Solve (-39)+2.17-(-17.83)-[67/8-(-15/8)]

$$( - 39 ) + 2.17 - ( - 17.83 ) - [ 6 \frac { 7 } { 8 } - ( - 1 \frac { 5 } { 8 } ) ]$$

Evaluate

$$-27.5$$

Solution Steps

Add -39 and 2.17 to get -36.83.

$$-36.83-\left(-17.83\right)-\left(\frac{6\times 8+7}{8}-\left(-\frac{1\times 8+5}{8}\right)\right)$$

The opposite of -17.83 is 17.83.

$$-36.83+17.83-\left(\frac{6\times 8+7}{8}-\left(-\frac{1\times 8+5}{8}\right)\right)$$

Add -36.83 and 17.83 to get -19.

$$-19-\left(\frac{6\times 8+7}{8}-\left(-\frac{1\times 8+5}{8}\right)\right)$$

Multiply 6 and 8 to get 48.

$$-19-\left(\frac{48+7}{8}-\left(-\frac{1\times 8+5}{8}\right)\right)$$

Add 48 and 7 to get 55.

$$-19-\left(\frac{55}{8}-\left(-\frac{1\times 8+5}{8}\right)\right)$$

Multiply 1 and 8 to get 8.

$$-19-\left(\frac{55}{8}-\left(-\frac{8+5}{8}\right)\right)$$

Add 8 and 5 to get 13.

$$-19-\left(\frac{55}{8}-\left(-\frac{13}{8}\right)\right)$$

The opposite of -\frac{13}{8} is \frac{13}{8}.

$$-19-\left(\frac{55}{8}+\frac{13}{8}\right)$$

Since \frac{55}{8} and \frac{13}{8} have the same denominator, add them by adding their numerators.

$$-19-\frac{55+13}{8}$$

Add 55 and 13 to get 68.

$$-19-\frac{68}{8}$$

Reduce the fraction \frac{68}{8} to lowest terms by extracting and canceling out 4.

$$-19-\frac{17}{2}$$

Convert -19 to fraction -\frac{38}{2}.

$$-\frac{38}{2}-\frac{17}{2}$$

Since -\frac{38}{2} and \frac{17}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-38-17}{2}$$

Subtract 17 from -38 to get -55.

$$-\frac{55}{2}$$

Factor

$$-27.5$$