Solve 1/3+(-1/9)+1/27+(-1/81)

$$\frac { 1 } { 3 } + ( - \frac { 1 } { 9 } ) + \frac { 1 } { 27 } + ( - \frac { 1 } { 81 } )$$

Evaluate

$$\frac{20}{81}\approx 0.24691358$$

Solution Steps

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

$$\frac{3}{9}-\frac{1}{9}+\frac{1}{27}-\frac{1}{81}$$

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

$$\frac{3-1}{9}+\frac{1}{27}-\frac{1}{81}$$

Subtract 1 from 3 to get 2.

$$\frac{2}{9}+\frac{1}{27}-\frac{1}{81}$$

Least common multiple of 9 and 27 is 27. Convert \frac{2}{9} and \frac{1}{27} to fractions with denominator 27.

$$\frac{6}{27}+\frac{1}{27}-\frac{1}{81}$$

Since \frac{6}{27} and \frac{1}{27} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{27}-\frac{1}{81}$$

Add 6 and 1 to get 7.

$$\frac{7}{27}-\frac{1}{81}$$

Least common multiple of 27 and 81 is 81. Convert \frac{7}{27} and \frac{1}{81} to fractions with denominator 81.

$$\frac{21}{81}-\frac{1}{81}$$

Since \frac{21}{81} and \frac{1}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-1}{81}$$

Subtract 1 from 21 to get 20.

$$\frac{20}{81}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{3 ^ {4}} = 0.24691358024691357$$