Solve [21/2-(-1/2)^3]*(-11/7)

$$[ 2 \frac { 1 } { 2 } - ( - \frac { 1 } { 2 } ) ^ { 3 } ] \times ( - 1 \frac { 1 } { 7 } )$$

Evaluate

$$-3$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

$$\left(\frac{5}{2}-\left(-\frac{1}{2}\right)^{3}\right)\left(-\frac{1\times 7+1}{7}\right)$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$\left(\frac{5}{2}-\left(-\frac{1}{8}\right)\right)\left(-\frac{1\times 7+1}{7}\right)$$

The opposite of -\frac{1}{8} is \frac{1}{8}.

$$\left(\frac{5}{2}+\frac{1}{8}\right)\left(-\frac{1\times 7+1}{7}\right)$$

Least common multiple of 2 and 8 is 8. Convert \frac{5}{2} and \frac{1}{8} to fractions with denominator 8.

$$\left(\frac{20}{8}+\frac{1}{8}\right)\left(-\frac{1\times 7+1}{7}\right)$$

Since \frac{20}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{20+1}{8}\left(-\frac{1\times 7+1}{7}\right)$$

Add 20 and 1 to get 21.

$$\frac{21}{8}\left(-\frac{1\times 7+1}{7}\right)$$

Multiply 1 and 7 to get 7.

$$\frac{21}{8}\left(-\frac{7+1}{7}\right)$$

Add 7 and 1 to get 8.

$$\frac{21}{8}\left(-\frac{8}{7}\right)$$

Multiply \frac{21}{8} times -\frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\left(-8\right)}{8\times 7}$$

Do the multiplications in the fraction \frac{21\left(-8\right)}{8\times 7}.

$$\frac{-168}{56}$$

Divide -168 by 56 to get -3.

$$-3$$

Factor

$$-3$$