Solve (-1/18)div(1/6-1/10+2/3-frac{2}{5})+(frac{1}{6}-frac{1}{10}+frac{2}{3}-frac{2}{5})+(frac{1}{6}-frac{1}{10}+frac{2}{3}-frac{2}{5})div(-frac{1}{18})=

$$(- \frac{ 1 }{ 18 } ) \div ( \frac{ 1 }{ 6 } - \frac{ 1 }{ 10 } + \frac{ 2 }{ 3 } - \frac{ 2 }{ 5 } )+( \frac{ 1 }{ 6 } - \frac{ 1 }{ 10 } + \frac{ 2 }{ 3 } - \frac{ 2 }{ 5 } )+( \frac{ 1 }{ 6 } - \frac{ 1 }{ 10 } + \frac{ 2 }{ 3 } - \frac{ 2 }{ 5 } ) \div (- \frac{ 1 }{ 18 } )=$$

Evaluate

$$-\frac{35}{6}\approx -5.833333333$$

Solution Steps

Least common multiple of 6 and 10 is 30. Convert \frac{1}{6} and \frac{1}{10} to fractions with denominator 30.

$$\frac{-\frac{1}{18}}{\frac{5}{30}-\frac{3}{30}+\frac{2}{3}-\frac{2}{5}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Since \frac{5}{30} and \frac{3}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{18}}{\frac{5-3}{30}+\frac{2}{3}-\frac{2}{5}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Subtract 3 from 5 to get 2.

$$\frac{-\frac{1}{18}}{\frac{2}{30}+\frac{2}{3}-\frac{2}{5}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{1}{18}}{\frac{1}{15}+\frac{2}{3}-\frac{2}{5}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Least common multiple of 15 and 3 is 15. Convert \frac{1}{15} and \frac{2}{3} to fractions with denominator 15.

$$\frac{-\frac{1}{18}}{\frac{1}{15}+\frac{10}{15}-\frac{2}{5}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Since \frac{1}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{18}}{\frac{1+10}{15}-\frac{2}{5}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Add 1 and 10 to get 11.

$$\frac{-\frac{1}{18}}{\frac{11}{15}-\frac{2}{5}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Least common multiple of 15 and 5 is 15. Convert \frac{11}{15} and \frac{2}{5} to fractions with denominator 15.

$$\frac{-\frac{1}{18}}{\frac{11}{15}-\frac{6}{15}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Since \frac{11}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{18}}{\frac{11-6}{15}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Subtract 6 from 11 to get 5.

$$\frac{-\frac{1}{18}}{\frac{5}{15}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{1}{18}}{\frac{1}{3}}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Divide -\frac{1}{18} by \frac{1}{3} by multiplying -\frac{1}{18} by the reciprocal of \frac{1}{3}.

$$-\frac{1}{18}\times 3+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Express -\frac{1}{18}\times 3 as a single fraction.

$$\frac{-3}{18}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Reduce the fraction \frac{-3}{18} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Add -\frac{1}{6} and \frac{1}{6} to get 0.

$$-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Least common multiple of 10 and 3 is 30. Convert -\frac{1}{10} and \frac{2}{3} to fractions with denominator 30.

$$-\frac{3}{30}+\frac{20}{30}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Since -\frac{3}{30} and \frac{20}{30} have the same denominator, add them by adding their numerators.

$$\frac{-3+20}{30}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Add -3 and 20 to get 17.

$$\frac{17}{30}-\frac{2}{5}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Least common multiple of 30 and 5 is 30. Convert \frac{17}{30} and \frac{2}{5} to fractions with denominator 30.

$$\frac{17}{30}-\frac{12}{30}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Since \frac{17}{30} and \frac{12}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-12}{30}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Subtract 12 from 17 to get 5.

$$\frac{5}{30}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Reduce the fraction \frac{5}{30} to lowest terms by extracting and canceling out 5.

$$\frac{1}{6}+\frac{\frac{1}{6}-\frac{1}{10}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Least common multiple of 6 and 10 is 30. Convert \frac{1}{6} and \frac{1}{10} to fractions with denominator 30.

$$\frac{1}{6}+\frac{\frac{5}{30}-\frac{3}{30}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Since \frac{5}{30} and \frac{3}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}+\frac{\frac{5-3}{30}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Subtract 3 from 5 to get 2.

$$\frac{1}{6}+\frac{\frac{2}{30}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}+\frac{\frac{1}{15}+\frac{2}{3}-\frac{2}{5}}{-\frac{1}{18}}$$

Least common multiple of 15 and 3 is 15. Convert \frac{1}{15} and \frac{2}{3} to fractions with denominator 15.

$$\frac{1}{6}+\frac{\frac{1}{15}+\frac{10}{15}-\frac{2}{5}}{-\frac{1}{18}}$$

Since \frac{1}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}+\frac{\frac{1+10}{15}-\frac{2}{5}}{-\frac{1}{18}}$$

Add 1 and 10 to get 11.

$$\frac{1}{6}+\frac{\frac{11}{15}-\frac{2}{5}}{-\frac{1}{18}}$$

Least common multiple of 15 and 5 is 15. Convert \frac{11}{15} and \frac{2}{5} to fractions with denominator 15.

$$\frac{1}{6}+\frac{\frac{11}{15}-\frac{6}{15}}{-\frac{1}{18}}$$

Since \frac{11}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}+\frac{\frac{11-6}{15}}{-\frac{1}{18}}$$

Subtract 6 from 11 to get 5.

$$\frac{1}{6}+\frac{\frac{5}{15}}{-\frac{1}{18}}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{1}{6}+\frac{\frac{1}{3}}{-\frac{1}{18}}$$

Divide \frac{1}{3} by -\frac{1}{18} by multiplying \frac{1}{3} by the reciprocal of -\frac{1}{18}.

$$\frac{1}{6}+\frac{1}{3}\left(-18\right)$$

Multiply \frac{1}{3} and -18 to get \frac{-18}{3}.

$$\frac{1}{6}+\frac{-18}{3}$$

Divide -18 by 3 to get -6.

$$\frac{1}{6}-6$$

Convert 6 to fraction \frac{36}{6}.

$$\frac{1}{6}-\frac{36}{6}$$

Since \frac{1}{6} and \frac{36}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-36}{6}$$

Subtract 36 from 1 to get -35.

$$-\frac{35}{6}$$

Factor

$$-\frac{35}{6} = -5\frac{5}{6} = -5.833333333333333$$