Solve {l}{text{(1)}(-4)+(-5)}{text{(3)}(-5)-(-2)}{text{(5)}2.4-(-1.6)quadtext{(2)}(-4)+7}{text{(7)}3-5+8quadtext{(6)}(-3/4)-(-1/6)}{text{(4)}7+(-9)-(-1)text{9-}13}

$$\left. \begin{array} { l } { \text { (1) } ( - 4 ) + ( - 5 ) } \\ { \text { (3) } ( - 5 ) - ( - 2 ) } \\ { \text { (5) } 2.4 - ( - 1.6 ) \quad \text { (2) } ( - 4 ) + 7 } \\ { \text { (7) } 3 - 5 + 8 \quad \text { (6) } ( - \frac { 3 } { 4 } ) - ( - \frac { 1 } { 6 } ) } \\ { \text { (4) } 7 + ( - 9 ) - ( - 1 ) \text { 9- } 13 } \end{array} \right.$$

Sort

$$-\frac{119}{6},-13,-9,6.2,15$$

Solution Steps

Multiply 1 and -4 to get -4.

$$sort(-4-5,3\left(-5\right)-\left(-2\right),5\times 2.4-\left(-1.6\times 2\left(-4\right)\right)+7,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Subtract 5 from -4 to get -9.

$$sort(-9,3\left(-5\right)-\left(-2\right),5\times 2.4-\left(-1.6\times 2\left(-4\right)\right)+7,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Multiply 3 and -5 to get -15.

$$sort(-9,-15-\left(-2\right),5\times 2.4-\left(-1.6\times 2\left(-4\right)\right)+7,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

The opposite of -2 is 2.

$$sort(-9,-15+2,5\times 2.4-\left(-1.6\times 2\left(-4\right)\right)+7,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Add -15 and 2 to get -13.

$$sort(-9,-13,5\times 2.4-\left(-1.6\times 2\left(-4\right)\right)+7,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Multiply 5 and 2.4 to get 12.

$$sort(-9,-13,12-\left(-1.6\times 2\left(-4\right)\right)+7,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Multiply -1.6 and 2 to get -3.2.

$$sort(-9,-13,12-\left(-3.2\left(-4\right)\right)+7,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Multiply -3.2 and -4 to get 12.8.

$$sort(-9,-13,12-12.8+7,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Subtract 12.8 from 12 to get -0.8.

$$sort(-9,-13,-0.8+7,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Add -0.8 and 7 to get 6.2.

$$sort(-9,-13,6.2,7\times 3-5+8\times 6\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Multiply 7 and 3 to get 21. Multiply 8 and 6 to get 48.

$$sort(-9,-13,6.2,21-5+48\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Subtract 5 from 21 to get 16.

$$sort(-9,-13,6.2,16+48\left(-\frac{3}{4}\right)-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Express 48\left(-\frac{3}{4}\right) as a single fraction.

$$sort(-9,-13,6.2,16+\frac{48\left(-3\right)}{4}-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Multiply 48 and -3 to get -144.

$$sort(-9,-13,6.2,16+\frac{-144}{4}-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Divide -144 by 4 to get -36.

$$sort(-9,-13,6.2,16-36-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

Subtract 36 from 16 to get -20.

$$sort(-9,-13,6.2,-20-\left(-\frac{1}{6}\right),4\times 7-9-\left(-9\right)-13)$$

The opposite of -\frac{1}{6} is \frac{1}{6}.

$$sort(-9,-13,6.2,-20+\frac{1}{6},4\times 7-9-\left(-9\right)-13)$$

Convert -20 to fraction -\frac{120}{6}.

$$sort(-9,-13,6.2,-\frac{120}{6}+\frac{1}{6},4\times 7-9-\left(-9\right)-13)$$

Since -\frac{120}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$sort(-9,-13,6.2,\frac{-120+1}{6},4\times 7-9-\left(-9\right)-13)$$

Add -120 and 1 to get -119.

$$sort(-9,-13,6.2,-\frac{119}{6},4\times 7-9-\left(-9\right)-13)$$

Multiply 4 and 7 to get 28.

$$sort(-9,-13,6.2,-\frac{119}{6},28-9-\left(-9\right)-13)$$

Subtract 9 from 28 to get 19.

$$sort(-9,-13,6.2,-\frac{119}{6},19-\left(-9\right)-13)$$

The opposite of -9 is 9.

$$sort(-9,-13,6.2,-\frac{119}{6},19+9-13)$$

Add 19 and 9 to get 28.

$$sort(-9,-13,6.2,-\frac{119}{6},28-13)$$

Subtract 13 from 28 to get 15.

$$sort(-9,-13,6.2,-\frac{119}{6},15)$$

Convert decimal numbers in the list -9,-13,6.2,-\frac{119}{6},15 to fractions.

$$-9,-13,\frac{31}{5},-\frac{119}{6},15$$

Least common denominator of the numbers in the list -9,-13,\frac{31}{5},-\frac{119}{6},15 is 30. Convert numbers in the list to fractions with denominator 30.

$$-\frac{270}{30},-\frac{390}{30},\frac{186}{30},-\frac{595}{30},\frac{450}{30}$$

To sort the list, start from a single element -\frac{270}{30}.

$$-\frac{270}{30}$$

Insert -\frac{390}{30} to the appropriate location in the new list.

$$-\frac{390}{30},-\frac{270}{30}$$

Insert \frac{186}{30} to the appropriate location in the new list.

$$-\frac{390}{30},-\frac{270}{30},\frac{186}{30}$$

Insert -\frac{595}{30} to the appropriate location in the new list.

$$-\frac{595}{30},-\frac{390}{30},-\frac{270}{30},\frac{186}{30}$$

Insert \frac{450}{30} to the appropriate location in the new list.

$$-\frac{595}{30},-\frac{390}{30},-\frac{270}{30},\frac{186}{30},\frac{450}{30}$$

Replace the obtained fractions with the initial values.

$$-\frac{119}{6},-13,-9,6.2,15$$

Evaluate

$$-9,\ -13,\ 6.2,\ -\frac{119}{6},\ 15$$