Solve 1/2:(-3/2)^2+5(1-4/5)=

$$\frac { 1 } { 2 } : ( - \frac { 3 } { 2 } ) ^ { 2 } + 5 ( 1 - \frac { 4 } { 5 } ) =$$

Evaluate

$$\frac{11}{9}\approx 1.222222222$$

Solution Steps

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{\frac{1}{2}}{\frac{9}{4}}+5\left(1-\frac{4}{5}\right)$$

Divide \frac{1}{2} by \frac{9}{4} by multiplying \frac{1}{2} by the reciprocal of \frac{9}{4}.

$$\frac{1}{2}\times \frac{4}{9}+5\left(1-\frac{4}{5}\right)$$

Multiply \frac{1}{2} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{2\times 9}+5\left(1-\frac{4}{5}\right)$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 9}.

$$\frac{4}{18}+5\left(1-\frac{4}{5}\right)$$

Reduce the fraction \frac{4}{18} to lowest terms by extracting and canceling out 2.

$$\frac{2}{9}+5\left(1-\frac{4}{5}\right)$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{2}{9}+5\left(\frac{5}{5}-\frac{4}{5}\right)$$

Since \frac{5}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 5 to get 1.

$$\frac{2}{9}+5\times \frac{1}{5}$$

Cancel out 5 and 5.

$$\frac{2}{9}+1$$

Convert 1 to fraction \frac{9}{9}.

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

Since \frac{2}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

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

Add 2 and 9 to get 11.

$$\frac{11}{9}$$

Factor

$$\frac{11}{3 ^ {2}} = 1\frac{2}{9} = 1.2222222222222223$$