Finite Math Examples

$2 + \frac{2}{7} + \frac{2}{7^{2}} + \frac{2}{7^{3}}$

Step 1

Find the common denominator.

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Step 1.1

Raise $7$ to the power of $2$ .

$2 + \frac{2}{7} + \frac{2}{49} + \frac{2}{7^{3}}$

Step 1.2

Raise $7$ to the power of $3$ .

$2 + \frac{2}{7} + \frac{2}{49} + \frac{2}{343}$

Step 1.3

Write $2$ as a fraction with denominator $1$ .

$\frac{2}{1} + \frac{2}{7} + \frac{2}{49} + \frac{2}{343}$

Step 1.4

Multiply $\frac{2}{1}$ by $\frac{343}{343}$ .

$\frac{2}{1} \cdot \frac{343}{343} + \frac{2}{7} + \frac{2}{49} + \frac{2}{343}$

Step 1.5

Multiply $\frac{2}{1}$ by $\frac{343}{343}$ .

$\frac{2 \cdot 343}{343} + \frac{2}{7} + \frac{2}{49} + \frac{2}{343}$

Step 1.6

Multiply $\frac{2}{7}$ by $\frac{49}{49}$ .

$\frac{2 \cdot 343}{343} + \frac{2}{7} \cdot \frac{49}{49} + \frac{2}{49} + \frac{2}{343}$

Step 1.7

Multiply $\frac{2}{7}$ by $\frac{49}{49}$ .

$\frac{2 \cdot 343}{343} + \frac{2 \cdot 49}{7 \cdot 49} + \frac{2}{49} + \frac{2}{343}$

Step 1.8

Multiply $\frac{2}{49}$ by $\frac{7}{7}$ .

$\frac{2 \cdot 343}{343} + \frac{2 \cdot 49}{7 \cdot 49} + \frac{2}{49} \cdot \frac{7}{7} + \frac{2}{343}$

Step 1.9

Multiply $\frac{2}{49}$ by $\frac{7}{7}$ .

$\frac{2 \cdot 343}{343} + \frac{2 \cdot 49}{7 \cdot 49} + \frac{2 \cdot 7}{49 \cdot 7} + \frac{2}{343}$

Step 1.10

Multiply $7$ by $49$ .

$\frac{2 \cdot 343}{343} + \frac{2 \cdot 49}{343} + \frac{2 \cdot 7}{49 \cdot 7} + \frac{2}{343}$

Step 1.11

Reorder the factors of $49 \cdot 7$ .

$\frac{2 \cdot 343}{343} + \frac{2 \cdot 49}{343} + \frac{2 \cdot 7}{7 \cdot 49} + \frac{2}{343}$

Step 1.12

Multiply $7$ by $49$ .

$\frac{2 \cdot 343}{343} + \frac{2 \cdot 49}{343} + \frac{2 \cdot 7}{343} + \frac{2}{343}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 \cdot 343 + 2 \cdot 49 + 2 \cdot 7 + 2}{343}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $343$ .

$\frac{686 + 2 \cdot 49 + 2 \cdot 7 + 2}{343}$

Step 3.2

Multiply $2$ by $49$ .

$\frac{686 + 98 + 2 \cdot 7 + 2}{343}$

Step 3.3

Multiply $2$ by $7$ .

$\frac{686 + 98 + 14 + 2}{343}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $686$ and $98$ .

$\frac{784 + 14 + 2}{343}$

Step 4.2

Add $784$ and $14$ .

$\frac{798 + 2}{343}$

Step 4.3

Add $798$ and $2$ .

$\frac{800}{343}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{800}{343}$

Decimal Form:

$2.33236151 \dots$

Mixed Number Form:

$2 \frac{114}{343}$