Solve [1/4(-1/2-1/8)]div[3/4+frac{1}{8}]

$$[ \frac { 1 } { 4 } ( \frac { - 1 } { 2 } - \frac { 1 } { 8 } ) ] \div [ \frac { 3 } { 4 } + \frac { 1 } { 8 } ]$$

Evaluate

$$-\frac{5}{28}\approx -0.178571429$$

Solution Steps

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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

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

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

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

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

Subtract 1 from -4 to get -5.

$$\frac{\frac{1}{4}\left(-\frac{5}{8}\right)}{\frac{3}{4}+\frac{1}{8}}$$

Multiply \frac{1}{4} times -\frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\left(-5\right)}{4\times 8}}{\frac{3}{4}+\frac{1}{8}}$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{4\times 8}.

$$\frac{\frac{-5}{32}}{\frac{3}{4}+\frac{1}{8}}$$

Fraction \frac{-5}{32} can be rewritten as -\frac{5}{32} by extracting the negative sign.

$$\frac{-\frac{5}{32}}{\frac{3}{4}+\frac{1}{8}}$$

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{-\frac{5}{32}}{\frac{6}{8}+\frac{1}{8}}$$

Since \frac{6}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{5}{32}}{\frac{6+1}{8}}$$

Add 6 and 1 to get 7.

$$\frac{-\frac{5}{32}}{\frac{7}{8}}$$

Divide -\frac{5}{32} by \frac{7}{8} by multiplying -\frac{5}{32} by the reciprocal of \frac{7}{8}.

$$-\frac{5}{32}\times \frac{8}{7}$$

Multiply -\frac{5}{32} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 8}{32\times 7}$$

Do the multiplications in the fraction \frac{-5\times 8}{32\times 7}.

$$\frac{-40}{224}$$

Reduce the fraction \frac{-40}{224} to lowest terms by extracting and canceling out 8.

$$-\frac{5}{28}$$

Factor

$$-\frac{5}{28} = -0.17857142857142858$$