Basic Math Examples

$\frac{9^{2}}{2} = 3 w$

Step 1

Rewrite the equation as $3 w = \frac{9^{2}}{2}$ .

$3 w = \frac{9^{2}}{2}$

Step 2

Raise $9$ to the power of $2$ .

$3 w = \frac{81}{2}$

Step 3

Divide each term in $3 w = \frac{81}{2}$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 w = \frac{81}{2}$ by $3$ .

$\frac{3 w}{3} = \frac{\frac{81}{2}}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 w}{3} = \frac{\frac{81}{2}}{3}$

Step 3.2.1.2

Divide $w$ by $1$ .

$w = \frac{\frac{81}{2}}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$w = \frac{81}{2} \cdot \frac{1}{3}$

Step 3.3.2

Cancel the common factor of $3$ .

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Step 3.3.2.1

Factor $3$ out of $81$ .

$w = \frac{3 (27)}{2} \cdot \frac{1}{3}$

Step 3.3.2.2

Cancel the common factor.

$w = \frac{3 \cdot 27}{2} \cdot \frac{1}{3}$

Step 3.3.2.3

Rewrite the expression.

$w = \frac{27}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$w = \frac{27}{2}$

Decimal Form:

$w = 13.5$

Mixed Number Form:

$w = 13 \frac{1}{2}$