Pre-Algebra Examples

 $\begin{array}{r} h = & 80 \\ l = & \frac{2}{3} \\ w = & 90 \end{array}$

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 $l = \frac{2}{3}$ , the width $w = 90$ , and the height $h = 80$ into the formula.

$2 \cdot \frac{2}{3} \cdot 90 + 2 \cdot \frac{2}{3} \cdot 80 + 2 \cdot 90 \cdot 80$

Step 3

Simplify each term.

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Step 3.1

Multiply $2 (\frac{2}{3})$ .

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Step 3.1.1

Combine $2$ and $\frac{2}{3}$ .

$\frac{2 \cdot 2}{3} \cdot 90 + 2 \cdot \frac{2}{3} \cdot 80 + 2 \cdot 90 \cdot 80$

Step 3.1.2

Multiply $2$ by $2$ .

$\frac{4}{3} \cdot 90 + 2 \cdot \frac{2}{3} \cdot 80 + 2 \cdot 90 \cdot 80$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Factor $3$ out of $90$ .

$\frac{4}{3} \cdot (3 (30)) + 2 \cdot \frac{2}{3} \cdot 80 + 2 \cdot 90 \cdot 80$

Step 3.2.2

Cancel the common factor.

$\frac{4}{3} \cdot (3 \cdot 30) + 2 \cdot \frac{2}{3} \cdot 80 + 2 \cdot 90 \cdot 80$

Step 3.2.3

Rewrite the expression.

$4 \cdot 30 + 2 \cdot \frac{2}{3} \cdot 80 + 2 \cdot 90 \cdot 80$

Step 3.3

Multiply $4$ by $30$ .

$120 + 2 \cdot \frac{2}{3} \cdot 80 + 2 \cdot 90 \cdot 80$

Step 3.4

Multiply $2 (\frac{2}{3})$ .

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Step 3.4.1

Combine $2$ and $\frac{2}{3}$ .

$120 + \frac{2 \cdot 2}{3} \cdot 80 + 2 \cdot 90 \cdot 80$

Step 3.4.2

Multiply $2$ by $2$ .

$120 + \frac{4}{3} \cdot 80 + 2 \cdot 90 \cdot 80$

Step 3.5

Multiply $\frac{4}{3} \cdot 80$ .

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Step 3.5.1

Combine $\frac{4}{3}$ and $80$ .

$120 + \frac{4 \cdot 80}{3} + 2 \cdot 90 \cdot 80$

Step 3.5.2

Multiply $4$ by $80$ .

$120 + \frac{320}{3} + 2 \cdot 90 \cdot 80$

Step 3.6

Multiply $2 \cdot 90 \cdot 80$ .

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Step 3.6.1

Multiply $2$ by $90$ .

$120 + \frac{320}{3} + 180 \cdot 80$

Step 3.6.2

Multiply $180$ by $80$ .

$120 + \frac{320}{3} + 14400$

Step 4

Find the common denominator.

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Step 4.1

Write $120$ as a fraction with denominator $1$ .

$\frac{120}{1} + \frac{320}{3} + 14400$

Step 4.2

Multiply $\frac{120}{1}$ by $\frac{3}{3}$ .

$\frac{120}{1} \cdot \frac{3}{3} + \frac{320}{3} + 14400$

Step 4.3

Multiply $\frac{120}{1}$ by $\frac{3}{3}$ .

$\frac{120 \cdot 3}{3} + \frac{320}{3} + 14400$

Step 4.4

Write $14400$ as a fraction with denominator $1$ .

$\frac{120 \cdot 3}{3} + \frac{320}{3} + \frac{14400}{1}$

Step 4.5

Multiply $\frac{14400}{1}$ by $\frac{3}{3}$ .

$\frac{120 \cdot 3}{3} + \frac{320}{3} + \frac{14400}{1} \cdot \frac{3}{3}$

Step 4.6

Multiply $\frac{14400}{1}$ by $\frac{3}{3}$ .

$\frac{120 \cdot 3}{3} + \frac{320}{3} + \frac{14400 \cdot 3}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{120 \cdot 3 + 320 + 14400 \cdot 3}{3}$

Step 6

Simplify each term.

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Step 6.1

Multiply $120$ by $3$ .

$\frac{360 + 320 + 14400 \cdot 3}{3}$

Step 6.2

Multiply $14400$ by $3$ .

$\frac{360 + 320 + 43200}{3}$

Step 7

Simplify by adding numbers.

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Step 7.1

Add $360$ and $320$ .

$\frac{680 + 43200}{3}$

Step 7.2

Add $680$ and $43200$ .

$\frac{43880}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{43880}{3}$

Decimal Form:

$14626.\overline{6}$

Mixed Number Form:

$14626 \frac{2}{3}$