Pre-Algebra Examples

 $\begin{array}{r} l = & \frac{2}{9} \\ w = & \frac{2}{3} \end{array}$

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 $l = \frac{2}{9}$ and width $w = \frac{2}{3}$ into the formula for the perimeter of a rectangle.

$2 \cdot \frac{2}{9} + 2 \cdot \frac{2}{3}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

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

$\frac{2 \cdot 2}{9} + 2 \cdot \frac{2}{3}$

Step 3.1.2

Multiply $2$ by $2$ .

$\frac{4}{9} + 2 \cdot \frac{2}{3}$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

$\frac{4}{9} + \frac{2 \cdot 2}{3}$

Step 3.2.2

Multiply $2$ by $2$ .

$\frac{4}{9} + \frac{4}{3}$

Step 4

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4}{9} + \frac{4}{3} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 5.1

Multiply $\frac{4}{3}$ by $\frac{3}{3}$ .

$\frac{4}{9} + \frac{4 \cdot 3}{3 \cdot 3}$

Step 5.2

Multiply $3$ by $3$ .

$\frac{4}{9} + \frac{4 \cdot 3}{9}$

Step 6

Combine the numerators over the common denominator.

$\frac{4 + 4 \cdot 3}{9}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Multiply $4$ by $3$ .

$\frac{4 + 12}{9}$

Step 7.2

Add $4$ and $12$ .

$\frac{16}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{9}$

Decimal Form:

$1.\overline{7}$

Mixed Number Form:

$1 \frac{7}{9}$