Solve -4/6+7/8/frac{-5{8}-11/20}

$$\frac { \frac { - 4 } { 6 } + \frac { 7 } { 8 } } { \frac { - 5 } { 8 } - \frac { 11 } { 20 } }$$

Evaluate

$$-\frac{25}{141}\approx -0.177304965$$

Solution Steps

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{2}{3}+\frac{7}{8}}{\frac{-5}{8}-\frac{11}{20}}$$

Least common multiple of 3 and 8 is 24. Convert -\frac{2}{3} and \frac{7}{8} to fractions with denominator 24.

$$\frac{-\frac{16}{24}+\frac{21}{24}}{\frac{-5}{8}-\frac{11}{20}}$$

Since -\frac{16}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-16+21}{24}}{\frac{-5}{8}-\frac{11}{20}}$$

Add -16 and 21 to get 5.

$$\frac{\frac{5}{24}}{\frac{-5}{8}-\frac{11}{20}}$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$\frac{\frac{5}{24}}{-\frac{5}{8}-\frac{11}{20}}$$

Least common multiple of 8 and 20 is 40. Convert -\frac{5}{8} and \frac{11}{20} to fractions with denominator 40.

$$\frac{\frac{5}{24}}{-\frac{25}{40}-\frac{22}{40}}$$

Since -\frac{25}{40} and \frac{22}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{24}}{\frac{-25-22}{40}}$$

Subtract 22 from -25 to get -47.

$$\frac{\frac{5}{24}}{-\frac{47}{40}}$$

Divide \frac{5}{24} by -\frac{47}{40} by multiplying \frac{5}{24} by the reciprocal of -\frac{47}{40}.

$$\frac{5}{24}\left(-\frac{40}{47}\right)$$

Multiply \frac{5}{24} times -\frac{40}{47} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-40\right)}{24\times 47}$$

Do the multiplications in the fraction \frac{5\left(-40\right)}{24\times 47}.

$$\frac{-200}{1128}$$

Reduce the fraction \frac{-200}{1128} to lowest terms by extracting and canceling out 8.

$$-\frac{25}{141}$$

Factor

$$-\frac{25}{141} = -0.1773049645390071$$