Solve 31/2div(-7/8)*(-11/6)

$$3 \frac { 1 } { 2 } \div ( - \frac { 7 } { 8 } ) \times ( - 1 \frac { 1 } { 6 } )$$

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

Divide \frac{3\times 2+1}{2} by -\frac{7}{8} by multiplying \frac{3\times 2+1}{2} by the reciprocal of -\frac{7}{8}.

$$\frac{\left(3\times 2+1\right)\times 8}{2\left(-7\right)}\left(-\frac{1\times 6+1}{6}\right)$$

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

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

Add 1 and 6 to get 7.

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

Multiply 4 and 7 to get 28.

$$\frac{28}{-7}\left(-\frac{1\times 6+1}{6}\right)$$

Divide 28 by -7 to get -4.

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

Add 6 and 1 to get 7.

$$-4\left(-\frac{7}{6}\right)$$

Express -4\left(-\frac{7}{6}\right) as a single fraction.

$$\frac{-4\left(-7\right)}{6}$$

Multiply -4 and -7 to get 28.

$$\frac{28}{6}$$

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

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$