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

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

Evaluate

$$-\frac{5}{18}\approx -0.277777778$$

Solution Steps

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

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

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since \frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{9}\times \frac{1-2}{4}-\frac{2}{3}\times \frac{1}{4}$$

Subtract 2 from 1 to get -1.

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

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

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

Cancel out 4 in both numerator and denominator.

$$\frac{-1}{9}-\frac{2}{3}\times \frac{1}{4}$$

Fraction \frac{-1}{9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$-\frac{1}{9}-\frac{2}{3}\times \frac{1}{4}$$

Multiply \frac{2}{3} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{9}-\frac{2\times 1}{3\times 4}$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 4}.

$$-\frac{1}{9}-\frac{2}{12}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{9}-\frac{1}{6}$$

Least common multiple of 9 and 6 is 18. Convert -\frac{1}{9} and \frac{1}{6} to fractions with denominator 18.

$$-\frac{2}{18}-\frac{3}{18}$$

Since -\frac{2}{18} and \frac{3}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2-3}{18}$$

Subtract 3 from -2 to get -5.

$$-\frac{5}{18}$$

Factor

$$-\frac{5}{18} = -0.2777777777777778$$