Solve (1/5-3/5)div(4/3-1/2)

$$( \frac { 1 } { 5 } - \frac { 3 } { 5 } ) \div ( \frac { 4 } { 3 } - \frac { 1 } { 2 } )$$

Evaluate

$$-\frac{12}{25}=-0.48$$

Solution Steps

Since \frac{1}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-3}{5}}{\frac{4}{3}-\frac{1}{2}}$$

Subtract 3 from 1 to get -2.

$$\frac{-\frac{2}{5}}{\frac{4}{3}-\frac{1}{2}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{-\frac{2}{5}}{\frac{8}{6}-\frac{3}{6}}$$

Since \frac{8}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{2}{5}}{\frac{8-3}{6}}$$

Subtract 3 from 8 to get 5.

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

Divide -\frac{2}{5} by \frac{5}{6} by multiplying -\frac{2}{5} by the reciprocal of \frac{5}{6}.

$$-\frac{2}{5}\times \frac{6}{5}$$

Multiply -\frac{2}{5} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 6}{5\times 5}$$

Do the multiplications in the fraction \frac{-2\times 6}{5\times 5}.

$$\frac{-12}{25}$$

Fraction \frac{-12}{25} can be rewritten as -\frac{12}{25} by extracting the negative sign.

$$-\frac{12}{25}$$

Factor

$$-\frac{12}{25} = -0.48$$