Solve -(2/3)^2+7(2/3)-5

$$- ( \frac { 2 } { 3 } ) ^ { 2 } + 7 ( \frac { 2 } { 3 } ) - 5$$

Evaluate

$$-\frac{7}{9}\approx -0.777777778$$

Solution Steps

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

$$-\frac{4}{9}+7\times \frac{2}{3}-5$$

Express 7\times \frac{2}{3} as a single fraction.

$$-\frac{4}{9}+\frac{7\times 2}{3}-5$$

Multiply 7 and 2 to get 14.

$$-\frac{4}{9}+\frac{14}{3}-5$$

Least common multiple of 9 and 3 is 9. Convert -\frac{4}{9} and \frac{14}{3} to fractions with denominator 9.

$$-\frac{4}{9}+\frac{42}{9}-5$$

Since -\frac{4}{9} and \frac{42}{9} have the same denominator, add them by adding their numerators.

$$\frac{-4+42}{9}-5$$

Add -4 and 42 to get 38.

$$\frac{38}{9}-5$$

Convert 5 to fraction \frac{45}{9}.

$$\frac{38}{9}-\frac{45}{9}$$

Since \frac{38}{9} and \frac{45}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{38-45}{9}$$

Subtract 45 from 38 to get -7.

$$-\frac{7}{9}$$

Factor

$$-\frac{7}{9} = -0.7777777777777778$$