Solve {l}{1/2+1/3-1/4}{11/12-frac{8}{15}-frac{3}{20}}

$$\left. \begin{array} { l } { \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 4 } } \\ { \frac { 11 } { 12 } - \frac { 8 } { 15 } - \frac { 3 } { 20 } } \end{array} \right.$$

Sort

$$\frac{7}{30},\frac{7}{12}$$

Solution Steps

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

$$sort(\frac{3}{6}+\frac{2}{6}-\frac{1}{4},\frac{11}{12}-\frac{8}{15}-\frac{3}{20})$$

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

$$sort(\frac{3+2}{6}-\frac{1}{4},\frac{11}{12}-\frac{8}{15}-\frac{3}{20})$$

Add 3 and 2 to get 5.

$$sort(\frac{5}{6}-\frac{1}{4},\frac{11}{12}-\frac{8}{15}-\frac{3}{20})$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$sort(\frac{10}{12}-\frac{3}{12},\frac{11}{12}-\frac{8}{15}-\frac{3}{20})$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{10-3}{12},\frac{11}{12}-\frac{8}{15}-\frac{3}{20})$$

Subtract 3 from 10 to get 7.

$$sort(\frac{7}{12},\frac{11}{12}-\frac{8}{15}-\frac{3}{20})$$

Least common multiple of 12 and 15 is 60. Convert \frac{11}{12} and \frac{8}{15} to fractions with denominator 60.

$$sort(\frac{7}{12},\frac{55}{60}-\frac{32}{60}-\frac{3}{20})$$

Since \frac{55}{60} and \frac{32}{60} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{7}{12},\frac{55-32}{60}-\frac{3}{20})$$

Subtract 32 from 55 to get 23.

$$sort(\frac{7}{12},\frac{23}{60}-\frac{3}{20})$$

Least common multiple of 60 and 20 is 60. Convert \frac{23}{60} and \frac{3}{20} to fractions with denominator 60.

$$sort(\frac{7}{12},\frac{23}{60}-\frac{9}{60})$$

Since \frac{23}{60} and \frac{9}{60} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{7}{12},\frac{23-9}{60})$$

Subtract 9 from 23 to get 14.

$$sort(\frac{7}{12},\frac{14}{60})$$

Reduce the fraction \frac{14}{60} to lowest terms by extracting and canceling out 2.

$$sort(\frac{7}{12},\frac{7}{30})$$

Least common denominator of the numbers in the list \frac{7}{12},\frac{7}{30} is 60. Convert numbers in the list to fractions with denominator 60.

$$\frac{35}{60},\frac{14}{60}$$

To sort the list, start from a single element \frac{35}{60}.

$$\frac{35}{60}$$

Insert \frac{14}{60} to the appropriate location in the new list.

$$\frac{14}{60},\frac{35}{60}$$

Replace the obtained fractions with the initial values.

$$\frac{7}{30},\frac{7}{12}$$

Evaluate

$$\frac{7}{12},\ \frac{7}{30}$$