Solve 5{left(2/3right)}^2-8(2/3)-3

$$5 { \left( \frac{ 2 }{ 3 } \right) }^{ 2 } -8( \frac{ 2 }{ 3 } )-3$$

Evaluate

$$-\frac{55}{9}\approx -6.111111111$$

Solution Steps

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

$$5\times \frac{4}{9}-8\times \frac{2}{3}-3$$

Express 5\times \frac{4}{9} as a single fraction.

$$\frac{5\times 4}{9}-8\times \frac{2}{3}-3$$

Multiply 5 and 4 to get 20.

$$\frac{20}{9}-8\times \frac{2}{3}-3$$

Express 8\times \frac{2}{3} as a single fraction.

$$\frac{20}{9}-\frac{8\times 2}{3}-3$$

Multiply 8 and 2 to get 16.

$$\frac{20}{9}-\frac{16}{3}-3$$

Least common multiple of 9 and 3 is 9. Convert \frac{20}{9} and \frac{16}{3} to fractions with denominator 9.

$$\frac{20}{9}-\frac{48}{9}-3$$

Since \frac{20}{9} and \frac{48}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-48}{9}-3$$

Subtract 48 from 20 to get -28.

$$-\frac{28}{9}-3$$

Convert 3 to fraction \frac{27}{9}.

$$-\frac{28}{9}-\frac{27}{9}$$

Since -\frac{28}{9} and \frac{27}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-28-27}{9}$$

Subtract 27 from -28 to get -55.

$$-\frac{55}{9}$$

Factor

$$-\frac{55}{9} = -6\frac{1}{9} = -6.111111111111111$$