Solve (-8/5+2/4)div(6/10-5/2)

$$( \frac { - 8 } { 5 } + \frac { 2 } { 4 } ) \div ( \frac { 6 } { 10 } - \frac { 5 } { 2 } )$$

Evaluate

$$\frac{11}{19}\approx 0.578947368$$

Solution Steps

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

$$\frac{-\frac{8}{5}+\frac{2}{4}}{\frac{6}{10}-\frac{5}{2}}$$

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

$$\frac{-\frac{8}{5}+\frac{1}{2}}{\frac{6}{10}-\frac{5}{2}}$$

Least common multiple of 5 and 2 is 10. Convert -\frac{8}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{-\frac{16}{10}+\frac{5}{10}}{\frac{6}{10}-\frac{5}{2}}$$

Since -\frac{16}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-16+5}{10}}{\frac{6}{10}-\frac{5}{2}}$$

Add -16 and 5 to get -11.

$$\frac{-\frac{11}{10}}{\frac{6}{10}-\frac{5}{2}}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{11}{10}}{\frac{3}{5}-\frac{5}{2}}$$

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{5}{2} to fractions with denominator 10.

$$\frac{-\frac{11}{10}}{\frac{6}{10}-\frac{25}{10}}$$

Since \frac{6}{10} and \frac{25}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{11}{10}}{\frac{6-25}{10}}$$

Subtract 25 from 6 to get -19.

$$\frac{-\frac{11}{10}}{-\frac{19}{10}}$$

Divide -\frac{11}{10} by -\frac{19}{10} by multiplying -\frac{11}{10} by the reciprocal of -\frac{19}{10}.

$$-\frac{11}{10}\left(-\frac{10}{19}\right)$$

Multiply -\frac{11}{10} times -\frac{10}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-11\left(-10\right)}{10\times 19}$$

Do the multiplications in the fraction \frac{-11\left(-10\right)}{10\times 19}.

$$\frac{110}{190}$$

Reduce the fraction \frac{110}{190} to lowest terms by extracting and canceling out 10.

$$\frac{11}{19}$$

Factor

$$\frac{11}{19} = 0.5789473684210527$$