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

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

Evaluate

$$-\frac{53}{9}\approx -5.888888889$$

Solution Steps

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

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

Since \frac{1}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

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

Add 1 and 9 to get 10.

$$\frac{10}{3}\left(\frac{1}{3}-2\right)-\frac{1}{3}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{10}{3}\left(\frac{1}{3}-\frac{6}{3}\right)-\frac{1}{3}$$

Since \frac{1}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}\times \frac{1-6}{3}-\frac{1}{3}$$

Subtract 6 from 1 to get -5.

$$\frac{10}{3}\left(-\frac{5}{3}\right)-\frac{1}{3}$$

Multiply \frac{10}{3} times -\frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\left(-5\right)}{3\times 3}-\frac{1}{3}$$

Do the multiplications in the fraction \frac{10\left(-5\right)}{3\times 3}.

$$\frac{-50}{9}-\frac{1}{3}$$

Fraction \frac{-50}{9} can be rewritten as -\frac{50}{9} by extracting the negative sign.

$$-\frac{50}{9}-\frac{1}{3}$$

Least common multiple of 9 and 3 is 9. Convert -\frac{50}{9} and \frac{1}{3} to fractions with denominator 9.

$$-\frac{50}{9}-\frac{3}{9}$$

Since -\frac{50}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-50-3}{9}$$

Subtract 3 from -50 to get -53.

$$-\frac{53}{9}$$

Factor

$$-\frac{53}{9} = -5\frac{8}{9} = -5.888888888888889$$