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

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

Evaluate

$$-\frac{157}{420}\approx -0.373809524$$

Solution Steps

Multiply \frac{2}{5} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 7}.

$$\frac{-6}{35}-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{3}$$

Fraction \frac{-6}{35} can be rewritten as -\frac{6}{35} by extracting the negative sign.

$$-\frac{6}{35}-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{3}$$

Multiply \frac{1}{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{6}{35}-\frac{1\times 3}{6\times 2}+\frac{1}{14}\times \frac{2}{3}$$

Do the multiplications in the fraction \frac{1\times 3}{6\times 2}.

$$-\frac{6}{35}-\frac{3}{12}+\frac{1}{14}\times \frac{2}{3}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{6}{35}-\frac{1}{4}+\frac{1}{14}\times \frac{2}{3}$$

Least common multiple of 35 and 4 is 140. Convert -\frac{6}{35} and \frac{1}{4} to fractions with denominator 140.

$$-\frac{24}{140}-\frac{35}{140}+\frac{1}{14}\times \frac{2}{3}$$

Since -\frac{24}{140} and \frac{35}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-24-35}{140}+\frac{1}{14}\times \frac{2}{3}$$

Subtract 35 from -24 to get -59.

$$-\frac{59}{140}+\frac{1}{14}\times \frac{2}{3}$$

Multiply \frac{1}{14} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{59}{140}+\frac{1\times 2}{14\times 3}$$

Do the multiplications in the fraction \frac{1\times 2}{14\times 3}.

$$-\frac{59}{140}+\frac{2}{42}$$

Reduce the fraction \frac{2}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{59}{140}+\frac{1}{21}$$

Least common multiple of 140 and 21 is 420. Convert -\frac{59}{140} and \frac{1}{21} to fractions with denominator 420.

$$-\frac{177}{420}+\frac{20}{420}$$

Since -\frac{177}{420} and \frac{20}{420} have the same denominator, add them by adding their numerators.

$$\frac{-177+20}{420}$$

Add -177 and 20 to get -157.

$$-\frac{157}{420}$$

Factor

$$-\frac{157}{420} = -0.3738095238095238$$