Solve A=(-1/5)+(-5/6)+(+1/2)+(-1/19)+(-frac{2}{3})+(+frac{1}{9})

$$A = ( - \frac { 1 } { 5 } ) + ( - \frac { 5 } { 6 } ) + ( + \frac { 1 } { 2 } ) + ( - \frac { 1 } { 19 } ) + ( - \frac { 2 } { 3 } ) + ( + \frac { 1 } { 9 } )$$

Solve for A

$$A = -\frac{976}{855} = -1\frac{121}{855} \approx -1.141520468$$

Steps for Solving Linear Equation

Least common multiple of 5 and 6 is 30. Convert -\frac{1}{5} and \frac{5}{6} to fractions with denominator 30.

$$A=-\frac{6}{30}-\frac{25}{30}+\frac{1}{2}-\frac{1}{19}-\frac{2}{3}+\frac{1}{9}$$

Since -\frac{6}{30} and \frac{25}{30} have the same denominator, subtract them by subtracting their numerators.

$$A=\frac{-6-25}{30}+\frac{1}{2}-\frac{1}{19}-\frac{2}{3}+\frac{1}{9}$$

Subtract 25 from -6 to get -31.

$$A=-\frac{31}{30}+\frac{1}{2}-\frac{1}{19}-\frac{2}{3}+\frac{1}{9}$$

Least common multiple of 30 and 2 is 30. Convert -\frac{31}{30} and \frac{1}{2} to fractions with denominator 30.

$$A=-\frac{31}{30}+\frac{15}{30}-\frac{1}{19}-\frac{2}{3}+\frac{1}{9}$$

Since -\frac{31}{30} and \frac{15}{30} have the same denominator, add them by adding their numerators.

$$A=\frac{-31+15}{30}-\frac{1}{19}-\frac{2}{3}+\frac{1}{9}$$

Add -31 and 15 to get -16.

$$A=\frac{-16}{30}-\frac{1}{19}-\frac{2}{3}+\frac{1}{9}$$

Reduce the fraction \frac{-16}{30} to lowest terms by extracting and canceling out 2.

$$A=-\frac{8}{15}-\frac{1}{19}-\frac{2}{3}+\frac{1}{9}$$

Least common multiple of 15 and 19 is 285. Convert -\frac{8}{15} and \frac{1}{19} to fractions with denominator 285.

$$A=-\frac{152}{285}-\frac{15}{285}-\frac{2}{3}+\frac{1}{9}$$

Since -\frac{152}{285} and \frac{15}{285} have the same denominator, subtract them by subtracting their numerators.

$$A=\frac{-152-15}{285}-\frac{2}{3}+\frac{1}{9}$$

Subtract 15 from -152 to get -167.

$$A=-\frac{167}{285}-\frac{2}{3}+\frac{1}{9}$$

Least common multiple of 285 and 3 is 285. Convert -\frac{167}{285} and \frac{2}{3} to fractions with denominator 285.

$$A=-\frac{167}{285}-\frac{190}{285}+\frac{1}{9}$$

Since -\frac{167}{285} and \frac{190}{285} have the same denominator, subtract them by subtracting their numerators.

$$A=\frac{-167-190}{285}+\frac{1}{9}$$

Subtract 190 from -167 to get -357.

$$A=\frac{-357}{285}+\frac{1}{9}$$

Reduce the fraction \frac{-357}{285} to lowest terms by extracting and canceling out 3.

$$A=-\frac{119}{95}+\frac{1}{9}$$

Least common multiple of 95 and 9 is 855. Convert -\frac{119}{95} and \frac{1}{9} to fractions with denominator 855.

$$A=-\frac{1071}{855}+\frac{95}{855}$$

Since -\frac{1071}{855} and \frac{95}{855} have the same denominator, add them by adding their numerators.

$$A=\frac{-1071+95}{855}$$

Add -1071 and 95 to get -976.

$$A=-\frac{976}{855}$$

Assign A

$$A≔-\frac{976}{855}$$