Pre-Algebra Examples

 $\begin{array}{r} l = & \frac{3}{16} \\ w = & \frac{3}{8} \end{array}$

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 $l = \frac{3}{16}$ and width $w = \frac{3}{8}$ into the formula for the perimeter of a rectangle.

$2 \cdot \frac{3}{16} + 2 \cdot \frac{3}{8}$

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 $16$ .

$2 \cdot \frac{3}{2 (8)} + 2 \cdot \frac{3}{8}$

Step 3.1.2

Cancel the common factor.

$2 \cdot \frac{3}{2 \cdot 8} + 2 \cdot \frac{3}{8}$

Step 3.1.3

Rewrite the expression.

$\frac{3}{8} + 2 \cdot \frac{3}{8}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $8$ .

$\frac{3}{8} + 2 \cdot \frac{3}{2 (4)}$

Step 3.2.2

Cancel the common factor.

$\frac{3}{8} + 2 \cdot \frac{3}{2 \cdot 4}$

Step 3.2.3

Rewrite the expression.

$\frac{3}{8} + \frac{3}{4}$

Step 4

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{8} + \frac{3}{4} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$\frac{3}{8} + \frac{3 \cdot 2}{4 \cdot 2}$

Step 5.2

Multiply $4$ by $2$ .

$\frac{3}{8} + \frac{3 \cdot 2}{8}$

Step 6

Combine the numerators over the common denominator.

$\frac{3 + 3 \cdot 2}{8}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $3$ by $2$ .

$\frac{3 + 6}{8}$

Step 7.2

Add $3$ and $6$ .

$\frac{9}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{8}$

Decimal Form:

$1.125$

Mixed Number Form:

$1 \frac{1}{8}$