Solve {[33/4div(3/4-1)+(1-0.6)*(-5/2)^2]div(-5/3)-20}div(-1)^39

$$\{ [ 3 \frac { 3 } { 4 } \div ( \frac { 3 } { 4 } - 1 ) + ( 1 - 0.6 ) \times ( - \frac { 5 } { 2 } ) ^ { 2 } ] \div ( - \frac { 5 } { 3 } ) - 20 \} \div ( - 1 ) ^ { 39 }$$

Evaluate

$$12.5$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{\frac{\frac{\frac{12+3}{4}}{\frac{3}{4}-1}+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Add 12 and 3 to get 15.

$$\frac{\frac{\frac{\frac{15}{4}}{\frac{3}{4}-1}+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

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

$$\frac{\frac{\frac{\frac{15}{4}}{\frac{3}{4}-\frac{4}{4}}+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

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

$$\frac{\frac{\frac{\frac{15}{4}}{\frac{3-4}{4}}+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Subtract 4 from 3 to get -1.

$$\frac{\frac{\frac{\frac{15}{4}}{-\frac{1}{4}}+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

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

$$\frac{\frac{\frac{15}{4}\left(-4\right)+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

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

$$\frac{\frac{\frac{15\left(-4\right)}{4}+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Multiply 15 and -4 to get -60.

$$\frac{\frac{\frac{-60}{4}+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Divide -60 by 4 to get -15.

$$\frac{\frac{-15+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Subtract 0.6 from 1 to get 0.4.

$$\frac{\frac{-15+0.4\left(-\frac{5}{2}\right)^{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

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

$$\frac{\frac{-15+0.4\times \frac{25}{4}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{-15+\frac{2}{5}\times \frac{25}{4}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Multiply \frac{2}{5} times \frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-15+\frac{2\times 25}{5\times 4}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Do the multiplications in the fraction \frac{2\times 25}{5\times 4}.

$$\frac{\frac{-15+\frac{50}{20}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Reduce the fraction \frac{50}{20} to lowest terms by extracting and canceling out 10.

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

Convert -15 to fraction -\frac{30}{2}.

$$\frac{\frac{-\frac{30}{2}+\frac{5}{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Since -\frac{30}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{-30+5}{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Add -30 and 5 to get -25.

$$\frac{\frac{-\frac{25}{2}}{-\frac{5}{3}}-20}{\left(-1\right)^{39}}$$

Divide -\frac{25}{2} by -\frac{5}{3} by multiplying -\frac{25}{2} by the reciprocal of -\frac{5}{3}.

$$\frac{-\frac{25}{2}\left(-\frac{3}{5}\right)-20}{\left(-1\right)^{39}}$$

Multiply -\frac{25}{2} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-25\left(-3\right)}{2\times 5}-20}{\left(-1\right)^{39}}$$

Do the multiplications in the fraction \frac{-25\left(-3\right)}{2\times 5}.

$$\frac{\frac{75}{10}-20}{\left(-1\right)^{39}}$$

Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

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

Convert 20 to fraction \frac{40}{2}.

$$\frac{\frac{15}{2}-\frac{40}{2}}{\left(-1\right)^{39}}$$

Since \frac{15}{2} and \frac{40}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-40}{2}}{\left(-1\right)^{39}}$$

Subtract 40 from 15 to get -25.

$$\frac{-\frac{25}{2}}{\left(-1\right)^{39}}$$

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

$$\frac{-\frac{25}{2}}{-1}$$

Express \frac{-\frac{25}{2}}{-1} as a single fraction.

$$\frac{-25}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$\frac{-25}{-2}$$

Fraction \frac{-25}{-2} can be simplified to \frac{25}{2} by removing the negative sign from both the numerator and the denominator.

$$\frac{25}{2}$$

Factor

$$\frac{5 ^ {2}}{2} = 12\frac{1}{2} = 12.5$$