Solve 3*(1/2)^2+1/4/2*(-frac{1{3})^2-3/2}

$$\frac { 3 \cdot ( \frac { 1 } { 2 } ) ^ { 2 } + \frac { 1 } { 4 } } { 2 \cdot ( - \frac { 1 } { 3 } ) ^ { 2 } - \frac { 3 } { 2 } }$$

Evaluate

$$-\frac{18}{23}\approx -0.782608696$$

Solution Steps

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{3\times \frac{1}{4}+\frac{1}{4}}{2\left(-\frac{1}{3}\right)^{2}-\frac{3}{2}}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{\frac{3}{4}+\frac{1}{4}}{2\left(-\frac{1}{3}\right)^{2}-\frac{3}{2}}$$

Since \frac{3}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+1}{4}}{2\left(-\frac{1}{3}\right)^{2}-\frac{3}{2}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{4}{4}}{2\left(-\frac{1}{3}\right)^{2}-\frac{3}{2}}$$

Divide 4 by 4 to get 1.

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

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{2\times \frac{1}{9}-\frac{3}{2}}$$

Multiply 2 and \frac{1}{9} to get \frac{2}{9}.

$$\frac{1}{\frac{2}{9}-\frac{3}{2}}$$

Least common multiple of 9 and 2 is 18. Convert \frac{2}{9} and \frac{3}{2} to fractions with denominator 18.

$$\frac{1}{\frac{4}{18}-\frac{27}{18}}$$

Since \frac{4}{18} and \frac{27}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{4-27}{18}}$$

Subtract 27 from 4 to get -23.

$$\frac{1}{-\frac{23}{18}}$$

Divide 1 by -\frac{23}{18} by multiplying 1 by the reciprocal of -\frac{23}{18}.

$$1\left(-\frac{18}{23}\right)$$

Multiply 1 and -\frac{18}{23} to get -\frac{18}{23}.

$$-\frac{18}{23}$$

Factor

$$-\frac{18}{23} = -0.782608695652174$$