Solve {[33/4div(3/4-1)+(1-06)*(-5/2)^2]div(-5/3)-20}div(-1)^39

$$\{ [ 3 \frac { 3 } { 4 } \div ( \frac { 3 } { 4 } - 1 ) + ( 1 - 06 ) \times ( - \frac { 5 } { 2 } ) ^ { 2 } ] \div ( - \frac { 5 } { 3 } ) - 20 \} \div ( - 1 ) ^ { 39 }$$

Evaluate

$$\frac{59}{4}=14.75$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{\frac{\frac{\frac{12+3}{4}}{\frac{3}{4}-1}+\left(1-0\times 6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Add 12 and 3 to get 15.

$$\frac{\frac{\frac{\frac{15}{4}}{\frac{3}{4}-1}+\left(1-0\times 6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{\frac{\frac{15}{4}}{\frac{3}{4}-\frac{4}{4}}+\left(1-0\times 6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Since \frac{3}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{\frac{15}{4}}{\frac{3-4}{4}}+\left(1-0\times 6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Subtract 4 from 3 to get -1.

$$\frac{\frac{\frac{\frac{15}{4}}{-\frac{1}{4}}+\left(1-0\times 6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Divide \frac{15}{4} by -\frac{1}{4} by multiplying \frac{15}{4} by the reciprocal of -\frac{1}{4}.

$$\frac{\frac{\frac{15}{4}\left(-4\right)+\left(1-0\times 6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Express \frac{15}{4}\left(-4\right) as a single fraction.

$$\frac{\frac{\frac{15\left(-4\right)}{4}+\left(1-0\times 6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Multiply 15 and -4 to get -60.

$$\frac{\frac{\frac{-60}{4}+\left(1-0\times 6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Divide -60 by 4 to get -15.

$$\frac{\frac{-15+\left(1-0\times 6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Multiply 0 and 6 to get 0.

$$\frac{\frac{-15+\left(1-0\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Subtract 0 from 1 to get 1.

$$\frac{\frac{-15+1\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Calculate -\frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{\frac{-15+1\times \frac{25}{4}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Multiply 1 and \frac{25}{4} to get \frac{25}{4}.

$$\frac{\frac{-15+\frac{25}{4}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Convert -15 to fraction -\frac{60}{4}.

$$\frac{\frac{-\frac{60}{4}+\frac{25}{4}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Since -\frac{60}{4} and \frac{25}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{-60+25}{4}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Add -60 and 25 to get -35.

$$\frac{\frac{-\frac{35}{4}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Divide -\frac{35}{4} by -\frac{5}{3} by multiplying -\frac{35}{4} by the reciprocal of -\frac{5}{3}.

$$\frac{-\frac{35}{4}\left(-\frac{3}{5}\right)-20}{\left(-1\right)^{39}}$$

Multiply -\frac{35}{4} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-35\left(-3\right)}{4\times 5}-20}{\left(-1\right)^{39}}$$

Do the multiplications in the fraction \frac{-35\left(-3\right)}{4\times 5}.

$$\frac{\frac{105}{20}-20}{\left(-1\right)^{39}}$$

Reduce the fraction \frac{105}{20} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{21}{4}-20}{\left(-1\right)^{39}}$$

Convert 20 to fraction \frac{80}{4}.

$$\frac{\frac{21}{4}-\frac{80}{4}}{\left(-1\right)^{39}}$$

Since \frac{21}{4} and \frac{80}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21-80}{4}}{\left(-1\right)^{39}}$$

Subtract 80 from 21 to get -59.

$$\frac{-\frac{59}{4}}{\left(-1\right)^{39}}$$

Calculate -1 to the power of 39 and get -1.

$$\frac{-\frac{59}{4}}{-1}$$

Express \frac{-\frac{59}{4}}{-1} as a single fraction.

$$\frac{-59}{4\left(-1\right)}$$

Multiply 4 and -1 to get -4.

$$\frac{-59}{-4}$$

Fraction \frac{-59}{-4} can be simplified to \frac{59}{4} by removing the negative sign from both the numerator and the denominator.

$$\frac{59}{4}$$

Factor

$$\frac{59}{2 ^ {2}} = 14\frac{3}{4} = 14.75$$