Solve (1/2-1/8):(-2)-161/4:(-4)

$$( \frac { 1 } { 2 } - \frac { 1 } { 8 } ) : ( - 2 ) - 16 \frac { 1 } { 4 } : ( - 4 )$$

Evaluate

$$\frac{31}{8}=3.875$$

Solution Steps

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

$$\frac{\frac{4}{8}-\frac{1}{8}}{-2}-\frac{\frac{16\times 4+1}{4}}{-4}$$

Since \frac{4}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-1}{8}}{-2}-\frac{\frac{16\times 4+1}{4}}{-4}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{3}{8}}{-2}-\frac{\frac{16\times 4+1}{4}}{-4}$$

Express \frac{\frac{3}{8}}{-2} as a single fraction.

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

Multiply 8 and -2 to get -16.

$$\frac{3}{-16}-\frac{\frac{16\times 4+1}{4}}{-4}$$

Fraction \frac{3}{-16} can be rewritten as -\frac{3}{16} by extracting the negative sign.

$$-\frac{3}{16}-\frac{\frac{16\times 4+1}{4}}{-4}$$

Express \frac{\frac{16\times 4+1}{4}}{-4} as a single fraction.

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

Multiply 16 and 4 to get 64.

$$-\frac{3}{16}-\frac{64+1}{4\left(-4\right)}$$

Add 64 and 1 to get 65.

$$-\frac{3}{16}-\frac{65}{4\left(-4\right)}$$

Multiply 4 and -4 to get -16.

$$-\frac{3}{16}-\frac{65}{-16}$$

Fraction \frac{65}{-16} can be rewritten as -\frac{65}{16} by extracting the negative sign.

$$-\frac{3}{16}-\left(-\frac{65}{16}\right)$$

The opposite of -\frac{65}{16} is \frac{65}{16}.

$$-\frac{3}{16}+\frac{65}{16}$$

Since -\frac{3}{16} and \frac{65}{16} have the same denominator, add them by adding their numerators.

$$\frac{-3+65}{16}$$

Add -3 and 65 to get 62.

$$\frac{62}{16}$$

Reduce the fraction \frac{62}{16} to lowest terms by extracting and canceling out 2.

$$\frac{31}{8}$$

Factor

$$\frac{31}{2 ^ {3}} = 3\frac{7}{8} = 3.875$$