Solve {l}{(703*307-123*864+11754):31:13}{(100024:8-11754)*13+507*75:9}{(609*23:7-1239+9327):9+111*89}

$$\left. \begin{array} { l } { ( 703 \times 307 - 123 \times 864 + 11754 ) : 31 : 13 } \\ { ( 100024 : 8 - 11754 ) \times 13 + 507 \times 75 : 9 } \\ { ( 609 \times 23 : 7 - 1239 + 9327 ) : 9 + 111 \times 89 } \end{array} \right.$$

Sort

$$301,11000,13962$$

Solution Steps

Express \frac{\frac{703\times 307-123\times 864+11754}{31}}{13} as a single fraction.

$$sort(\frac{703\times 307-123\times 864+11754}{31\times 13},\left(\frac{100024}{8}-11754\right)\times 13+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Multiply 703 and 307 to get 215821.

$$sort(\frac{215821-123\times 864+11754}{31\times 13},\left(\frac{100024}{8}-11754\right)\times 13+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Multiply 123 and 864 to get 106272.

$$sort(\frac{215821-106272+11754}{31\times 13},\left(\frac{100024}{8}-11754\right)\times 13+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Subtract 106272 from 215821 to get 109549.

$$sort(\frac{109549+11754}{31\times 13},\left(\frac{100024}{8}-11754\right)\times 13+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Add 109549 and 11754 to get 121303.

$$sort(\frac{121303}{31\times 13},\left(\frac{100024}{8}-11754\right)\times 13+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Multiply 31 and 13 to get 403.

$$sort(\frac{121303}{403},\left(\frac{100024}{8}-11754\right)\times 13+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Divide 121303 by 403 to get 301.

$$sort(301,\left(\frac{100024}{8}-11754\right)\times 13+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Divide 100024 by 8 to get 12503.

$$sort(301,\left(12503-11754\right)\times 13+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Subtract 11754 from 12503 to get 749.

$$sort(301,749\times 13+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Multiply 749 and 13 to get 9737.

$$sort(301,9737+\frac{507\times 75}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Multiply 507 and 75 to get 38025.

$$sort(301,9737+\frac{38025}{9},\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Divide 38025 by 9 to get 4225.

$$sort(301,9737+4225,\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Add 9737 and 4225 to get 13962.

$$sort(301,13962,\frac{\frac{609\times 23}{7}-1239+9327}{9}+111\times 89)$$

Multiply 609 and 23 to get 14007.

$$sort(301,13962,\frac{\frac{14007}{7}-1239+9327}{9}+111\times 89)$$

Divide 14007 by 7 to get 2001.

$$sort(301,13962,\frac{2001-1239+9327}{9}+111\times 89)$$

Subtract 1239 from 2001 to get 762.

$$sort(301,13962,\frac{762+9327}{9}+111\times 89)$$

Add 762 and 9327 to get 10089.

$$sort(301,13962,\frac{10089}{9}+111\times 89)$$

Divide 10089 by 9 to get 1121.

$$sort(301,13962,1121+111\times 89)$$

Multiply 111 and 89 to get 9879.

$$sort(301,13962,1121+9879)$$

Add 1121 and 9879 to get 11000.

$$sort(301,13962,11000)$$

To sort the list, start from a single element 301.

$$301$$

Insert 13962 to the appropriate location in the new list.

$$301,13962$$

Insert 11000 to the appropriate location in the new list.

$$301,11000,13962$$

Evaluate

$$301,\ 13962,\ 11000$$