Solve {c}{(-20):(+5)-(-40)*(+0):(-30)}{(-4)-(-100):(-30)}

$$\left. \begin{array} { c } { ( - 20 ) : ( + 5 ) - ( - 40 ) \cdot ( + 0 ) : ( - 30 ) } \\ { ( - 4 ) - ( - 100 ) : ( - 30 ) } \end{array} \right.$$

Sort

$$-\frac{22}{3},-4$$

Solution Steps

Divide -20 by 5 to get -4.

$$sort(-4-\frac{-40\times 0}{-30},-4-\frac{-100}{-30})$$

Multiply -40 and 0 to get 0.

$$sort(-4-\frac{0}{-30},-4-\frac{-100}{-30})$$

Zero divided by any non-zero number gives zero.

$$sort(-4+0,-4-\frac{-100}{-30})$$

Add -4 and 0 to get -4.

$$sort(-4,-4-\frac{-100}{-30})$$

Reduce the fraction \frac{-100}{-30} to lowest terms by extracting and canceling out -10.

$$sort(-4,-4-\frac{10}{3})$$

Convert -4 to fraction -\frac{12}{3}.

$$sort(-4,-\frac{12}{3}-\frac{10}{3})$$

Since -\frac{12}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$sort(-4,\frac{-12-10}{3})$$

Subtract 10 from -12 to get -22.

$$sort(-4,-\frac{22}{3})$$

Convert decimal numbers in the list -4,-\frac{22}{3} to fractions.

$$-4,-\frac{22}{3}$$

To sort the list, start from a single element -4.

$$-4$$

Insert -\frac{22}{3} to the appropriate location in the new list.

$$-\frac{22}{3},-4$$

Evaluate

$$-4,\ -\frac{22}{3}$$