Solve (1/2+2/3-3/3)*(2+1/3-2frac{1}{9})

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

Evaluate

$$\frac{1}{27}\approx 0.037037037$$

Solution Steps

Divide 3 by 3 to get 1.

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

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\left(\frac{3}{6}+\frac{4}{6}-1\right)\left(2+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\left(\frac{3+4}{6}-1\right)\left(2+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

Add 3 and 4 to get 7.

$$\left(\frac{7}{6}-1\right)\left(2+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

Convert 1 to fraction \frac{6}{6}.

$$\left(\frac{7}{6}-\frac{6}{6}\right)\left(2+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

Since \frac{7}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-6}{6}\left(2+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

Subtract 6 from 7 to get 1.

$$\frac{1}{6}\left(2+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

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

$$\frac{1}{6}\left(\frac{6}{3}+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

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

$$\frac{1}{6}\left(\frac{6+1}{3}-\frac{2\times 9+1}{9}\right)$$

Add 6 and 1 to get 7.

$$\frac{1}{6}\left(\frac{7}{3}-\frac{2\times 9+1}{9}\right)$$

Multiply 2 and 9 to get 18.

$$\frac{1}{6}\left(\frac{7}{3}-\frac{18+1}{9}\right)$$

Add 18 and 1 to get 19.

$$\frac{1}{6}\left(\frac{7}{3}-\frac{19}{9}\right)$$

Least common multiple of 3 and 9 is 9. Convert \frac{7}{3} and \frac{19}{9} to fractions with denominator 9.

$$\frac{1}{6}\left(\frac{21}{9}-\frac{19}{9}\right)$$

Since \frac{21}{9} and \frac{19}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}\times \frac{21-19}{9}$$

Subtract 19 from 21 to get 2.

$$\frac{1}{6}\times \frac{2}{9}$$

Multiply \frac{1}{6} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{6\times 9}$$

Do the multiplications in the fraction \frac{1\times 2}{6\times 9}.

$$\frac{2}{54}$$

Reduce the fraction \frac{2}{54} to lowest terms by extracting and canceling out 2.

$$\frac{1}{27}$$

Factor

$$\frac{1}{3 ^ {3}} = 0.037037037037037035$$