Solve 2/3-1/2(8/3)^2-(1/3)^2

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

Evaluate

$$-3$$

Solution Steps

Calculate \frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\frac{2}{3}-\frac{1}{2}\times \frac{64}{9}-\left(\frac{1}{3}\right)^{2}$$

Multiply \frac{1}{2} times \frac{64}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{1\times 64}{2\times 9}-\left(\frac{1}{3}\right)^{2}$$

Do the multiplications in the fraction \frac{1\times 64}{2\times 9}.

$$\frac{2}{3}-\frac{64}{18}-\left(\frac{1}{3}\right)^{2}$$

Reduce the fraction \frac{64}{18} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}-\frac{32}{9}-\left(\frac{1}{3}\right)^{2}$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{32}{9} to fractions with denominator 9.

$$\frac{6}{9}-\frac{32}{9}-\left(\frac{1}{3}\right)^{2}$$

Since \frac{6}{9} and \frac{32}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-32}{9}-\left(\frac{1}{3}\right)^{2}$$

Subtract 32 from 6 to get -26.

$$-\frac{26}{9}-\left(\frac{1}{3}\right)^{2}$$

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

$$-\frac{26}{9}-\frac{1}{9}$$

Since -\frac{26}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-26-1}{9}$$

Subtract 1 from -26 to get -27.

$$\frac{-27}{9}$$

Divide -27 by 9 to get -3.

$$-3$$

Factor

$$-3$$