Solve 1/5-(-1/9)+(-51/3)+5/9-0,2

$$\frac { 1 } { 5 } - ( - \frac { 1 } { 9 } ) + ( - 5 \frac { 1 } { 3 } ) + \frac { 5 } { 9 } - 0,2$$

Evaluate

$$-\frac{14}{3}\approx -4,666666667$$

Solution Steps

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

$$\frac{1}{5}+\frac{1}{9}-\frac{5\times 3+1}{3}+\frac{5}{9}-0,2$$

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

$$\frac{9}{45}+\frac{5}{45}-\frac{5\times 3+1}{3}+\frac{5}{9}-0,2$$

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

$$\frac{9+5}{45}-\frac{5\times 3+1}{3}+\frac{5}{9}-0,2$$

Add 9 and 5 to get 14.

$$\frac{14}{45}-\frac{5\times 3+1}{3}+\frac{5}{9}-0,2$$

Multiply 5 and 3 to get 15.

$$\frac{14}{45}-\frac{15+1}{3}+\frac{5}{9}-0,2$$

Add 15 and 1 to get 16.

$$\frac{14}{45}-\frac{16}{3}+\frac{5}{9}-0,2$$

Least common multiple of 45 and 3 is 45. Convert \frac{14}{45} and \frac{16}{3} to fractions with denominator 45.

$$\frac{14}{45}-\frac{240}{45}+\frac{5}{9}-0,2$$

Since \frac{14}{45} and \frac{240}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-240}{45}+\frac{5}{9}-0,2$$

Subtract 240 from 14 to get -226.

$$-\frac{226}{45}+\frac{5}{9}-0,2$$

Least common multiple of 45 and 9 is 45. Convert -\frac{226}{45} and \frac{5}{9} to fractions with denominator 45.

$$-\frac{226}{45}+\frac{25}{45}-0,2$$

Since -\frac{226}{45} and \frac{25}{45} have the same denominator, add them by adding their numerators.

$$\frac{-226+25}{45}-0,2$$

Add -226 and 25 to get -201.

$$\frac{-201}{45}-0,2$$

Reduce the fraction \frac{-201}{45} to lowest terms by extracting and canceling out 3.

$$-\frac{67}{15}-0,2$$

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.

$$-\frac{67}{15}-\frac{1}{5}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{67}{15} and \frac{1}{5} to fractions with denominator 15.

$$-\frac{67}{15}-\frac{3}{15}$$

Since -\frac{67}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-67-3}{15}$$

Subtract 3 from -67 to get -70.

$$\frac{-70}{15}$$

Reduce the fraction \frac{-70}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{14}{3}$$

Factor

$$-\frac{14}{3} = -4\frac{2}{3} = -4.666666666666667$$