Pre-Algebra Examples

 $\begin{array}{r} l = & \frac{4}{5} m \\ w = & \frac{7}{9} m \end{array}$

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 $l = \frac{4}{5}$ and width $w = \frac{7}{9}$ into the formula for the perimeter of a rectangle.

$2 \cdot \frac{4}{5} + 2 \cdot \frac{7}{9}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2 (\frac{4}{5})$ .

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Step 3.1.1

Combine $2$ and $\frac{4}{5}$ .

$\frac{2 \cdot 4}{5} + 2 \cdot \frac{7}{9}$

Step 3.1.2

Multiply $2$ by $4$ .

$\frac{8}{5} + 2 \cdot \frac{7}{9}$

Step 3.2

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

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Step 3.2.1

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

$\frac{8}{5} + \frac{2 \cdot 7}{9}$

Step 3.2.2

Multiply $2$ by $7$ .

$\frac{8}{5} + \frac{14}{9}$

Step 4

To write $\frac{8}{5}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{8}{5} \cdot \frac{9}{9} + \frac{14}{9}$

Step 5

To write $\frac{14}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{8}{5} \cdot \frac{9}{9} + \frac{14}{9} \cdot \frac{5}{5}$

Step 6

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{8}{5}$ by $\frac{9}{9}$ .

$\frac{8 \cdot 9}{5 \cdot 9} + \frac{14}{9} \cdot \frac{5}{5}$

Step 6.2

Multiply $5$ by $9$ .

$\frac{8 \cdot 9}{45} + \frac{14}{9} \cdot \frac{5}{5}$

Step 6.3

Multiply $\frac{14}{9}$ by $\frac{5}{5}$ .

$\frac{8 \cdot 9}{45} + \frac{14 \cdot 5}{9 \cdot 5}$

Step 6.4

Multiply $9$ by $5$ .

$\frac{8 \cdot 9}{45} + \frac{14 \cdot 5}{45}$

Step 7

Combine the numerators over the common denominator.

$\frac{8 \cdot 9 + 14 \cdot 5}{45}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $8$ by $9$ .

$\frac{72 + 14 \cdot 5}{45}$

Step 8.2

Multiply $14$ by $5$ .

$\frac{72 + 70}{45}$

Step 8.3

Add $72$ and $70$ .

$\frac{142}{45}$

$\frac{142}{45} m$