Solve (-1/42)*[1/2-1/3+5/7+(-frac{2}{3})^2*(-6)]

$$( - \frac { 1 } { 42 } ) \times [ \frac { 1 } { 2 } - \frac { 1 } { 3 } + \frac { 5 } { 7 } + ( - \frac { 2 } { 3 } ) ^ { 2 } \times ( - 6 ) ]$$

Evaluate

$$\frac{25}{588}\approx 0.042517007$$

Solution Steps

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

$$-\frac{1}{42}\left(\frac{3}{6}-\frac{2}{6}+\frac{5}{7}+\left(-\frac{2}{3}\right)^{2}\left(-6\right)\right)$$

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

$$-\frac{1}{42}\left(\frac{3-2}{6}+\frac{5}{7}+\left(-\frac{2}{3}\right)^{2}\left(-6\right)\right)$$

Subtract 2 from 3 to get 1.

$$-\frac{1}{42}\left(\frac{1}{6}+\frac{5}{7}+\left(-\frac{2}{3}\right)^{2}\left(-6\right)\right)$$

Least common multiple of 6 and 7 is 42. Convert \frac{1}{6} and \frac{5}{7} to fractions with denominator 42.

$$-\frac{1}{42}\left(\frac{7}{42}+\frac{30}{42}+\left(-\frac{2}{3}\right)^{2}\left(-6\right)\right)$$

Since \frac{7}{42} and \frac{30}{42} have the same denominator, add them by adding their numerators.

$$-\frac{1}{42}\left(\frac{7+30}{42}+\left(-\frac{2}{3}\right)^{2}\left(-6\right)\right)$$

Add 7 and 30 to get 37.

$$-\frac{1}{42}\left(\frac{37}{42}+\left(-\frac{2}{3}\right)^{2}\left(-6\right)\right)$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-\frac{1}{42}\left(\frac{37}{42}+\frac{4}{9}\left(-6\right)\right)$$

Express \frac{4}{9}\left(-6\right) as a single fraction.

$$-\frac{1}{42}\left(\frac{37}{42}+\frac{4\left(-6\right)}{9}\right)$$

Multiply 4 and -6 to get -24.

$$-\frac{1}{42}\left(\frac{37}{42}+\frac{-24}{9}\right)$$

Reduce the fraction \frac{-24}{9} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{42}\left(\frac{37}{42}-\frac{8}{3}\right)$$

Least common multiple of 42 and 3 is 42. Convert \frac{37}{42} and \frac{8}{3} to fractions with denominator 42.

$$-\frac{1}{42}\left(\frac{37}{42}-\frac{112}{42}\right)$$

Since \frac{37}{42} and \frac{112}{42} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{42}\times \frac{37-112}{42}$$

Subtract 112 from 37 to get -75.

$$-\frac{1}{42}\times \frac{-75}{42}$$

Reduce the fraction \frac{-75}{42} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{42}\left(-\frac{25}{14}\right)$$

Multiply -\frac{1}{42} times -\frac{25}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-25\right)}{42\times 14}$$

Do the multiplications in the fraction \frac{-\left(-25\right)}{42\times 14}.

$$\frac{25}{588}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2} \cdot 3 \cdot 7 ^ {2}} = 0.04251700680272109$$