Pre-Algebra Examples

${(3)}^{2} - {(\frac{1}{2})}^{2}$

Step 1

Simplify each term.

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Step 1.1

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

$9 - {(\frac{1}{2})}^{2}$

Step 1.2

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

$9 - \frac{1^{2}}{2^{2}}$

Step 1.3

One to any power is one.

$9 - \frac{1}{2^{2}}$

Step 1.4

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

$9 - \frac{1}{4}$

Step 2

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$9 \cdot \frac{4}{4} - \frac{1}{4}$

Step 3

Combine $9$ and $\frac{4}{4}$ .

$\frac{9 \cdot 4}{4} - \frac{1}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \cdot 4 - 1}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $9$ by $4$ .

$\frac{36 - 1}{4}$

Step 5.2

Subtract $1$ from $36$ .

$\frac{35}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{4}$

Decimal Form:

$8.75$

Mixed Number Form:

$8 \frac{3}{4}$