Solve 1-1/3+1/9-1/27

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

Evaluate

$$\frac{20}{27}\approx 0.740740741$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

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

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

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

Subtract 1 from 3 to get 2.

$$\frac{2}{3}+\frac{1}{9}-\frac{1}{27}$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{6}{9}+\frac{1}{9}-\frac{1}{27}$$

Since \frac{6}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{9}-\frac{1}{27}$$

Add 6 and 1 to get 7.

$$\frac{7}{9}-\frac{1}{27}$$

Least common multiple of 9 and 27 is 27. Convert \frac{7}{9} and \frac{1}{27} to fractions with denominator 27.

$$\frac{21}{27}-\frac{1}{27}$$

Since \frac{21}{27} and \frac{1}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-1}{27}$$

Subtract 1 from 21 to get 20.

$$\frac{20}{27}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{3 ^ {3}} = 0.7407407407407407$$