Solve 3,(+73/4)+(-54/11)+(-31/4)+(-67/11)

$$3 , ( + 7 \frac { 3 } { 4 } ) + ( - 5 \frac { 4 } { 11 } ) + ( - 3 \frac { 1 } { 4 } ) + ( - 6 \frac { 7 } { 11 } )$$

Sort

$$-\frac{15}{2},3$$

Solution Steps

Multiply 7 and 4 to get 28.

$$sort(3,\frac{28+3}{4}-\frac{5\times 11+4}{11}-\frac{3\times 4+1}{4}-\frac{6\times 11+7}{11})$$

Add 28 and 3 to get 31.

$$sort(3,\frac{31}{4}-\frac{5\times 11+4}{11}-\frac{3\times 4+1}{4}-\frac{6\times 11+7}{11})$$

Multiply 5 and 11 to get 55.

$$sort(3,\frac{31}{4}-\frac{55+4}{11}-\frac{3\times 4+1}{4}-\frac{6\times 11+7}{11})$$

Add 55 and 4 to get 59.

$$sort(3,\frac{31}{4}-\frac{59}{11}-\frac{3\times 4+1}{4}-\frac{6\times 11+7}{11})$$

Least common multiple of 4 and 11 is 44. Convert \frac{31}{4} and \frac{59}{11} to fractions with denominator 44.

$$sort(3,\frac{341}{44}-\frac{236}{44}-\frac{3\times 4+1}{4}-\frac{6\times 11+7}{11})$$

Since \frac{341}{44} and \frac{236}{44} have the same denominator, subtract them by subtracting their numerators.

$$sort(3,\frac{341-236}{44}-\frac{3\times 4+1}{4}-\frac{6\times 11+7}{11})$$

Subtract 236 from 341 to get 105.

$$sort(3,\frac{105}{44}-\frac{3\times 4+1}{4}-\frac{6\times 11+7}{11})$$

Multiply 3 and 4 to get 12.

$$sort(3,\frac{105}{44}-\frac{12+1}{4}-\frac{6\times 11+7}{11})$$

Add 12 and 1 to get 13.

$$sort(3,\frac{105}{44}-\frac{13}{4}-\frac{6\times 11+7}{11})$$

Least common multiple of 44 and 4 is 44. Convert \frac{105}{44} and \frac{13}{4} to fractions with denominator 44.

$$sort(3,\frac{105}{44}-\frac{143}{44}-\frac{6\times 11+7}{11})$$

Since \frac{105}{44} and \frac{143}{44} have the same denominator, subtract them by subtracting their numerators.

$$sort(3,\frac{105-143}{44}-\frac{6\times 11+7}{11})$$

Subtract 143 from 105 to get -38.

$$sort(3,\frac{-38}{44}-\frac{6\times 11+7}{11})$$

Reduce the fraction \frac{-38}{44} to lowest terms by extracting and canceling out 2.

$$sort(3,-\frac{19}{22}-\frac{6\times 11+7}{11})$$

Multiply 6 and 11 to get 66.

$$sort(3,-\frac{19}{22}-\frac{66+7}{11})$$

Add 66 and 7 to get 73.

$$sort(3,-\frac{19}{22}-\frac{73}{11})$$

Least common multiple of 22 and 11 is 22. Convert -\frac{19}{22} and \frac{73}{11} to fractions with denominator 22.

$$sort(3,-\frac{19}{22}-\frac{146}{22})$$

Since -\frac{19}{22} and \frac{146}{22} have the same denominator, subtract them by subtracting their numerators.

$$sort(3,\frac{-19-146}{22})$$

Subtract 146 from -19 to get -165.

$$sort(3,\frac{-165}{22})$$

Reduce the fraction \frac{-165}{22} to lowest terms by extracting and canceling out 11.

$$sort(3,-\frac{15}{2})$$

Convert decimal numbers in the list 3,-\frac{15}{2} to fractions.

$$3,-\frac{15}{2}$$

To sort the list, start from a single element 3.

$$3$$

Insert -\frac{15}{2} to the appropriate location in the new list.

$$-\frac{15}{2},3$$

Evaluate

$$3,-\frac{15}{2}$$