Calculus Examples

$\frac{1}{3} \cdot 2^{3} + \frac{5}{2} \cdot 2^{2} - 6 \cdot 2 + 4$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{3} \cdot 8 + \frac{5}{2} \cdot 2^{2} - 6 \cdot 2 + 4$

Step 1.2

Combine $\frac{1}{3}$ and $8$ .

$\frac{8}{3} + \frac{5}{2} \cdot 2^{2} - 6 \cdot 2 + 4$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $2^{2}$ .

$\frac{8}{3} + \frac{5}{2} \cdot (2 \cdot 2) - 6 \cdot 2 + 4$

Step 1.3.2

Cancel the common factor.

$\frac{8}{3} + \frac{5}{2} \cdot (2 \cdot 2) - 6 \cdot 2 + 4$

Step 1.3.3

Rewrite the expression.

$\frac{8}{3} + 5 \cdot 2 - 6 \cdot 2 + 4$

Step 1.4

Multiply $5$ by $2$ .

$\frac{8}{3} + 10 - 6 \cdot 2 + 4$

Step 1.5

Multiply $- 6$ by $2$ .

$\frac{8}{3} + 10 - 12 + 4$

Step 2

Find the common denominator.

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Step 2.1

Write $10$ as a fraction with denominator $1$ .

$\frac{8}{3} + \frac{10}{1} - 12 + 4$

Step 2.2

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{8}{3} + \frac{10}{1} \cdot \frac{3}{3} - 12 + 4$

Step 2.3

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{8}{3} + \frac{10 \cdot 3}{3} - 12 + 4$

Step 2.4

Write $- 12$ as a fraction with denominator $1$ .

$\frac{8}{3} + \frac{10 \cdot 3}{3} + \frac{- 12}{1} + 4$

Step 2.5

Multiply $\frac{- 12}{1}$ by $\frac{3}{3}$ .

$\frac{8}{3} + \frac{10 \cdot 3}{3} + \frac{- 12}{1} \cdot \frac{3}{3} + 4$

Step 2.6

Multiply $\frac{- 12}{1}$ by $\frac{3}{3}$ .

$\frac{8}{3} + \frac{10 \cdot 3}{3} + \frac{- 12 \cdot 3}{3} + 4$

Step 2.7

Write $4$ as a fraction with denominator $1$ .

$\frac{8}{3} + \frac{10 \cdot 3}{3} + \frac{- 12 \cdot 3}{3} + \frac{4}{1}$

Step 2.8

Multiply $\frac{4}{1}$ by $\frac{3}{3}$ .

$\frac{8}{3} + \frac{10 \cdot 3}{3} + \frac{- 12 \cdot 3}{3} + \frac{4}{1} \cdot \frac{3}{3}$

Step 2.9

Multiply $\frac{4}{1}$ by $\frac{3}{3}$ .

$\frac{8}{3} + \frac{10 \cdot 3}{3} + \frac{- 12 \cdot 3}{3} + \frac{4 \cdot 3}{3}$

Step 3

Combine the numerators over the common denominator.

$\frac{8 + 10 \cdot 3 - 12 \cdot 3 + 4 \cdot 3}{3}$

Step 4

Simplify each term.

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Step 4.1

Multiply $10$ by $3$ .

$\frac{8 + 30 - 12 \cdot 3 + 4 \cdot 3}{3}$

Step 4.2

Multiply $- 12$ by $3$ .

$\frac{8 + 30 - 36 + 4 \cdot 3}{3}$

Step 4.3

Multiply $4$ by $3$ .

$\frac{8 + 30 - 36 + 12}{3}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $8$ and $30$ .

$\frac{38 - 36 + 12}{3}$

Step 5.2

Subtract $36$ from $38$ .

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

Step 5.3

Add $2$ and $12$ .

$\frac{14}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{14}{3}$

Decimal Form:

$4.\overline{6}$

Mixed Number Form:

$4 \frac{2}{3}$