Solve 234,3/2-5/6+7/12-9/20+frac{11}{30}-frac{13}{42}

$$234 , \frac { 3 } { 2 } - \frac { 5 } { 6 } + \frac { 7 } { 12 } - \frac { 9 } { 20 } + \frac { 11 } { 30 } - \frac { 13 } { 42 }$$

Sort

$$\frac{6}{7},234$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert \frac{3}{2} and \frac{5}{6} to fractions with denominator 6.

$$sort(234,\frac{9}{6}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42})$$

Since \frac{9}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$sort(234,\frac{9-5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42})$$

Subtract 5 from 9 to get 4.

$$sort(234,\frac{4}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42})$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$sort(234,\frac{2}{3}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42})$$

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{7}{12} to fractions with denominator 12.

$$sort(234,\frac{8}{12}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42})$$

Since \frac{8}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$sort(234,\frac{8+7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42})$$

Add 8 and 7 to get 15.

$$sort(234,\frac{15}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42})$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$sort(234,\frac{5}{4}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42})$$

Least common multiple of 4 and 20 is 20. Convert \frac{5}{4} and \frac{9}{20} to fractions with denominator 20.

$$sort(234,\frac{25}{20}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42})$$

Since \frac{25}{20} and \frac{9}{20} have the same denominator, subtract them by subtracting their numerators.

$$sort(234,\frac{25-9}{20}+\frac{11}{30}-\frac{13}{42})$$

Subtract 9 from 25 to get 16.

$$sort(234,\frac{16}{20}+\frac{11}{30}-\frac{13}{42})$$

Reduce the fraction \frac{16}{20} to lowest terms by extracting and canceling out 4.

$$sort(234,\frac{4}{5}+\frac{11}{30}-\frac{13}{42})$$

Least common multiple of 5 and 30 is 30. Convert \frac{4}{5} and \frac{11}{30} to fractions with denominator 30.

$$sort(234,\frac{24}{30}+\frac{11}{30}-\frac{13}{42})$$

Since \frac{24}{30} and \frac{11}{30} have the same denominator, add them by adding their numerators.

$$sort(234,\frac{24+11}{30}-\frac{13}{42})$$

Add 24 and 11 to get 35.

$$sort(234,\frac{35}{30}-\frac{13}{42})$$

Reduce the fraction \frac{35}{30} to lowest terms by extracting and canceling out 5.

$$sort(234,\frac{7}{6}-\frac{13}{42})$$

Least common multiple of 6 and 42 is 42. Convert \frac{7}{6} and \frac{13}{42} to fractions with denominator 42.

$$sort(234,\frac{49}{42}-\frac{13}{42})$$

Since \frac{49}{42} and \frac{13}{42} have the same denominator, subtract them by subtracting their numerators.

$$sort(234,\frac{49-13}{42})$$

Subtract 13 from 49 to get 36.

$$sort(234,\frac{36}{42})$$

Reduce the fraction \frac{36}{42} to lowest terms by extracting and canceling out 6.

$$sort(234,\frac{6}{7})$$

Convert decimal numbers in the list 234,\frac{6}{7} to fractions.

$$234,\frac{6}{7}$$

To sort the list, start from a single element 234.

$$234$$

Insert \frac{6}{7} to the appropriate location in the new list.

$$\frac{6}{7},234$$

Evaluate

$$234,\frac{6}{7}$$