Solve 2/5-1/2/frac{1{2}*2/5}

$$\frac{ \frac{ 2 }{ 5 } - \frac{ 1 }{ 2 } }{ \frac{ 1 }{ 2 } \times \frac{ 2 }{ 5 } }$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

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

$$\frac{\frac{4}{10}-\frac{5}{10}}{\frac{1}{2}\times \frac{2}{5}}$$

Since \frac{4}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-5}{10}}{\frac{1}{2}\times \frac{2}{5}}$$

Subtract 5 from 4 to get -1.

$$\frac{-\frac{1}{10}}{\frac{1}{2}\times \frac{2}{5}}$$

Multiply \frac{1}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{1}{10}}{\frac{1\times 2}{2\times 5}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\frac{1}{10}}{\frac{1}{5}}$$

Divide -\frac{1}{10} by \frac{1}{5} by multiplying -\frac{1}{10} by the reciprocal of \frac{1}{5}.

$$-\frac{1}{10}\times 5$$

Express -\frac{1}{10}\times 5 as a single fraction.

$$\frac{-5}{10}$$

Reduce the fraction \frac{-5}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$