Solve (-3-1/5)*(3/8-1/2+2)+frac{17/4:(frac{3}{2}-frac{1}{4}+frac{1}{6})}{frac{2}{11}*(-frac{1}{3}+frac{5}{4})+frac{9}{2}+frac{1}{3}}

$$\frac { ( - 3 - \frac { 1 } { 5 } ) \cdot ( \frac { 3 } { 8 } - \frac { 1 } { 2 } + 2 ) + \frac { 17 } { 4 } : ( \frac { 3 } { 2 } - \frac { 1 } { 4 } + \frac { 1 } { 6 } ) } { \frac { 2 } { 11 } \cdot ( - \frac { 1 } { 3 } + \frac { 5 } { 4 } ) + \frac { 9 } { 2 } + \frac { 1 } { 3 } }$$

Evaluate

$$-\frac{3}{5}=-0.6$$

Solution Steps

Convert -3 to fraction -\frac{15}{5}.

$$\frac{\left(-\frac{15}{5}-\frac{1}{5}\right)\left(\frac{3}{8}-\frac{1}{2}+2\right)+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Since -\frac{15}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-15-1}{5}\left(\frac{3}{8}-\frac{1}{2}+2\right)+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Subtract 1 from -15 to get -16.

$$\frac{-\frac{16}{5}\left(\frac{3}{8}-\frac{1}{2}+2\right)+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Least common multiple of 8 and 2 is 8. Convert \frac{3}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{-\frac{16}{5}\left(\frac{3}{8}-\frac{4}{8}+2\right)+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Since \frac{3}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{16}{5}\left(\frac{3-4}{8}+2\right)+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Subtract 4 from 3 to get -1.

$$\frac{-\frac{16}{5}\left(-\frac{1}{8}+2\right)+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{-\frac{16}{5}\left(-\frac{1}{8}+\frac{16}{8}\right)+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Since -\frac{1}{8} and \frac{16}{8} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{16}{5}\times \frac{-1+16}{8}+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Add -1 and 16 to get 15.

$$\frac{-\frac{16}{5}\times \frac{15}{8}+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Multiply -\frac{16}{5} times \frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-16\times 15}{5\times 8}+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Do the multiplications in the fraction \frac{-16\times 15}{5\times 8}.

$$\frac{\frac{-240}{40}+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Divide -240 by 40 to get -6.

$$\frac{-6+\frac{\frac{17}{4}}{\frac{3}{2}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{-6+\frac{\frac{17}{4}}{\frac{6}{4}-\frac{1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-6+\frac{\frac{17}{4}}{\frac{6-1}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Subtract 1 from 6 to get 5.

$$\frac{-6+\frac{\frac{17}{4}}{\frac{5}{4}+\frac{1}{6}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Least common multiple of 4 and 6 is 12. Convert \frac{5}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{-6+\frac{\frac{17}{4}}{\frac{15}{12}+\frac{2}{12}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Since \frac{15}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{-6+\frac{\frac{17}{4}}{\frac{15+2}{12}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Add 15 and 2 to get 17.

$$\frac{-6+\frac{\frac{17}{4}}{\frac{17}{12}}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Divide \frac{17}{4} by \frac{17}{12} by multiplying \frac{17}{4} by the reciprocal of \frac{17}{12}.

$$\frac{-6+\frac{17}{4}\times \frac{12}{17}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Multiply \frac{17}{4} times \frac{12}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-6+\frac{17\times 12}{4\times 17}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Cancel out 17 in both numerator and denominator.

$$\frac{-6+\frac{12}{4}}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Divide 12 by 4 to get 3.

$$\frac{-6+3}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Add -6 and 3 to get -3.

$$\frac{-3}{\frac{2}{11}\left(-\frac{1}{3}+\frac{5}{4}\right)+\frac{9}{2}+\frac{1}{3}}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{1}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{-3}{\frac{2}{11}\left(-\frac{4}{12}+\frac{15}{12}\right)+\frac{9}{2}+\frac{1}{3}}$$

Since -\frac{4}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{-3}{\frac{2}{11}\times \frac{-4+15}{12}+\frac{9}{2}+\frac{1}{3}}$$

Add -4 and 15 to get 11.

$$\frac{-3}{\frac{2}{11}\times \frac{11}{12}+\frac{9}{2}+\frac{1}{3}}$$

Multiply \frac{2}{11} times \frac{11}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3}{\frac{2\times 11}{11\times 12}+\frac{9}{2}+\frac{1}{3}}$$

Cancel out 11 in both numerator and denominator.

$$\frac{-3}{\frac{2}{12}+\frac{9}{2}+\frac{1}{3}}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 6 and 2 is 6. Convert \frac{1}{6} and \frac{9}{2} to fractions with denominator 6.

$$\frac{-3}{\frac{1}{6}+\frac{27}{6}+\frac{1}{3}}$$

Since \frac{1}{6} and \frac{27}{6} have the same denominator, add them by adding their numerators.

$$\frac{-3}{\frac{1+27}{6}+\frac{1}{3}}$$

Add 1 and 27 to get 28.

$$\frac{-3}{\frac{28}{6}+\frac{1}{3}}$$

Reduce the fraction \frac{28}{6} to lowest terms by extracting and canceling out 2.

$$\frac{-3}{\frac{14}{3}+\frac{1}{3}}$$

Since \frac{14}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{-3}{\frac{14+1}{3}}$$

Add 14 and 1 to get 15.

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

Divide 15 by 3 to get 5.

$$\frac{-3}{5}$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$-\frac{3}{5}$$

Factor

$$-\frac{3}{5} = -0.6$$