Solve (1/4)^2div(-1/2)^3*(-1)-(13/8-33/4)*24

$$( \frac { 1 } { 4 } ) ^ { 2 } \div ( - \frac { 1 } { 2 } ) ^ { 3 } \times ( - 1 ) - ( 1 \frac { 3 } { 8 } - 3 \frac { 3 } { 4 } ) \times 24$$

Evaluate

$$\frac{115}{2}=57.5$$

Solution Steps

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}}{\left(-\frac{1}{2}\right)^{3}}\left(-1\right)-\left(\frac{1\times 8+3}{8}-\frac{3\times 4+3}{4}\right)\times 24$$

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

$$\frac{\frac{1}{16}}{-\frac{1}{8}}\left(-1\right)-\left(\frac{1\times 8+3}{8}-\frac{3\times 4+3}{4}\right)\times 24$$

Divide \frac{1}{16} by -\frac{1}{8} by multiplying \frac{1}{16} by the reciprocal of -\frac{1}{8}.

$$\frac{1}{16}\left(-8\right)\left(-1\right)-\left(\frac{1\times 8+3}{8}-\frac{3\times 4+3}{4}\right)\times 24$$

Multiply \frac{1}{16} and -8 to get \frac{-8}{16}.

$$\frac{-8}{16}\left(-1\right)-\left(\frac{1\times 8+3}{8}-\frac{3\times 4+3}{4}\right)\times 24$$

Reduce the fraction \frac{-8}{16} to lowest terms by extracting and canceling out 8.

$$-\frac{1}{2}\left(-1\right)-\left(\frac{1\times 8+3}{8}-\frac{3\times 4+3}{4}\right)\times 24$$

Multiply -\frac{1}{2} and -1 to get \frac{1}{2}.

$$\frac{1}{2}-\left(\frac{1\times 8+3}{8}-\frac{3\times 4+3}{4}\right)\times 24$$

Multiply 1 and 8 to get 8.

$$\frac{1}{2}-\left(\frac{8+3}{8}-\frac{3\times 4+3}{4}\right)\times 24$$

Add 8 and 3 to get 11.

$$\frac{1}{2}-\left(\frac{11}{8}-\frac{3\times 4+3}{4}\right)\times 24$$

Multiply 3 and 4 to get 12.

$$\frac{1}{2}-\left(\frac{11}{8}-\frac{12+3}{4}\right)\times 24$$

Add 12 and 3 to get 15.

$$\frac{1}{2}-\left(\frac{11}{8}-\frac{15}{4}\right)\times 24$$

Least common multiple of 8 and 4 is 8. Convert \frac{11}{8} and \frac{15}{4} to fractions with denominator 8.

$$\frac{1}{2}-\left(\frac{11}{8}-\frac{30}{8}\right)\times 24$$

Since \frac{11}{8} and \frac{30}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}-\frac{11-30}{8}\times 24$$

Subtract 30 from 11 to get -19.

$$\frac{1}{2}-\left(-\frac{19}{8}\times 24\right)$$

Express -\frac{19}{8}\times 24 as a single fraction.

$$\frac{1}{2}-\frac{-19\times 24}{8}$$

Multiply -19 and 24 to get -456.

$$\frac{1}{2}-\frac{-456}{8}$$

Divide -456 by 8 to get -57.

$$\frac{1}{2}-\left(-57\right)$$

The opposite of -57 is 57.

$$\frac{1}{2}+57$$

Convert 57 to fraction \frac{114}{2}.

$$\frac{1}{2}+\frac{114}{2}$$

Since \frac{1}{2} and \frac{114}{2} have the same denominator, add them by adding their numerators.

$$\frac{1+114}{2}$$

Add 1 and 114 to get 115.

$$\frac{115}{2}$$

Factor

$$\frac{5 \cdot 23}{2} = 57\frac{1}{2} = 57.5$$