Pre-Algebra Examples

 $\begin{array}{r} l = & \frac{7}{18} \\ w = & \frac{7}{9} \end{array}$

Step 1

The perimeter of a rectangle is equal to the sum of all sides of the rectangle.

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

Step 2

Substitute the values of the length $l = \frac{7}{18}$ and width $w = \frac{7}{9}$ into the formula for the perimeter of a rectangle.

$2 \cdot \frac{7}{18} + 2 \cdot \frac{7}{9}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $18$ .

$2 \cdot \frac{7}{2 (9)} + 2 \cdot \frac{7}{9}$

Step 3.1.2

Cancel the common factor.

$2 \cdot \frac{7}{2 \cdot 9} + 2 \cdot \frac{7}{9}$

Step 3.1.3

Rewrite the expression.

$\frac{7}{9} + 2 \cdot \frac{7}{9}$

Step 3.2

Multiply $2 (\frac{7}{9})$ .

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Step 3.2.1

Combine $2$ and $\frac{7}{9}$ .

$\frac{7}{9} + \frac{2 \cdot 7}{9}$

Step 3.2.2

Multiply $2$ by $7$ .

$\frac{7}{9} + \frac{14}{9}$

Step 4

Simplify terms.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{7 + 14}{9}$

Step 4.2

Add $7$ and $14$ .

$\frac{21}{9}$

Step 4.3

Cancel the common factor of $21$ and $9$ .

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Step 4.3.1

Factor $3$ out of $21$ .

$\frac{3 (7)}{9}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $3$ out of $9$ .

$\frac{3 \cdot 7}{3 \cdot 3}$

Step 4.3.2.2

Cancel the common factor.

$\frac{3 \cdot 7}{3 \cdot 3}$

Step 4.3.2.3

Rewrite the expression.

$\frac{7}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{3}$

Decimal Form:

$2.\overline{3}$

Mixed Number Form:

$2 \frac{1}{3}$