Calculus Examples

$\frac{3}{2} \cdot {(3)}^{2} - 5 \cdot 3$

Step 1

Simplify each term.

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Step 1.1

Raise $3$ to the power of $2$ .

$\frac{3}{2} \cdot 9 - 5 \cdot 3$

Step 1.2

Multiply $\frac{3}{2} \cdot 9$ .

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Step 1.2.1

Combine $\frac{3}{2}$ and $9$ .

$\frac{3 \cdot 9}{2} - 5 \cdot 3$

Step 1.2.2

Multiply $3$ by $9$ .

$\frac{27}{2} - 5 \cdot 3$

Step 1.3

Multiply $- 5$ by $3$ .

$\frac{27}{2} - 15$

Step 2

To write $- 15$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{27}{2} - 15 \cdot \frac{2}{2}$

Step 3

Combine $- 15$ and $\frac{2}{2}$ .

$\frac{27}{2} + \frac{- 15 \cdot 2}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{27 - 15 \cdot 2}{2}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 15$ by $2$ .

$\frac{27 - 30}{2}$

Step 5.2

Subtract $30$ from $27$ .

$\frac{- 3}{2}$

Step 6

Move the negative in front of the fraction.

$- \frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{2}$

Decimal Form:

$- 1.5$

Mixed Number Form:

$- 1 \frac{1}{2}$