Solve (1/3-1/2)*1/5-1/6

$$( \frac{ 1 }{ 3 } - \frac{ 1 }{ 2 } ) \times \frac{ 1 }{ 5 } - \frac{ 1 }{ 6 }$$

Evaluate

$$-\frac{1}{5}=-0.2$$

Solution Steps

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

$$\left(\frac{2}{6}-\frac{3}{6}\right)\times \frac{1}{5}-\frac{1}{6}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-3}{6}\times \frac{1}{5}-\frac{1}{6}$$

Subtract 3 from 2 to get -1.

$$-\frac{1}{6}\times \frac{1}{5}-\frac{1}{6}$$

Multiply -\frac{1}{6} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1}{6\times 5}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{-1}{6\times 5}.

$$\frac{-1}{30}-\frac{1}{6}$$

Fraction \frac{-1}{30} can be rewritten as -\frac{1}{30} by extracting the negative sign.

$$-\frac{1}{30}-\frac{1}{6}$$

Least common multiple of 30 and 6 is 30. Convert -\frac{1}{30} and \frac{1}{6} to fractions with denominator 30.

$$-\frac{1}{30}-\frac{5}{30}$$

Since -\frac{1}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-5}{30}$$

Subtract 5 from -1 to get -6.

$$\frac{-6}{30}$$

Reduce the fraction \frac{-6}{30} to lowest terms by extracting and canceling out 6.

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

Factor

$$-\frac{1}{5} = -0.2$$