Solve 1/5--1/9+-5/9-0.2

$$\frac{ 1 }{ 5 } -- \frac{ 1 }{ 9 } +- \frac{ 5 }{ 9 } -0.2$$

Evaluate

$$-\frac{4}{9}\approx -0.444444444$$

Solution Steps

The opposite of -\frac{1}{9} is \frac{1}{9}.

$$\frac{1}{5}+\frac{1}{9}-\frac{5}{9}-0.2$$

Least common multiple of 5 and 9 is 45. Convert \frac{1}{5} and \frac{1}{9} to fractions with denominator 45.

$$\frac{9}{45}+\frac{5}{45}-\frac{5}{9}-0.2$$

Since \frac{9}{45} and \frac{5}{45} have the same denominator, add them by adding their numerators.

$$\frac{9+5}{45}-\frac{5}{9}-0.2$$

Add 9 and 5 to get 14.

$$\frac{14}{45}-\frac{5}{9}-0.2$$

Least common multiple of 45 and 9 is 45. Convert \frac{14}{45} and \frac{5}{9} to fractions with denominator 45.

$$\frac{14}{45}-\frac{25}{45}-0.2$$

Since \frac{14}{45} and \frac{25}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-25}{45}-0.2$$

Subtract 25 from 14 to get -11.

$$-\frac{11}{45}-0.2$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{45}-\frac{1}{5}$$

Least common multiple of 45 and 5 is 45. Convert -\frac{11}{45} and \frac{1}{5} to fractions with denominator 45.

$$-\frac{11}{45}-\frac{9}{45}$$

Since -\frac{11}{45} and \frac{9}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-9}{45}$$

Subtract 9 from -11 to get -20.

$$\frac{-20}{45}$$

Reduce the fraction \frac{-20}{45} to lowest terms by extracting and canceling out 5.

$$-\frac{4}{9}$$

Factor

$$-\frac{4}{9} = -0.4444444444444444$$