Solve (2)4/9div(-22/3)-(-1/2)^2

$$( 2 ) \frac { 4 } { 9 } \div ( - 2 \frac { 2 } { 3 } ) - ( - \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$-\frac{7}{12}\approx -0.583333333$$

Solution Steps

Express 2\times \frac{4}{9} as a single fraction.

$$\frac{\frac{2\times 4}{9}}{-\frac{2\times 3+2}{3}}-\left(-\frac{1}{2}\right)^{2}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{8}{9}}{-\frac{2\times 3+2}{3}}-\left(-\frac{1}{2}\right)^{2}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{8}{9}}{-\frac{6+2}{3}}-\left(-\frac{1}{2}\right)^{2}$$

Add 6 and 2 to get 8.

$$\frac{\frac{8}{9}}{-\frac{8}{3}}-\left(-\frac{1}{2}\right)^{2}$$

Divide \frac{8}{9} by -\frac{8}{3} by multiplying \frac{8}{9} by the reciprocal of -\frac{8}{3}.

$$\frac{8}{9}\left(-\frac{3}{8}\right)-\left(-\frac{1}{2}\right)^{2}$$

Multiply \frac{8}{9} times -\frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\left(-3\right)}{9\times 8}-\left(-\frac{1}{2}\right)^{2}$$

Cancel out 8 in both numerator and denominator.

$$\frac{-3}{9}-\left(-\frac{1}{2}\right)^{2}$$

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

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

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

$$-\frac{1}{3}-\frac{1}{4}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$-\frac{4}{12}-\frac{3}{12}$$

Since -\frac{4}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4-3}{12}$$

Subtract 3 from -4 to get -7.

$$-\frac{7}{12}$$

Factor

$$-\frac{7}{12} = -0.5833333333333334$$