Solve 2/5:(1/4-6/5)

$$\frac { 2 } { 5 } : ( \frac { 1 } { 4 } - \frac { 6 } { 5 } )$$

Evaluate

$$-\frac{8}{19}\approx -0.421052632$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{6}{5} to fractions with denominator 20.

$$\frac{\frac{2}{5}}{\frac{5}{20}-\frac{24}{20}}$$

Since \frac{5}{20} and \frac{24}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{5}}{\frac{5-24}{20}}$$

Subtract 24 from 5 to get -19.

$$\frac{\frac{2}{5}}{-\frac{19}{20}}$$

Divide \frac{2}{5} by -\frac{19}{20} by multiplying \frac{2}{5} by the reciprocal of -\frac{19}{20}.

$$\frac{2}{5}\left(-\frac{20}{19}\right)$$

Multiply \frac{2}{5} times -\frac{20}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-20\right)}{5\times 19}$$

Do the multiplications in the fraction \frac{2\left(-20\right)}{5\times 19}.

$$\frac{-40}{95}$$

Reduce the fraction \frac{-40}{95} to lowest terms by extracting and canceling out 5.

$$-\frac{8}{19}$$

Factor

$$-\frac{8}{19} = -0.42105263157894735$$