Solve {[-3/2*(1/6-2/3)+(2/3-frac{7}{4})(2-frac{1}{2})]*4-frac{2}{3}}*3-frac{1}{12}+2

$$\{ [ - \frac { 3 } { 2 } \cdot ( \frac { 1 } { 6 } - \frac { 2 } { 3 } ) + ( \frac { 2 } { 3 } - \frac { 7 } { 4 } ) ( 2 - \frac { 1 } { 2 } ) ] \cdot 4 - \frac { 2 } { 3 } \} \cdot 3 - \frac { 1 } { 12 } + 2$$

Evaluate

$$-\frac{127}{12}\approx -10.583333333$$

Solution Steps

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{2}{3} to fractions with denominator 6.

$$\left(\left(-\frac{3}{2}\left(\frac{1}{6}-\frac{4}{6}\right)+\left(\frac{2}{3}-\frac{7}{4}\right)\left(2-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

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

$$\left(\left(-\frac{3}{2}\times \frac{1-4}{6}+\left(\frac{2}{3}-\frac{7}{4}\right)\left(2-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Subtract 4 from 1 to get -3.

$$\left(\left(-\frac{3}{2}\times \frac{-3}{6}+\left(\frac{2}{3}-\frac{7}{4}\right)\left(2-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

$$\left(\left(-\frac{3}{2}\left(-\frac{1}{2}\right)+\left(\frac{2}{3}-\frac{7}{4}\right)\left(2-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

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

$$\left(\left(\frac{-3\left(-1\right)}{2\times 2}+\left(\frac{2}{3}-\frac{7}{4}\right)\left(2-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Do the multiplications in the fraction \frac{-3\left(-1\right)}{2\times 2}.

$$\left(\left(\frac{3}{4}+\left(\frac{2}{3}-\frac{7}{4}\right)\left(2-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{7}{4} to fractions with denominator 12.

$$\left(\left(\frac{3}{4}+\left(\frac{8}{12}-\frac{21}{12}\right)\left(2-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Since \frac{8}{12} and \frac{21}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\left(\frac{3}{4}+\frac{8-21}{12}\left(2-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Subtract 21 from 8 to get -13.

$$\left(\left(\frac{3}{4}-\frac{13}{12}\left(2-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

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

$$\left(\left(\frac{3}{4}-\frac{13}{12}\left(\frac{4}{2}-\frac{1}{2}\right)\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

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

$$\left(\left(\frac{3}{4}-\frac{13}{12}\times \frac{4-1}{2}\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Subtract 1 from 4 to get 3.

$$\left(\left(\frac{3}{4}-\frac{13}{12}\times \frac{3}{2}\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Multiply -\frac{13}{12} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\left(\left(\frac{3}{4}+\frac{-13\times 3}{12\times 2}\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Do the multiplications in the fraction \frac{-13\times 3}{12\times 2}.

$$\left(\left(\frac{3}{4}+\frac{-39}{24}\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Reduce the fraction \frac{-39}{24} to lowest terms by extracting and canceling out 3.

$$\left(\left(\frac{3}{4}-\frac{13}{8}\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{13}{8} to fractions with denominator 8.

$$\left(\left(\frac{6}{8}-\frac{13}{8}\right)\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Since \frac{6}{8} and \frac{13}{8} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{6-13}{8}\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Subtract 13 from 6 to get -7.

$$\left(-\frac{7}{8}\times 4-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Express -\frac{7}{8}\times 4 as a single fraction.

$$\left(\frac{-7\times 4}{8}-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Multiply -7 and 4 to get -28.

$$\left(\frac{-28}{8}-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Reduce the fraction \frac{-28}{8} to lowest terms by extracting and canceling out 4.

$$\left(-\frac{7}{2}-\frac{2}{3}\right)\times 3-\frac{1}{12}+2$$

Least common multiple of 2 and 3 is 6. Convert -\frac{7}{2} and \frac{2}{3} to fractions with denominator 6.

$$\left(-\frac{21}{6}-\frac{4}{6}\right)\times 3-\frac{1}{12}+2$$

Since -\frac{21}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-21-4}{6}\times 3-\frac{1}{12}+2$$

Subtract 4 from -21 to get -25.

$$-\frac{25}{6}\times 3-\frac{1}{12}+2$$

Express -\frac{25}{6}\times 3 as a single fraction.

$$\frac{-25\times 3}{6}-\frac{1}{12}+2$$

Multiply -25 and 3 to get -75.

$$\frac{-75}{6}-\frac{1}{12}+2$$

Reduce the fraction \frac{-75}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{25}{2}-\frac{1}{12}+2$$

Least common multiple of 2 and 12 is 12. Convert -\frac{25}{2} and \frac{1}{12} to fractions with denominator 12.

$$-\frac{150}{12}-\frac{1}{12}+2$$

Since -\frac{150}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-150-1}{12}+2$$

Subtract 1 from -150 to get -151.

$$-\frac{151}{12}+2$$

Convert 2 to fraction \frac{24}{12}.

$$-\frac{151}{12}+\frac{24}{12}$$

Since -\frac{151}{12} and \frac{24}{12} have the same denominator, add them by adding their numerators.

$$\frac{-151+24}{12}$$

Add -151 and 24 to get -127.

$$-\frac{127}{12}$$

Factor

$$-\frac{127}{12} = -10\frac{7}{12} = -10.583333333333334$$