Solve 11/2*((-7/6)div(14/3)-11/4)

$$\frac { 11 } { 2 } \cdot ( ( \frac { - 7 } { 6 } ) \div ( \frac { 14 } { 3 } ) - \frac { 11 } { 4 } )$$

Evaluate

$$-\frac{33}{2}=-16.5$$

Solution Steps

Divide \frac{-7}{6} by \frac{14}{3} by multiplying \frac{-7}{6} by the reciprocal of \frac{14}{3}.

$$\frac{11}{2}\left(\frac{-7\times 3}{6\times 14}-\frac{11}{4}\right)$$

Cancel out 3\times 7 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{11}{2}\left(\frac{-1}{4}-\frac{11}{4}\right)$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{11}{2}\left(-\frac{1}{4}-\frac{11}{4}\right)$$

Since -\frac{1}{4} and \frac{11}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{2}\times \frac{-1-11}{4}$$

Subtract 11 from -1 to get -12.

$$\frac{11}{2}\times \frac{-12}{4}$$

Divide -12 by 4 to get -3.

$$\frac{11}{2}\left(-3\right)$$

Express \frac{11}{2}\left(-3\right) as a single fraction.

$$\frac{11\left(-3\right)}{2}$$

Multiply 11 and -3 to get -33.

$$\frac{-33}{2}$$

Fraction \frac{-33}{2} can be rewritten as -\frac{33}{2} by extracting the negative sign.

$$-\frac{33}{2}$$

Factor

$$-\frac{33}{2} = -16\frac{1}{2} = -16.5$$