Solve -2/frac{2{3}-5/2-1/3}-frac{1/2frac{3}{2}left(-3+frac{4}{3}right)}{-frac{1}{6}}

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

Evaluate

$$-\frac{171}{26}\approx -6.576923077$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{-2}{\frac{4}{6}-\frac{15}{6}-\frac{1}{3}}-\frac{\frac{1}{2}\times \frac{3}{2}\left(-3+\frac{4}{3}\right)}{-\frac{1}{6}}$$

Since \frac{4}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2}{\frac{4-15}{6}-\frac{1}{3}}-\frac{\frac{1}{2}\times \frac{3}{2}\left(-3+\frac{4}{3}\right)}{-\frac{1}{6}}$$

Subtract 15 from 4 to get -11.

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

Least common multiple of 6 and 3 is 6. Convert -\frac{11}{6} and \frac{1}{3} to fractions with denominator 6.

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

Since -\frac{11}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from -11 to get -13.

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

Divide -2 by -\frac{13}{6} by multiplying -2 by the reciprocal of -\frac{13}{6}.

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

Express -2\left(-\frac{6}{13}\right) as a single fraction.

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

Multiply -2 and -6 to get 12.

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

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

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

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

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

Convert -3 to fraction -\frac{9}{3}.

$$\frac{12}{13}-\frac{\frac{3}{4}\left(-\frac{9}{3}+\frac{4}{3}\right)}{-\frac{1}{6}}$$

Since -\frac{9}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{12}{13}-\frac{\frac{3}{4}\times \frac{-9+4}{3}}{-\frac{1}{6}}$$

Add -9 and 4 to get -5.

$$\frac{12}{13}-\frac{\frac{3}{4}\left(-\frac{5}{3}\right)}{-\frac{1}{6}}$$

Multiply \frac{3}{4} times -\frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{13}-\frac{\frac{3\left(-5\right)}{4\times 3}}{-\frac{1}{6}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{12}{13}-\frac{\frac{-5}{4}}{-\frac{1}{6}}$$

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$\frac{12}{13}-\frac{-\frac{5}{4}}{-\frac{1}{6}}$$

Divide -\frac{5}{4} by -\frac{1}{6} by multiplying -\frac{5}{4} by the reciprocal of -\frac{1}{6}.

$$\frac{12}{13}-\left(-\frac{5}{4}\left(-6\right)\right)$$

Express -\frac{5}{4}\left(-6\right) as a single fraction.

$$\frac{12}{13}-\frac{-5\left(-6\right)}{4}$$

Multiply -5 and -6 to get 30.

$$\frac{12}{13}-\frac{30}{4}$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\frac{12}{13}-\frac{15}{2}$$

Least common multiple of 13 and 2 is 26. Convert \frac{12}{13} and \frac{15}{2} to fractions with denominator 26.

$$\frac{24}{26}-\frac{195}{26}$$

Since \frac{24}{26} and \frac{195}{26} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-195}{26}$$

Subtract 195 from 24 to get -171.

$$-\frac{171}{26}$$

Factor

$$-\frac{171}{26} = -6\frac{15}{26} = -6.576923076923077$$