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

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

Evaluate

$$-\frac{3}{8}=-0.375$$

Solution Steps

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{3\times \frac{1}{16}+\frac{1}{4}}{3\left(-\frac{1}{3}\right)^{2}-\frac{3}{2}}$$

Multiply 3 and \frac{1}{16} to get \frac{3}{16}.

$$\frac{\frac{3}{16}+\frac{1}{4}}{3\left(-\frac{1}{3}\right)^{2}-\frac{3}{2}}$$

Least common multiple of 16 and 4 is 16. Convert \frac{3}{16} and \frac{1}{4} to fractions with denominator 16.

$$\frac{\frac{3}{16}+\frac{4}{16}}{3\left(-\frac{1}{3}\right)^{2}-\frac{3}{2}}$$

Since \frac{3}{16} and \frac{4}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+4}{16}}{3\left(-\frac{1}{3}\right)^{2}-\frac{3}{2}}$$

Add 3 and 4 to get 7.

$$\frac{\frac{7}{16}}{3\left(-\frac{1}{3}\right)^{2}-\frac{3}{2}}$$

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

$$\frac{\frac{7}{16}}{3\times \frac{1}{9}-\frac{3}{2}}$$

Multiply 3 and \frac{1}{9} to get \frac{3}{9}.

$$\frac{\frac{7}{16}}{\frac{3}{9}-\frac{3}{2}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{7}{16}}{\frac{1}{3}-\frac{3}{2}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{\frac{7}{16}}{\frac{2}{6}-\frac{9}{6}}$$

Since \frac{2}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{16}}{\frac{2-9}{6}}$$

Subtract 9 from 2 to get -7.

$$\frac{\frac{7}{16}}{-\frac{7}{6}}$$

Divide \frac{7}{16} by -\frac{7}{6} by multiplying \frac{7}{16} by the reciprocal of -\frac{7}{6}.

$$\frac{7}{16}\left(-\frac{6}{7}\right)$$

Multiply \frac{7}{16} times -\frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-6\right)}{16\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{-6}{16}$$

Reduce the fraction \frac{-6}{16} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{8}$$

Factor

$$-\frac{3}{8} = -0.375$$