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

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

Evaluate

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

Solution Steps

Fraction \frac{-5}{7} can be rewritten as -\frac{5}{7} by extracting the negative sign.

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

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

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

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

$$\frac{-10}{21}-\frac{1}{6}\times \frac{3}{7}+\frac{1}{14}\times \frac{2}{3}$$

Fraction \frac{-10}{21} can be rewritten as -\frac{10}{21} by extracting the negative sign.

$$-\frac{10}{21}-\frac{1}{6}\times \frac{3}{7}+\frac{1}{14}\times \frac{2}{3}$$

Multiply \frac{1}{6} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{10}{21}-\frac{1\times 3}{6\times 7}+\frac{1}{14}\times \frac{2}{3}$$

Do the multiplications in the fraction \frac{1\times 3}{6\times 7}.

$$-\frac{10}{21}-\frac{3}{42}+\frac{1}{14}\times \frac{2}{3}$$

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

$$-\frac{10}{21}-\frac{1}{14}+\frac{1}{14}\times \frac{2}{3}$$

Least common multiple of 21 and 14 is 42. Convert -\frac{10}{21} and \frac{1}{14} to fractions with denominator 42.

$$-\frac{20}{42}-\frac{3}{42}+\frac{1}{14}\times \frac{2}{3}$$

Since -\frac{20}{42} and \frac{3}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-20-3}{42}+\frac{1}{14}\times \frac{2}{3}$$

Subtract 3 from -20 to get -23.

$$-\frac{23}{42}+\frac{1}{14}\times \frac{2}{3}$$

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

$$-\frac{23}{42}+\frac{1\times 2}{14\times 3}$$

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

$$-\frac{23}{42}+\frac{2}{42}$$

Since -\frac{23}{42} and \frac{2}{42} have the same denominator, add them by adding their numerators.

$$\frac{-23+2}{42}$$

Add -23 and 2 to get -21.

$$\frac{-21}{42}$$

Reduce the fraction \frac{-21}{42} to lowest terms by extracting and canceling out 21.

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

Factor

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