Solve 21/7div33/14-11/3*(-11/2)^3

$$2 \frac { 1 } { 7 } \div 3 \frac { 3 } { 14 } - 1 \frac { 1 } { 3 } \times ( - 1 \frac { 1 } { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{31}{6}\approx 5.166666667$$

Solution Steps

Divide \frac{2\times 7+1}{7} by \frac{3\times 14+3}{14} by multiplying \frac{2\times 7+1}{7} by the reciprocal of \frac{3\times 14+3}{14}.

$$\frac{\left(2\times 7+1\right)\times 14}{7\left(3\times 14+3\right)}-\frac{1\times 3+1}{3}\left(-\frac{1\times 2+1}{2}\right)^{3}$$

Cancel out 7 in both numerator and denominator.

$$\frac{2\left(1+2\times 7\right)}{3+3\times 14}-\frac{1\times 3+1}{3}\left(-\frac{1\times 2+1}{2}\right)^{3}$$

Multiply 2 and 7 to get 14.

$$\frac{2\left(1+14\right)}{3+3\times 14}-\frac{1\times 3+1}{3}\left(-\frac{1\times 2+1}{2}\right)^{3}$$

Add 1 and 14 to get 15.

$$\frac{2\times 15}{3+3\times 14}-\frac{1\times 3+1}{3}\left(-\frac{1\times 2+1}{2}\right)^{3}$$

Multiply 2 and 15 to get 30.

$$\frac{30}{3+3\times 14}-\frac{1\times 3+1}{3}\left(-\frac{1\times 2+1}{2}\right)^{3}$$

Multiply 3 and 14 to get 42.

$$\frac{30}{3+42}-\frac{1\times 3+1}{3}\left(-\frac{1\times 2+1}{2}\right)^{3}$$

Add 3 and 42 to get 45.

$$\frac{30}{45}-\frac{1\times 3+1}{3}\left(-\frac{1\times 2+1}{2}\right)^{3}$$

Reduce the fraction \frac{30}{45} to lowest terms by extracting and canceling out 15.

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

Multiply 1 and 3 to get 3.

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

Add 3 and 1 to get 4.

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

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

$$\frac{2}{3}-\frac{4}{3}\left(-\frac{3}{2}\right)^{3}$$

Calculate -\frac{3}{2} to the power of 3 and get -\frac{27}{8}.

$$\frac{2}{3}-\frac{4}{3}\left(-\frac{27}{8}\right)$$

Multiply \frac{4}{3} and -\frac{27}{8} to get -\frac{9}{2}.

$$\frac{2}{3}-\left(-\frac{9}{2}\right)$$

The opposite of -\frac{9}{2} is \frac{9}{2}.

$$\frac{2}{3}+\frac{9}{2}$$

Add \frac{2}{3} and \frac{9}{2} to get \frac{31}{6}.

$$\frac{31}{6}$$

Factor

$$\frac{31}{2 \cdot 3} = 5\frac{1}{6} = 5.166666666666667$$