Solve [(2-1/2):2+(1+1/5)*(1-1/6)-1/9*frac{3}{2})]*(1+frac{1}{19})

$$[ ( 2 - \frac { 1 } { 2 } ) : 2 + ( 1 + \frac { 1 } { 5 } ) \times ( 1 - \frac { 1 } { 6 } ) - \frac { 1 } { 9 } \times \frac { 3 } { 2 } ) ] \times ( 1 + \frac { 1 } { 19 } )$$

Evaluate

$$\frac{19}{12}\approx 1.583333333$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

$$\frac{\frac{4}{2}-\frac{1}{2}}{2}+\left(1+\frac{1}{5}\right)\left(1-\frac{1}{6}\right)-\frac{1}{9}\times \frac{3}{2}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-1}{2}}{2}+\left(1+\frac{1}{5}\right)\left(1-\frac{1}{6}\right)-\frac{1}{9}\times \frac{3}{2}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{3}{2}}{2}+\left(1+\frac{1}{5}\right)\left(1-\frac{1}{6}\right)-\frac{1}{9}\times \frac{3}{2}$$

Express \frac{\frac{3}{2}}{2} as a single fraction.

$$\frac{3}{2\times 2}+\left(1+\frac{1}{5}\right)\left(1-\frac{1}{6}\right)-\frac{1}{9}\times \frac{3}{2}$$

Multiply 2 and 2 to get 4.

$$\frac{3}{4}+\left(1+\frac{1}{5}\right)\left(1-\frac{1}{6}\right)-\frac{1}{9}\times \frac{3}{2}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{3}{4}+\left(\frac{5}{5}+\frac{1}{5}\right)\left(1-\frac{1}{6}\right)-\frac{1}{9}\times \frac{3}{2}$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}+\frac{5+1}{5}\left(1-\frac{1}{6}\right)-\frac{1}{9}\times \frac{3}{2}$$

Add 5 and 1 to get 6.

$$\frac{3}{4}+\frac{6}{5}\left(1-\frac{1}{6}\right)-\frac{1}{9}\times \frac{3}{2}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{3}{4}+\frac{6}{5}\left(\frac{6}{6}-\frac{1}{6}\right)-\frac{1}{9}\times \frac{3}{2}$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}+\frac{6}{5}\times \frac{6-1}{6}-\frac{1}{9}\times \frac{3}{2}$$

Subtract 1 from 6 to get 5.

$$\frac{3}{4}+\frac{6}{5}\times \frac{5}{6}-\frac{1}{9}\times \frac{3}{2}$$

Cancel out \frac{6}{5} and its reciprocal \frac{5}{6}.

$$\frac{3}{4}+1-\frac{1}{9}\times \frac{3}{2}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{3}{4}+\frac{4}{4}-\frac{1}{9}\times \frac{3}{2}$$

Since \frac{3}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{4}-\frac{1}{9}\times \frac{3}{2}$$

Add 3 and 4 to get 7.

$$\frac{7}{4}-\frac{1}{9}\times \frac{3}{2}$$

Multiply \frac{1}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{4}-\frac{1\times 3}{9\times 2}$$

Do the multiplications in the fraction \frac{1\times 3}{9\times 2}.

$$\frac{7}{4}-\frac{3}{18}$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{7}{4}-\frac{1}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{7}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{21}{12}-\frac{2}{12}$$

Since \frac{21}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-2}{12}$$

Subtract 2 from 21 to get 19.

$$\frac{19}{12}$$

Factor

$$\frac{19}{2 ^ {2} \cdot 3} = 1\frac{7}{12} = 1.5833333333333333$$