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

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

Evaluate

$$\frac{1}{75}\approx 0.013333333$$

Solution Steps

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

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

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

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

Subtract 2 from 3 to get 1.

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

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

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

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

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

Add 7 and 30 to get 37.

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

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

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

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

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

Multiply 4 and -6 to get -24.

$$\frac{-\frac{1}{42}}{\frac{37}{42}+\frac{-24}{9}}$$

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

$$\frac{-\frac{1}{42}}{\frac{37}{42}-\frac{8}{3}}$$

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

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

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

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

Subtract 112 from 37 to get -75.

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

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

$$\frac{-\frac{1}{42}}{-\frac{25}{14}}$$

Divide -\frac{1}{42} by -\frac{25}{14} by multiplying -\frac{1}{42} by the reciprocal of -\frac{25}{14}.

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

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

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

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

$$\frac{14}{1050}$$

Reduce the fraction \frac{14}{1050} to lowest terms by extracting and canceling out 14.

$$\frac{1}{75}$$

Factor

$$\frac{1}{3 \cdot 5 ^ {2}} = 0.013333333333333334$$