Solve -2/3+{left(2/3right)}^2-2/3+51/3=

$$\frac{ -2 }{ 3 } + { \left( \frac{ 2 }{ 3 } \right) }^{ 2 } - \frac{ 2 }{ 3 } + \frac{ 51 }{ 3 } =$$

Evaluate

$$\frac{145}{9}\approx 16.111111111$$

Solution Steps

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$-\frac{2}{3}+\left(\frac{2}{3}\right)^{2}-\frac{2}{3}+\frac{51}{3}$$

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

$$-\frac{2}{3}+\frac{4}{9}-\frac{2}{3}+\frac{51}{3}$$

Least common multiple of 3 and 9 is 9. Convert -\frac{2}{3} and \frac{4}{9} to fractions with denominator 9.

$$-\frac{6}{9}+\frac{4}{9}-\frac{2}{3}+\frac{51}{3}$$

Since -\frac{6}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{-6+4}{9}-\frac{2}{3}+\frac{51}{3}$$

Add -6 and 4 to get -2.

$$-\frac{2}{9}-\frac{2}{3}+\frac{51}{3}$$

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

$$-\frac{2}{9}-\frac{6}{9}+\frac{51}{3}$$

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

$$\frac{-2-6}{9}+\frac{51}{3}$$

Subtract 6 from -2 to get -8.

$$-\frac{8}{9}+\frac{51}{3}$$

Divide 51 by 3 to get 17.

$$-\frac{8}{9}+17$$

Convert 17 to fraction \frac{153}{9}.

$$-\frac{8}{9}+\frac{153}{9}$$

Since -\frac{8}{9} and \frac{153}{9} have the same denominator, add them by adding their numerators.

$$\frac{-8+153}{9}$$

Add -8 and 153 to get 145.

$$\frac{145}{9}$$

Factor

$$\frac{5 \cdot 29}{3 ^ {2}} = 16\frac{1}{9} = 16.11111111111111$$