Solve {l}{(151/2-23/8)-(55/6+63/4)+(10frac{2}{3}-5frac{5}{8})}{(20-19frac{3}{4})+(17frac{3}{4}-17)+(2frac{1}{3}-frac{17}{4})}

$$\left. \begin{array} { l } { ( 15 \frac { 1 } { 2 } - 2 \frac { 3 } { 8 } ) - ( 5 \frac { 5 } { 6 } + 6 \frac { 3 } { 4 } ) + ( 10 \frac { 2 } { 3 } - 5 \frac { 5 } { 8 } ) } \\ { ( 20 - 19 \frac { 3 } { 4 } ) + ( 17 \frac { 3 } { 4 } - 17 ) + ( 2 \frac { 1 } { 3 } - \frac { 17 } { 4 } ) } \end{array} \right.$$

Sort

$$-\frac{11}{12},\frac{67}{12}$$

Solution Steps

Multiply 15 and 2 to get 30.

$$sort(\frac{30+1}{2}-\frac{2\times 8+3}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 30 and 1 to get 31.

$$sort(\frac{31}{2}-\frac{2\times 8+3}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Multiply 2 and 8 to get 16.

$$sort(\frac{31}{2}-\frac{16+3}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 16 and 3 to get 19.

$$sort(\frac{31}{2}-\frac{19}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Least common multiple of 2 and 8 is 8. Convert \frac{31}{2} and \frac{19}{8} to fractions with denominator 8.

$$sort(\frac{124}{8}-\frac{19}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Since \frac{124}{8} and \frac{19}{8} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{124-19}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Subtract 19 from 124 to get 105.

$$sort(\frac{105}{8}-\left(\frac{5\times 6+5}{6}+\frac{6\times 4+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Multiply 5 and 6 to get 30.

$$sort(\frac{105}{8}-\left(\frac{30+5}{6}+\frac{6\times 4+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 30 and 5 to get 35.

$$sort(\frac{105}{8}-\left(\frac{35}{6}+\frac{6\times 4+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Multiply 6 and 4 to get 24.

$$sort(\frac{105}{8}-\left(\frac{35}{6}+\frac{24+3}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 24 and 3 to get 27.

$$sort(\frac{105}{8}-\left(\frac{35}{6}+\frac{27}{4}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Least common multiple of 6 and 4 is 12. Convert \frac{35}{6} and \frac{27}{4} to fractions with denominator 12.

$$sort(\frac{105}{8}-\left(\frac{70}{12}+\frac{81}{12}\right)+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Since \frac{70}{12} and \frac{81}{12} have the same denominator, add them by adding their numerators.

$$sort(\frac{105}{8}-\frac{70+81}{12}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 70 and 81 to get 151.

$$sort(\frac{105}{8}-\frac{151}{12}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Least common multiple of 8 and 12 is 24. Convert \frac{105}{8} and \frac{151}{12} to fractions with denominator 24.

$$sort(\frac{315}{24}-\frac{302}{24}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Since \frac{315}{24} and \frac{302}{24} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{315-302}{24}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Subtract 302 from 315 to get 13.

$$sort(\frac{13}{24}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Multiply 10 and 3 to get 30.

$$sort(\frac{13}{24}+\frac{30+2}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 30 and 2 to get 32.

$$sort(\frac{13}{24}+\frac{32}{3}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Least common multiple of 24 and 3 is 24. Convert \frac{13}{24} and \frac{32}{3} to fractions with denominator 24.

$$sort(\frac{13}{24}+\frac{256}{24}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Since \frac{13}{24} and \frac{256}{24} have the same denominator, add them by adding their numerators.

$$sort(\frac{13+256}{24}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 13 and 256 to get 269.

$$sort(\frac{269}{24}-\frac{5\times 8+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Multiply 5 and 8 to get 40.

$$sort(\frac{269}{24}-\frac{40+5}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 40 and 5 to get 45.

$$sort(\frac{269}{24}-\frac{45}{8},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Least common multiple of 24 and 8 is 24. Convert \frac{269}{24} and \frac{45}{8} to fractions with denominator 24.

$$sort(\frac{269}{24}-\frac{135}{24},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Since \frac{269}{24} and \frac{135}{24} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{269-135}{24},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Subtract 135 from 269 to get 134.

$$sort(\frac{134}{24},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Reduce the fraction \frac{134}{24} to lowest terms by extracting and canceling out 2.

$$sort(\frac{67}{12},20-\frac{19\times 4+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Multiply 19 and 4 to get 76.

$$sort(\frac{67}{12},20-\frac{76+3}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 76 and 3 to get 79.

$$sort(\frac{67}{12},20-\frac{79}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Convert 20 to fraction \frac{80}{4}.

$$sort(\frac{67}{12},\frac{80}{4}-\frac{79}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Since \frac{80}{4} and \frac{79}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{67}{12},\frac{80-79}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Subtract 79 from 80 to get 1.

$$sort(\frac{67}{12},\frac{1}{4}+\frac{17\times 4+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Multiply 17 and 4 to get 68.

$$sort(\frac{67}{12},\frac{1}{4}+\frac{68+3}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 68 and 3 to get 71.

$$sort(\frac{67}{12},\frac{1}{4}+\frac{71}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Since \frac{1}{4} and \frac{71}{4} have the same denominator, add them by adding their numerators.

$$sort(\frac{67}{12},\frac{1+71}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Add 1 and 71 to get 72.

$$sort(\frac{67}{12},\frac{72}{4}-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Divide 72 by 4 to get 18.

$$sort(\frac{67}{12},18-17+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Subtract 17 from 18 to get 1.

$$sort(\frac{67}{12},1+\frac{2\times 3+1}{3}-\frac{17}{4})$$

Multiply 2 and 3 to get 6.

$$sort(\frac{67}{12},1+\frac{6+1}{3}-\frac{17}{4})$$

Add 6 and 1 to get 7.

$$sort(\frac{67}{12},1+\frac{7}{3}-\frac{17}{4})$$

Convert 1 to fraction \frac{3}{3}.

$$sort(\frac{67}{12},\frac{3}{3}+\frac{7}{3}-\frac{17}{4})$$

Since \frac{3}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$sort(\frac{67}{12},\frac{3+7}{3}-\frac{17}{4})$$

Add 3 and 7 to get 10.

$$sort(\frac{67}{12},\frac{10}{3}-\frac{17}{4})$$

Least common multiple of 3 and 4 is 12. Convert \frac{10}{3} and \frac{17}{4} to fractions with denominator 12.

$$sort(\frac{67}{12},\frac{40}{12}-\frac{51}{12})$$

Since \frac{40}{12} and \frac{51}{12} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{67}{12},\frac{40-51}{12})$$

Subtract 51 from 40 to get -11.

$$sort(\frac{67}{12},-\frac{11}{12})$$

To sort the list, start from a single element \frac{67}{12}.

$$\frac{67}{12}$$

Insert -\frac{11}{12} to the appropriate location in the new list.

$$-\frac{11}{12},\frac{67}{12}$$

Evaluate

$$\frac{67}{12},\ -\frac{11}{12}$$