Solve {l}{(-5/16)+(-1/4)+(+9/8)+(+5/4)+(-frac{11}{4})}{(+3)+(-frac{13}{6})+(-3)+(+frac{7}{2})+(-frac{5}{2})+(+frac{23}{6})+(+frac{1}{2})}

$$\left. \begin{array} { l } { ( - \frac { 5 } { 16 } ) + ( - \frac { 1 } { 4 } ) + ( + \frac { 9 } { 8 } ) + ( + \frac { 5 } { 4 } ) + ( - \frac { 11 } { 4 } ) } \\ { ( + 3 ) + ( - \frac { 13 } { 6 } ) + ( - 3 ) + ( + \frac { 7 } { 2 } ) + ( - \frac { 5 } { 2 } ) + ( + \frac { 23 } { 6 } ) + ( + \frac { 1 } { 2 } ) } \end{array} \right.$$

Sort

$$-\frac{15}{16},\ \frac{19}{6}$$

Solution Steps

Least common multiple of 16 and 4 is 16. Convert -\frac{5}{16} and \frac{1}{4} to fractions with denominator 16.

$$sort(-\frac{5}{16}-\frac{4}{16}+\frac{9}{8}+\frac{5}{4}-\frac{11}{4},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Since -\frac{5}{16} and \frac{4}{16} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{-5-4}{16}+\frac{9}{8}+\frac{5}{4}-\frac{11}{4},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Subtract 4 from -5 to get -9.

$$sort(-\frac{9}{16}+\frac{9}{8}+\frac{5}{4}-\frac{11}{4},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Least common multiple of 16 and 8 is 16. Convert -\frac{9}{16} and \frac{9}{8} to fractions with denominator 16.

$$sort(-\frac{9}{16}+\frac{18}{16}+\frac{5}{4}-\frac{11}{4},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Since -\frac{9}{16} and \frac{18}{16} have the same denominator, add them by adding their numerators.

$$sort(\frac{-9+18}{16}+\frac{5}{4}-\frac{11}{4},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Add -9 and 18 to get 9.

$$sort(\frac{9}{16}+\frac{5}{4}-\frac{11}{4},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Least common multiple of 16 and 4 is 16. Convert \frac{9}{16} and \frac{5}{4} to fractions with denominator 16.

$$sort(\frac{9}{16}+\frac{20}{16}-\frac{11}{4},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Since \frac{9}{16} and \frac{20}{16} have the same denominator, add them by adding their numerators.

$$sort(\frac{9+20}{16}-\frac{11}{4},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Add 9 and 20 to get 29.

$$sort(\frac{29}{16}-\frac{11}{4},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Least common multiple of 16 and 4 is 16. Convert \frac{29}{16} and \frac{11}{4} to fractions with denominator 16.

$$sort(\frac{29}{16}-\frac{44}{16},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Since \frac{29}{16} and \frac{44}{16} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{29-44}{16},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Subtract 44 from 29 to get -15.

$$sort(-\frac{15}{16},3-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Convert 3 to fraction \frac{18}{6}.

$$sort(-\frac{15}{16},\frac{18}{6}-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Since \frac{18}{6} and \frac{13}{6} have the same denominator, subtract them by subtracting their numerators.

$$sort(-\frac{15}{16},\frac{18-13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Subtract 13 from 18 to get 5.

$$sort(-\frac{15}{16},\frac{5}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Convert 3 to fraction \frac{18}{6}.

$$sort(-\frac{15}{16},\frac{5}{6}-\frac{18}{6}+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Since \frac{5}{6} and \frac{18}{6} have the same denominator, subtract them by subtracting their numerators.

$$sort(-\frac{15}{16},\frac{5-18}{6}+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Subtract 18 from 5 to get -13.

$$sort(-\frac{15}{16},-\frac{13}{6}+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Least common multiple of 6 and 2 is 6. Convert -\frac{13}{6} and \frac{7}{2} to fractions with denominator 6.

$$sort(-\frac{15}{16},-\frac{13}{6}+\frac{21}{6}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Since -\frac{13}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.

$$sort(-\frac{15}{16},\frac{-13+21}{6}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Add -13 and 21 to get 8.

$$sort(-\frac{15}{16},\frac{8}{6}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$sort(-\frac{15}{16},\frac{4}{3}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2})$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{5}{2} to fractions with denominator 6.

$$sort(-\frac{15}{16},\frac{8}{6}-\frac{15}{6}+\frac{23}{6}+\frac{1}{2})$$

Since \frac{8}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$sort(-\frac{15}{16},\frac{8-15}{6}+\frac{23}{6}+\frac{1}{2})$$

Subtract 15 from 8 to get -7.

$$sort(-\frac{15}{16},-\frac{7}{6}+\frac{23}{6}+\frac{1}{2})$$

Since -\frac{7}{6} and \frac{23}{6} have the same denominator, add them by adding their numerators.

$$sort(-\frac{15}{16},\frac{-7+23}{6}+\frac{1}{2})$$

Add -7 and 23 to get 16.

$$sort(-\frac{15}{16},\frac{16}{6}+\frac{1}{2})$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$sort(-\frac{15}{16},\frac{8}{3}+\frac{1}{2})$$

Least common multiple of 3 and 2 is 6. Convert \frac{8}{3} and \frac{1}{2} to fractions with denominator 6.

$$sort(-\frac{15}{16},\frac{16}{6}+\frac{3}{6})$$

Since \frac{16}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$sort(-\frac{15}{16},\frac{16+3}{6})$$

Add 16 and 3 to get 19.

$$sort(-\frac{15}{16},\frac{19}{6})$$

Least common denominator of the numbers in the list -\frac{15}{16},\frac{19}{6} is 48. Convert numbers in the list to fractions with denominator 48.

$$-\frac{45}{48},\frac{152}{48}$$

Evaluate

$$-\frac{15}{16},\ \frac{19}{6}$$