Calculus Examples

$\frac{1}{3} \cdot 6^{2} + \frac{2}{3}$

Step 1

Simplify each term.

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Step 1.1

Raise $6$ to the power of $2$ .

$\frac{1}{3} \cdot 36 + \frac{2}{3}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $36$ .

$\frac{1}{3} \cdot (3 (12)) + \frac{2}{3}$

Step 1.2.2

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 12) + \frac{2}{3}$

Step 1.2.3

Rewrite the expression.

$12 + \frac{2}{3}$

Step 2

To write $12$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$12 \cdot \frac{3}{3} + \frac{2}{3}$

Step 3

Combine $12$ and $\frac{3}{3}$ .

$\frac{12 \cdot 3}{3} + \frac{2}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{12 \cdot 3 + 2}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $12$ by $3$ .

$\frac{36 + 2}{3}$

Step 5.2

Add $36$ and $2$ .

$\frac{38}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{38}{3}$

Decimal Form:

$12.\overline{6}$

Mixed Number Form:

$12 \frac{2}{3}$