Solve 3/3div(3/2-1)+(1-0.6)*(-5/2)^2]div(-5/3)-20}div(-1)^30

$$\frac { 3 } { 3 } \div ( \frac { 3 } { 2 } - 1 ) + ( 1 - 0.6 ) \times ( - \frac { 5 } { 2 } ) ^ { 2 } ] \div ( - \frac { 5 } { 3 } ) - 20 \} \div ( - 1 ) ^ { 30 }$$

Evaluate

$$4.5$$

Solution Steps

Divide 3 by 3 to get 1.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{3}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

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

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

$$1\times 2+\left(1-0.6\right)\left(-\frac{5}{2}\right)^{2}$$

Multiply 1 and 2 to get 2.

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

Subtract 0.6 from 1 to get 0.4.

$$2+0.4\left(-\frac{5}{2}\right)^{2}$$

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

$$2+0.4\times \frac{25}{4}$$

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.

$$2+\frac{2}{5}\times \frac{25}{4}$$

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

$$2+\frac{2\times 25}{5\times 4}$$

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

$$2+\frac{50}{20}$$

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

$$2+\frac{5}{2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{4}{2}+\frac{5}{2}$$

Since \frac{4}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{4+5}{2}$$

Add 4 and 5 to get 9.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$