Basic Math Examples

$2 {(\frac{1}{2})}^{2} + 2 (\frac{1}{2}) + 8$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{1}{2}$ .

$2 \frac{1^{2}}{2^{2}} + 2 (\frac{1}{2}) + 8$

Step 1.2

One to any power is one.

$2 \frac{1}{2^{2}} + 2 (\frac{1}{2}) + 8$

Step 1.3

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

$2 (\frac{1}{4}) + 2 (\frac{1}{2}) + 8$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $4$ .

$2 \frac{1}{2 (2)} + 2 (\frac{1}{2}) + 8$

Step 1.4.2

Cancel the common factor.

$2 \frac{1}{2 \cdot 2} + 2 (\frac{1}{2}) + 8$

Step 1.4.3

Rewrite the expression.

$\frac{1}{2} + 2 (\frac{1}{2}) + 8$

$\frac{1}{2} + 2 (\frac{1}{2}) + 8$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Cancel the common factor.

$\frac{1}{2} + 2 (\frac{1}{2}) + 8$

Step 1.5.2

Rewrite the expression.

$\frac{1}{2} + 1 + 8$

$\frac{1}{2} + 1 + 8$

$\frac{1}{2} + 1 + 8$

Step 2

Find the common denominator.

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Step 2.1

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

$\frac{1}{2} + \frac{1}{1} + 8$

Step 2.2

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{1}{1} \cdot \frac{2}{2} + 8$

Step 2.3

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{2}{2} + 8$

Step 2.4

Write $8$ as a fraction with denominator $1$ .

$\frac{1}{2} + \frac{2}{2} + \frac{8}{1}$

Step 2.5

Multiply $\frac{8}{1}$ by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{2}{2} + \frac{8}{1} \cdot \frac{2}{2}$

Step 2.6

Multiply $\frac{8}{1}$ by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{2}{2} + \frac{8 \cdot 2}{2}$

$\frac{1}{2} + \frac{2}{2} + \frac{8 \cdot 2}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{1 + 2 + 8 \cdot 2}{2}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $8$ by $2$ .

$\frac{1 + 2 + 16}{2}$

Step 4.2

Add $1$ and $2$ .

$\frac{3 + 16}{2}$

Step 4.3

Add $3$ and $16$ .

$\frac{19}{2}$

$\frac{19}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{2}$

Decimal Form:

$9.5$

Mixed Number Form:

$9 \frac{1}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$