Solve {l}{1/2*(-3/2)-3/2*(-3/2)}{-2}

$$\left. \begin{array}{l}{ \frac { 1 } { 2 } \times ( - \frac { 3 } { 2 } ) - \frac { 3 } { 2 } \times ( - \frac { 3 } { 2 } ) }\\{ - 2 }\end{array} \right.$$

Sort

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

Solution Steps

Multiply \frac{1}{2} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{1\left(-3\right)}{2\times 2}-\frac{3}{2}\left(-\frac{3}{2}\right),-2)$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 2}.

$$sort(\frac{-3}{4}-\frac{3}{2}\left(-\frac{3}{2}\right),-2)$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$sort(-\frac{3}{4}-\frac{3}{2}\left(-\frac{3}{2}\right),-2)$$

Multiply \frac{3}{2} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$sort(-\frac{3}{4}-\frac{3\left(-3\right)}{2\times 2},-2)$$

Do the multiplications in the fraction \frac{3\left(-3\right)}{2\times 2}.

$$sort(-\frac{3}{4}-\frac{-9}{4},-2)$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$sort(-\frac{3}{4}-\left(-\frac{9}{4}\right),-2)$$

The opposite of -\frac{9}{4} is \frac{9}{4}.

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

Since -\frac{3}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

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

Add -3 and 9 to get 6.

$$sort(\frac{6}{4},-2)$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

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

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

To sort the list, start from a single element \frac{3}{2}.

$$\frac{3}{2}$$

Insert -2 to the appropriate location in the new list.

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

Evaluate

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