Solve 1/9-1/12+(1/8-23/9)-(frac{3}{8}+(frac{1}{3}-frac{5}{2})-frac{1}{6})+frac{4}{9}

$$\frac{ 1 }{ 9 } - \frac{ 1 }{ 12 } +( \frac{ 1 }{ 8 } - \frac{ 23 }{ 9 } )-( \frac{ 3 }{ 8 } +( \frac{ 1 }{ 3 } - \frac{ 5 }{ 2 } )- \frac{ 1 }{ 6 } )+ \frac{ 4 }{ 9 }$$

Evaluate

$$0$$

Solution Steps

Least common multiple of 9 and 12 is 36. Convert \frac{1}{9} and \frac{1}{12} to fractions with denominator 36.

$$\frac{4}{36}-\frac{3}{36}+\frac{1}{8}-\frac{23}{9}-\left(\frac{3}{8}+\frac{1}{3}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Since \frac{4}{36} and \frac{3}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{36}+\frac{1}{8}-\frac{23}{9}-\left(\frac{3}{8}+\frac{1}{3}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{36}+\frac{1}{8}-\frac{23}{9}-\left(\frac{3}{8}+\frac{1}{3}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Least common multiple of 36 and 8 is 72. Convert \frac{1}{36} and \frac{1}{8} to fractions with denominator 72.

$$\frac{2}{72}+\frac{9}{72}-\frac{23}{9}-\left(\frac{3}{8}+\frac{1}{3}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Since \frac{2}{72} and \frac{9}{72} have the same denominator, add them by adding their numerators.

$$\frac{2+9}{72}-\frac{23}{9}-\left(\frac{3}{8}+\frac{1}{3}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Add 2 and 9 to get 11.

$$\frac{11}{72}-\frac{23}{9}-\left(\frac{3}{8}+\frac{1}{3}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Least common multiple of 72 and 9 is 72. Convert \frac{11}{72} and \frac{23}{9} to fractions with denominator 72.

$$\frac{11}{72}-\frac{184}{72}-\left(\frac{3}{8}+\frac{1}{3}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Since \frac{11}{72} and \frac{184}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-184}{72}-\left(\frac{3}{8}+\frac{1}{3}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Subtract 184 from 11 to get -173.

$$-\frac{173}{72}-\left(\frac{3}{8}+\frac{1}{3}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Least common multiple of 8 and 3 is 24. Convert \frac{3}{8} and \frac{1}{3} to fractions with denominator 24.

$$-\frac{173}{72}-\left(\frac{9}{24}+\frac{8}{24}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Since \frac{9}{24} and \frac{8}{24} have the same denominator, add them by adding their numerators.

$$-\frac{173}{72}-\left(\frac{9+8}{24}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Add 9 and 8 to get 17.

$$-\frac{173}{72}-\left(\frac{17}{24}-\frac{5}{2}-\frac{1}{6}\right)+\frac{4}{9}$$

Least common multiple of 24 and 2 is 24. Convert \frac{17}{24} and \frac{5}{2} to fractions with denominator 24.

$$-\frac{173}{72}-\left(\frac{17}{24}-\frac{60}{24}-\frac{1}{6}\right)+\frac{4}{9}$$

Since \frac{17}{24} and \frac{60}{24} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{173}{72}-\left(\frac{17-60}{24}-\frac{1}{6}\right)+\frac{4}{9}$$

Subtract 60 from 17 to get -43.

$$-\frac{173}{72}-\left(-\frac{43}{24}-\frac{1}{6}\right)+\frac{4}{9}$$

Least common multiple of 24 and 6 is 24. Convert -\frac{43}{24} and \frac{1}{6} to fractions with denominator 24.

$$-\frac{173}{72}-\left(-\frac{43}{24}-\frac{4}{24}\right)+\frac{4}{9}$$

Since -\frac{43}{24} and \frac{4}{24} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{173}{72}-\frac{-43-4}{24}+\frac{4}{9}$$

Subtract 4 from -43 to get -47.

$$-\frac{173}{72}-\left(-\frac{47}{24}\right)+\frac{4}{9}$$

The opposite of -\frac{47}{24} is \frac{47}{24}.

$$-\frac{173}{72}+\frac{47}{24}+\frac{4}{9}$$

Least common multiple of 72 and 24 is 72. Convert -\frac{173}{72} and \frac{47}{24} to fractions with denominator 72.

$$-\frac{173}{72}+\frac{141}{72}+\frac{4}{9}$$

Since -\frac{173}{72} and \frac{141}{72} have the same denominator, add them by adding their numerators.

$$\frac{-173+141}{72}+\frac{4}{9}$$

Add -173 and 141 to get -32.

$$\frac{-32}{72}+\frac{4}{9}$$

Reduce the fraction \frac{-32}{72} to lowest terms by extracting and canceling out 8.

$$-\frac{4}{9}+\frac{4}{9}$$

Add -\frac{4}{9} and \frac{4}{9} to get 0.

$$0$$

Factor

$$0$$