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

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

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

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

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

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

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

Since -\frac{1}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{9}-\frac{-1-9}{3}-3$$

Subtract 9 from -1 to get -10.

$$\frac{1}{9}-\left(-\frac{10}{3}\right)-3$$

The opposite of -\frac{10}{3} is \frac{10}{3}.

$$\frac{1}{9}+\frac{10}{3}-3$$

Least common multiple of 9 and 3 is 9. Convert \frac{1}{9} and \frac{10}{3} to fractions with denominator 9.

$$\frac{1}{9}+\frac{30}{9}-3$$

Since \frac{1}{9} and \frac{30}{9} have the same denominator, add them by adding their numerators.

$$\frac{1+30}{9}-3$$

Add 1 and 30 to get 31.

$$\frac{31}{9}-3$$

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

$$\frac{31}{9}-\frac{27}{9}$$

Since \frac{31}{9} and \frac{27}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31-27}{9}$$

Subtract 27 from 31 to get 4.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$