Pre-Algebra Examples

 $\begin{array}{r} l = & \frac{1}{2} - 1 \\ w = & l \end{array}$

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 $l = \frac{1}{2} - 1$ and width $w = l$ into the formula for the perimeter of a rectangle.

$2 \cdot (\frac{1}{2} - 1) + 2 \cdot l$

Step 3

Simplify each term.

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Step 3.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 \cdot (\frac{1}{2} - 1 \cdot \frac{2}{2}) + 2 \cdot l$

Step 3.2

Combine $- 1$ and $\frac{2}{2}$ .

$2 \cdot (\frac{1}{2} + \frac{- 1 \cdot 2}{2}) + 2 \cdot l$

Step 3.3

Combine the numerators over the common denominator.

$2 \cdot \frac{1 - 1 \cdot 2}{2} + 2 \cdot l$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $- 1$ by $2$ .

$2 \cdot \frac{1 - 2}{2} + 2 \cdot l$

Step 3.4.2

Subtract $2$ from $1$ .

$2 \cdot \frac{- 1}{2} + 2 \cdot l$

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Cancel the common factor.

$2 \cdot \frac{- 1}{2} + 2 \cdot l$

Step 3.5.2

Rewrite the expression.

$- 1 + 2 \cdot l$

$- 1 + 2 l$