Solve 2/5(-3/7-1/6)3/2+frac{1}{14}

$$\frac { 2 } { 5 } ( \frac { - 3 } { 7 } - \frac { 1 } { 6 } ) \frac { 3 } { 2 } + \frac { 1 } { 14 }$$

Evaluate

$$-\frac{2}{7}\approx -0.285714286$$

Solution Steps

Fraction \frac{-3}{7} can be rewritten as -\frac{3}{7} by extracting the negative sign.

$$\frac{2}{5}\left(-\frac{3}{7}-\frac{1}{6}\right)\times \frac{3}{2}+\frac{1}{14}$$

Least common multiple of 7 and 6 is 42. Convert -\frac{3}{7} and \frac{1}{6} to fractions with denominator 42.

$$\frac{2}{5}\left(-\frac{18}{42}-\frac{7}{42}\right)\times \frac{3}{2}+\frac{1}{14}$$

Since -\frac{18}{42} and \frac{7}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}\times \frac{-18-7}{42}\times \frac{3}{2}+\frac{1}{14}$$

Subtract 7 from -18 to get -25.

$$\frac{2}{5}\left(-\frac{25}{42}\right)\times \frac{3}{2}+\frac{1}{14}$$

Multiply \frac{2}{5} times -\frac{25}{42} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-25\right)}{5\times 42}\times \frac{3}{2}+\frac{1}{14}$$

Do the multiplications in the fraction \frac{2\left(-25\right)}{5\times 42}.

$$\frac{-50}{210}\times \frac{3}{2}+\frac{1}{14}$$

Reduce the fraction \frac{-50}{210} to lowest terms by extracting and canceling out 10.

$$-\frac{5}{21}\times \frac{3}{2}+\frac{1}{14}$$

Multiply -\frac{5}{21} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 3}{21\times 2}+\frac{1}{14}$$

Do the multiplications in the fraction \frac{-5\times 3}{21\times 2}.

$$\frac{-15}{42}+\frac{1}{14}$$

Reduce the fraction \frac{-15}{42} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{14}+\frac{1}{14}$$

Since -\frac{5}{14} and \frac{1}{14} have the same denominator, add them by adding their numerators.

$$\frac{-5+1}{14}$$

Add -5 and 1 to get -4.

$$\frac{-4}{14}$$

Reduce the fraction \frac{-4}{14} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{7}$$

Factor

$$-\frac{2}{7} = -0.2857142857142857$$