Solve (-11/4+2*3/5):(-1/4)^3+sqrt{25/36}=

$$( - \frac { 11 } { 4 } + 2 \cdot \frac { 3 } { 5 } ) : ( - \frac { 1 } { 4 } ) ^ { 3 } + \sqrt { \frac { 25 } { 36 } } =$$

Evaluate

$$\frac{3001}{30}\approx 100.033333333$$

Solution Steps

Express 2\times \frac{3}{5} as a single fraction.

$$\frac{-\frac{11}{4}+\frac{2\times 3}{5}}{\left(-\frac{1}{4}\right)^{3}}+\sqrt{\frac{25}{36}}$$

Multiply 2 and 3 to get 6.

$$\frac{-\frac{11}{4}+\frac{6}{5}}{\left(-\frac{1}{4}\right)^{3}}+\sqrt{\frac{25}{36}}$$

Least common multiple of 4 and 5 is 20. Convert -\frac{11}{4} and \frac{6}{5} to fractions with denominator 20.

$$\frac{-\frac{55}{20}+\frac{24}{20}}{\left(-\frac{1}{4}\right)^{3}}+\sqrt{\frac{25}{36}}$$

Since -\frac{55}{20} and \frac{24}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-55+24}{20}}{\left(-\frac{1}{4}\right)^{3}}+\sqrt{\frac{25}{36}}$$

Add -55 and 24 to get -31.

$$\frac{-\frac{31}{20}}{\left(-\frac{1}{4}\right)^{3}}+\sqrt{\frac{25}{36}}$$

Calculate -\frac{1}{4} to the power of 3 and get -\frac{1}{64}.

$$\frac{-\frac{31}{20}}{-\frac{1}{64}}+\sqrt{\frac{25}{36}}$$

Divide -\frac{31}{20} by -\frac{1}{64} by multiplying -\frac{31}{20} by the reciprocal of -\frac{1}{64}.

$$-\frac{31}{20}\left(-64\right)+\sqrt{\frac{25}{36}}$$

Express -\frac{31}{20}\left(-64\right) as a single fraction.

$$\frac{-31\left(-64\right)}{20}+\sqrt{\frac{25}{36}}$$

Multiply -31 and -64 to get 1984.

$$\frac{1984}{20}+\sqrt{\frac{25}{36}}$$

Reduce the fraction \frac{1984}{20} to lowest terms by extracting and canceling out 4.

$$\frac{496}{5}+\sqrt{\frac{25}{36}}$$

Rewrite the square root of the division \frac{25}{36} as the division of square roots \frac{\sqrt{25}}{\sqrt{36}}. Take the square root of both numerator and denominator.

$$\frac{496}{5}+\frac{5}{6}$$

Least common multiple of 5 and 6 is 30. Convert \frac{496}{5} and \frac{5}{6} to fractions with denominator 30.

$$\frac{2976}{30}+\frac{25}{30}$$

Since \frac{2976}{30} and \frac{25}{30} have the same denominator, add them by adding their numerators.

$$\frac{2976+25}{30}$$

Add 2976 and 25 to get 3001.

$$\frac{3001}{30}$$

Factor

$$\frac{3001}{2 \cdot 3 \cdot 5} = 100\frac{1}{30} = 100.03333333333333$$