Solve {l}{+45/9}{+61/2}{1/3}{-3/4}{-1frac{2}{3}}

$$\left. \begin{array} { l } { + 4 \frac { 5 } { 9 } } \\ { + 6 \frac { 1 } { 2 } } \\ { \frac { 1 } { 3 } } \\ { - \frac { 3 } { 4 } } \\ { - 1 \frac { 2 } { 3 } } \end{array} \right.$$

Sort

$$-\frac{5}{3},-\frac{3}{4},\frac{1}{3},\frac{41}{9},\frac{13}{2}$$

Solution Steps

Multiply 4 and 9 to get 36.

$$sort(\frac{36+5}{9},\frac{6\times 2+1}{2},\frac{1}{3},-\frac{3}{4},-\frac{1\times 3+2}{3})$$

Add 36 and 5 to get 41.

$$sort(\frac{41}{9},\frac{6\times 2+1}{2},\frac{1}{3},-\frac{3}{4},-\frac{1\times 3+2}{3})$$

Multiply 6 and 2 to get 12.

$$sort(\frac{41}{9},\frac{12+1}{2},\frac{1}{3},-\frac{3}{4},-\frac{1\times 3+2}{3})$$

Add 12 and 1 to get 13.

$$sort(\frac{41}{9},\frac{13}{2},\frac{1}{3},-\frac{3}{4},-\frac{1\times 3+2}{3})$$

Multiply 1 and 3 to get 3.

$$sort(\frac{41}{9},\frac{13}{2},\frac{1}{3},-\frac{3}{4},-\frac{3+2}{3})$$

Add 3 and 2 to get 5.

$$sort(\frac{41}{9},\frac{13}{2},\frac{1}{3},-\frac{3}{4},-\frac{5}{3})$$

Least common denominator of the numbers in the list \frac{41}{9},\frac{13}{2},\frac{1}{3},-\frac{3}{4},-\frac{5}{3} is 36. Convert numbers in the list to fractions with denominator 36.

$$\frac{164}{36},\frac{234}{36},\frac{12}{36},-\frac{27}{36},-\frac{60}{36}$$

To sort the list, start from a single element \frac{164}{36}.

$$\frac{164}{36}$$

Insert \frac{234}{36} to the appropriate location in the new list.

$$\frac{164}{36},\frac{234}{36}$$

Insert \frac{12}{36} to the appropriate location in the new list.

$$\frac{12}{36},\frac{164}{36},\frac{234}{36}$$

Insert -\frac{27}{36} to the appropriate location in the new list.

$$-\frac{27}{36},\frac{12}{36},\frac{164}{36},\frac{234}{36}$$

Insert -\frac{60}{36} to the appropriate location in the new list.

$$-\frac{60}{36},-\frac{27}{36},\frac{12}{36},\frac{164}{36},\frac{234}{36}$$

Replace the obtained fractions with the initial values.

$$-\frac{5}{3},-\frac{3}{4},\frac{1}{3},\frac{41}{9},\frac{13}{2}$$

Evaluate

$$\frac{41}{9},\ \frac{13}{2},\ \frac{1}{3},\ -\frac{3}{4},\ -\frac{5}{3}$$