Pre-Algebra Examples

 $\begin{array}{r} l = & \frac{2}{9} \\ w = & \frac{3}{7} \end{array}$

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 $w = \frac{3}{7}$ into the formula for the perimeter of a rectangle.

$2 \cdot \frac{2}{9} + 2 \cdot \frac{3}{7}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

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

$\frac{2 \cdot 2}{9} + 2 \cdot \frac{3}{7}$

Step 3.1.2

Multiply $2$ by $2$ .

$\frac{4}{9} + 2 \cdot \frac{3}{7}$

Step 3.2

Multiply $2 (\frac{3}{7})$ .

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Step 3.2.1

Combine $2$ and $\frac{3}{7}$ .

$\frac{4}{9} + \frac{2 \cdot 3}{7}$

Step 3.2.2

Multiply $2$ by $3$ .

$\frac{4}{9} + \frac{6}{7}$

Step 4

To write $\frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{4}{9} \cdot \frac{7}{7} + \frac{6}{7}$

Step 5

To write $\frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{4}{9} \cdot \frac{7}{7} + \frac{6}{7} \cdot \frac{9}{9}$

Step 6

Write each expression with a common denominator of $63$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{4}{9}$ by $\frac{7}{7}$ .

$\frac{4 \cdot 7}{9 \cdot 7} + \frac{6}{7} \cdot \frac{9}{9}$

Step 6.2

Multiply $9$ by $7$ .

$\frac{4 \cdot 7}{63} + \frac{6}{7} \cdot \frac{9}{9}$

Step 6.3

Multiply $\frac{6}{7}$ by $\frac{9}{9}$ .

$\frac{4 \cdot 7}{63} + \frac{6 \cdot 9}{7 \cdot 9}$

Step 6.4

Multiply $7$ by $9$ .

$\frac{4 \cdot 7}{63} + \frac{6 \cdot 9}{63}$

Step 7

Combine the numerators over the common denominator.

$\frac{4 \cdot 7 + 6 \cdot 9}{63}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $4$ by $7$ .

$\frac{28 + 6 \cdot 9}{63}$

Step 8.2

Multiply $6$ by $9$ .

$\frac{28 + 54}{63}$

Step 8.3

Add $28$ and $54$ .

$\frac{82}{63}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{82}{63}$

Decimal Form:

$1.30158730 \dots$

Mixed Number Form:

$1 \frac{19}{63}$