Pre-Algebra Examples

 $\begin{array}{r} h = & \frac{9}{2} \\ l = & \frac{9}{2} \\ w = & \frac{9}{2} \end{array}$

Step 1

The surface area of a box is equal to the sum of the areas of each side of the box.

$2 \cdot (l e n g t h) \cdot (w i d t h) + 2 \cdot (l e n g t h) \cdot (h e i g h t) + 2 \cdot (w i d t h) \cdot (h e i g h t)$

Step 2

Substitute the values of the length $l = \frac{9}{2}$ , the width $w = \frac{9}{2}$ , and the height $h = \frac{9}{2}$ into the formula.

$2 \cdot \frac{9}{2} \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $2 \cdot \frac{9}{2}$ .

$2 (\frac{9}{2}) \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.1.2

Cancel the common factor.

$2 (\frac{9}{2}) \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.1.3

Rewrite the expression.

$\frac{9}{2} \cdot 9 + 2 \cdot \frac{9}{2} \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.2

Combine $\frac{9}{2}$ and $9$ .

$\frac{9 \cdot 9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.3

Multiply $9$ by $9$ .

$\frac{81}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.4.1

Factor $2$ out of $2 \cdot \frac{9}{2}$ .

$\frac{81}{2} + 2 (\frac{9}{2}) \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.4.2

Cancel the common factor.

$\frac{81}{2} + 2 (\frac{9}{2}) \cdot \frac{9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.4.3

Rewrite the expression.

$\frac{81}{2} + \frac{9}{2} \cdot 9 + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.5

Combine $\frac{9}{2}$ and $9$ .

$\frac{81}{2} + \frac{9 \cdot 9}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.6

Multiply $9$ by $9$ .

$\frac{81}{2} + \frac{81}{2} + 2 \cdot \frac{9}{2} \cdot \frac{9}{2}$

Step 3.7

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.7.1

Factor $2$ out of $2 \cdot \frac{9}{2}$ .

$\frac{81}{2} + \frac{81}{2} + 2 (\frac{9}{2}) \cdot \frac{9}{2}$

Step 3.7.2

Cancel the common factor.

$\frac{81}{2} + \frac{81}{2} + 2 (\frac{9}{2}) \cdot \frac{9}{2}$

Step 3.7.3

Rewrite the expression.

$\frac{81}{2} + \frac{81}{2} + \frac{9}{2} \cdot 9$

Step 3.8

Combine $\frac{9}{2}$ and $9$ .

$\frac{81}{2} + \frac{81}{2} + \frac{9 \cdot 9}{2}$

Step 3.9

Multiply $9$ by $9$ .

$\frac{81}{2} + \frac{81}{2} + \frac{81}{2}$

Step 4

Combine fractions.

Tap for more steps...

Step 4.1

Combine the numerators over the common denominator.

$\frac{81 + 81 + 81}{2}$

Step 4.2

Simplify by adding numbers.

Tap for more steps...

Step 4.2.1

Add $81$ and $81$ .

$\frac{162 + 81}{2}$

Step 4.2.2

Add $162$ and $81$ .

$\frac{243}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{243}{2}$

Decimal Form:

$121.5$

Mixed Number Form:

$121 \frac{1}{2}$