{4}$$

Subtract \frac{13}{4} from -\frac{13}{4} to get -\frac{13}{2}.

$$-\frac{13}{2}$$

Factor

$$-\frac{13}{2} = -6\frac{1}{2} = -6.5$$