Solve [(-8)(-7/64)-(-15):(-8)](-8)+(-27):(-9/8)

$$[ ( - 8 ) ( \frac { - 7 } { 64 } ) - ( - 15 ) : ( - 8 ) ] ( - 8 ) + ( - 27 ) : ( - \frac { 9 } { 8 } )$$

Evaluate

$$32$$

Solution Steps

Fraction \frac{-7}{64} can be rewritten as -\frac{7}{64} by extracting the negative sign.

$$\left(-8\left(-\frac{7}{64}\right)-\frac{-15}{-8}\right)\left(-8\right)+\frac{-27}{-\frac{9}{8}}$$

Express -8\left(-\frac{7}{64}\right) as a single fraction.

$$\left(\frac{-8\left(-7\right)}{64}-\frac{-15}{-8}\right)\left(-8\right)+\frac{-27}{-\frac{9}{8}}$$

Multiply -8 and -7 to get 56.

$$\left(\frac{56}{64}-\frac{-15}{-8}\right)\left(-8\right)+\frac{-27}{-\frac{9}{8}}$$

Reduce the fraction \frac{56}{64} to lowest terms by extracting and canceling out 8.

$$\left(\frac{7}{8}-\frac{-15}{-8}\right)\left(-8\right)+\frac{-27}{-\frac{9}{8}}$$

Fraction \frac{-15}{-8} can be simplified to \frac{15}{8} by removing the negative sign from both the numerator and the denominator.

$$\left(\frac{7}{8}-\frac{15}{8}\right)\left(-8\right)+\frac{-27}{-\frac{9}{8}}$$

Since \frac{7}{8} and \frac{15}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-15}{8}\left(-8\right)+\frac{-27}{-\frac{9}{8}}$$

Subtract 15 from 7 to get -8.

$$\frac{-8}{8}\left(-8\right)+\frac{-27}{-\frac{9}{8}}$$

Divide -8 by 8 to get -1.

$$-\left(-8\right)+\frac{-27}{-\frac{9}{8}}$$

Multiply -1 and -8 to get 8.

$$8+\frac{-27}{-\frac{9}{8}}$$

Divide -27 by -\frac{9}{8} by multiplying -27 by the reciprocal of -\frac{9}{8}.

$$8-27\left(-\frac{8}{9}\right)$$

Express -27\left(-\frac{8}{9}\right) as a single fraction.

$$8+\frac{-27\left(-8\right)}{9}$$

Multiply -27 and -8 to get 216.

$$8+\frac{216}{9}$$

Divide 216 by 9 to get 24.

$$8+24$$

Add 8 and 24 to get 32.

$$32$$

Factor

$$2^{5}$$