Solve 1/2{frac{1/3-4}}-3/2

$$\frac{ 1 }{ \frac{ 2 }{ \frac{ 1 }{ 3 } -4 } } - \frac{ 3 }{ 2 }$$

Evaluate

$$-\frac{10}{3}\approx -3.333333333$$

Solution Steps

Divide 1 by \frac{2}{\frac{1}{3}-4} by multiplying 1 by the reciprocal of \frac{2}{\frac{1}{3}-4}.

$$\frac{\frac{1}{3}-4}{2}-\frac{3}{2}$$

Convert 4 to fraction \frac{12}{3}.

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

Since \frac{1}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 12 from 1 to get -11.

$$\frac{-\frac{11}{3}}{2}-\frac{3}{2}$$

Express \frac{-\frac{11}{3}}{2} as a single fraction.

$$\frac{-11}{3\times 2}-\frac{3}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{-11}{6}-\frac{3}{2}$$

Fraction \frac{-11}{6} can be rewritten as -\frac{11}{6} by extracting the negative sign.

$$-\frac{11}{6}-\frac{3}{2}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{11}{6} and \frac{3}{2} to fractions with denominator 6.

$$-\frac{11}{6}-\frac{9}{6}$$

Since -\frac{11}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-9}{6}$$

Subtract 9 from -11 to get -20.

$$\frac{-20}{6}$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{10}{3}$$

Factor

$$-\frac{10}{3} = -3\frac{1}{3} = -3.3333333333333335$$