Solve [3/7+1/2*(-2/3)]*(-21/5

$$[ \frac { 3 } { 7 } + \frac { 1 } { 2 } \times ( - \frac { 2 } { 3 } ) ] \times ( - \frac { 21 } { 5 }$$

Evaluate

$$-\frac{2}{5}=-0.4$$

Solution Steps

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

$$\left(\frac{3}{7}+\frac{1\left(-2\right)}{2\times 3}\right)\left(-\frac{21}{5}\right)$$

Do the multiplications in the fraction \frac{1\left(-2\right)}{2\times 3}.

$$\left(\frac{3}{7}+\frac{-2}{6}\right)\left(-\frac{21}{5}\right)$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$\left(\frac{3}{7}-\frac{1}{3}\right)\left(-\frac{21}{5}\right)$$

Least common multiple of 7 and 3 is 21. Convert \frac{3}{7} and \frac{1}{3} to fractions with denominator 21.

$$\left(\frac{9}{21}-\frac{7}{21}\right)\left(-\frac{21}{5}\right)$$

Since \frac{9}{21} and \frac{7}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-7}{21}\left(-\frac{21}{5}\right)$$

Subtract 7 from 9 to get 2.

$$\frac{2}{21}\left(-\frac{21}{5}\right)$$

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

$$\frac{2\left(-21\right)}{21\times 5}$$

Do the multiplications in the fraction \frac{2\left(-21\right)}{21\times 5}.

$$\frac{-42}{105}$$

Reduce the fraction \frac{-42}{105} to lowest terms by extracting and canceling out 21.

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

Factor

$$-\frac{2}{5} = -0.4$$