Solve (1/3+1/9)(2/3-3)

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

Evaluate

$$-\frac{28}{27}\approx -1.037037037$$

Solution Steps

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

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

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

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

Add 3 and 1 to get 4.

$$\frac{4}{9}\left(\frac{2}{3}-3\right)$$

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

$$\frac{4}{9}\left(\frac{2}{3}-\frac{9}{3}\right)$$

Since \frac{2}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 9 from 2 to get -7.

$$\frac{4}{9}\left(-\frac{7}{3}\right)$$

Multiply \frac{4}{9} times -\frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-7\right)}{9\times 3}$$

Do the multiplications in the fraction \frac{4\left(-7\right)}{9\times 3}.

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

Fraction \frac{-28}{27} can be rewritten as -\frac{28}{27} by extracting the negative sign.

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

Factor

$$-\frac{28}{27} = -1\frac{1}{27} = -1.037037037037037$$