Solve {l}{4/7+0+-8/9+-13/7+17/9}{frac{3}{8}+frac{-5}{12}+frac{3}{7}+frac{3}{12}+frac{-5}{8}+frac{-2}{7}}

$$\left. \begin{array} { l } { \frac { 4 } { 7 } + 0 + \frac { - 8 } { 9 } + \frac { - 13 } { 7 } + \frac { 17 } { 9 } } \\ { \frac { 3 } { 8 } + \frac { - 5 } { 12 } + \frac { 3 } { 7 } + \frac { 3 } { 12 } + \frac { - 5 } { 8 } + \frac { - 2 } { 7 } } \end{array} \right.$$

Sort

$$-\frac{2}{7},\ -\frac{23}{84}$$

Solution Steps

Add \frac{4}{7} and 0 to get \frac{4}{7}.

$$sort(\frac{4}{7}+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{9},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$sort(\frac{4}{7}-\frac{8}{9}+\frac{-13}{7}+\frac{17}{9},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Least common multiple of 7 and 9 is 63. Convert \frac{4}{7} and \frac{8}{9} to fractions with denominator 63.

$$sort(\frac{36}{63}-\frac{56}{63}+\frac{-13}{7}+\frac{17}{9},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Since \frac{36}{63} and \frac{56}{63} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{36-56}{63}+\frac{-13}{7}+\frac{17}{9},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Subtract 56 from 36 to get -20.

$$sort(-\frac{20}{63}+\frac{-13}{7}+\frac{17}{9},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Fraction \frac{-13}{7} can be rewritten as -\frac{13}{7} by extracting the negative sign.

$$sort(-\frac{20}{63}-\frac{13}{7}+\frac{17}{9},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Least common multiple of 63 and 7 is 63. Convert -\frac{20}{63} and \frac{13}{7} to fractions with denominator 63.

$$sort(-\frac{20}{63}-\frac{117}{63}+\frac{17}{9},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Since -\frac{20}{63} and \frac{117}{63} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{-20-117}{63}+\frac{17}{9},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Subtract 117 from -20 to get -137.

$$sort(-\frac{137}{63}+\frac{17}{9},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Least common multiple of 63 and 9 is 63. Convert -\frac{137}{63} and \frac{17}{9} to fractions with denominator 63.

$$sort(-\frac{137}{63}+\frac{119}{63},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Since -\frac{137}{63} and \frac{119}{63} have the same denominator, add them by adding their numerators.

$$sort(\frac{-137+119}{63},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Add -137 and 119 to get -18.

$$sort(\frac{-18}{63},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Reduce the fraction \frac{-18}{63} to lowest terms by extracting and canceling out 9.

$$sort(-\frac{2}{7},\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Fraction \frac{-5}{12} can be rewritten as -\frac{5}{12} by extracting the negative sign.

$$sort(-\frac{2}{7},\frac{3}{8}-\frac{5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Least common multiple of 8 and 12 is 24. Convert \frac{3}{8} and \frac{5}{12} to fractions with denominator 24.

$$sort(-\frac{2}{7},\frac{9}{24}-\frac{10}{24}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Since \frac{9}{24} and \frac{10}{24} have the same denominator, subtract them by subtracting their numerators.

$$sort(-\frac{2}{7},\frac{9-10}{24}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Subtract 10 from 9 to get -1.

$$sort(-\frac{2}{7},-\frac{1}{24}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Least common multiple of 24 and 7 is 168. Convert -\frac{1}{24} and \frac{3}{7} to fractions with denominator 168.

$$sort(-\frac{2}{7},-\frac{7}{168}+\frac{72}{168}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Since -\frac{7}{168} and \frac{72}{168} have the same denominator, add them by adding their numerators.

$$sort(-\frac{2}{7},\frac{-7+72}{168}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

Add -7 and 72 to get 65.

$$sort(-\frac{2}{7},\frac{65}{168}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7})$$

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

$$sort(-\frac{2}{7},\frac{65}{168}+\frac{1}{4}+\frac{-5}{8}+\frac{-2}{7})$$

Least common multiple of 168 and 4 is 168. Convert \frac{65}{168} and \frac{1}{4} to fractions with denominator 168.

$$sort(-\frac{2}{7},\frac{65}{168}+\frac{42}{168}+\frac{-5}{8}+\frac{-2}{7})$$

Since \frac{65}{168} and \frac{42}{168} have the same denominator, add them by adding their numerators.

$$sort(-\frac{2}{7},\frac{65+42}{168}+\frac{-5}{8}+\frac{-2}{7})$$

Add 65 and 42 to get 107.

$$sort(-\frac{2}{7},\frac{107}{168}+\frac{-5}{8}+\frac{-2}{7})$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$sort(-\frac{2}{7},\frac{107}{168}-\frac{5}{8}+\frac{-2}{7})$$

Least common multiple of 168 and 8 is 168. Convert \frac{107}{168} and \frac{5}{8} to fractions with denominator 168.

$$sort(-\frac{2}{7},\frac{107}{168}-\frac{105}{168}+\frac{-2}{7})$$

Since \frac{107}{168} and \frac{105}{168} have the same denominator, subtract them by subtracting their numerators.

$$sort(-\frac{2}{7},\frac{107-105}{168}+\frac{-2}{7})$$

Subtract 105 from 107 to get 2.

$$sort(-\frac{2}{7},\frac{2}{168}+\frac{-2}{7})$$

Reduce the fraction \frac{2}{168} to lowest terms by extracting and canceling out 2.

$$sort(-\frac{2}{7},\frac{1}{84}+\frac{-2}{7})$$

Fraction \frac{-2}{7} can be rewritten as -\frac{2}{7} by extracting the negative sign.

$$sort(-\frac{2}{7},\frac{1}{84}-\frac{2}{7})$$

Least common multiple of 84 and 7 is 84. Convert \frac{1}{84} and \frac{2}{7} to fractions with denominator 84.

$$sort(-\frac{2}{7},\frac{1}{84}-\frac{24}{84})$$

Since \frac{1}{84} and \frac{24}{84} have the same denominator, subtract them by subtracting their numerators.

$$sort(-\frac{2}{7},\frac{1-24}{84})$$

Subtract 24 from 1 to get -23.

$$sort(-\frac{2}{7},-\frac{23}{84})$$

Least common denominator of the numbers in the list -\frac{2}{7},-\frac{23}{84} is 84. Convert numbers in the list to fractions with denominator 84.

$$-\frac{24}{84},-\frac{23}{84}$$

Evaluate

$$-\frac{2}{7},\ -\frac{23}{84}$$