Finite Math Examples

$1 - \frac{1}{8} + \frac{1}{64} - \frac{1}{512}$

Step 1

Find the common denominator.

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Step 1.1

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

$\frac{1}{1} - \frac{1}{8} + \frac{1}{64} - \frac{1}{512}$

Step 1.2

Multiply $\frac{1}{1}$ by $\frac{512}{512}$ .

$\frac{1}{1} \cdot \frac{512}{512} - \frac{1}{8} + \frac{1}{64} - \frac{1}{512}$

Step 1.3

Multiply $\frac{1}{1}$ by $\frac{512}{512}$ .

$\frac{512}{512} - \frac{1}{8} + \frac{1}{64} - \frac{1}{512}$

Step 1.4

Multiply $\frac{1}{8}$ by $\frac{64}{64}$ .

$\frac{512}{512} - (\frac{1}{8} \cdot \frac{64}{64}) + \frac{1}{64} - \frac{1}{512}$

Step 1.5

Multiply $\frac{1}{8}$ by $\frac{64}{64}$ .

$\frac{512}{512} - \frac{64}{8 \cdot 64} + \frac{1}{64} - \frac{1}{512}$

Step 1.6

Multiply $\frac{1}{64}$ by $\frac{8}{8}$ .

$\frac{512}{512} - \frac{64}{8 \cdot 64} + \frac{1}{64} \cdot \frac{8}{8} - \frac{1}{512}$

Step 1.7

Multiply $\frac{1}{64}$ by $\frac{8}{8}$ .

$\frac{512}{512} - \frac{64}{8 \cdot 64} + \frac{8}{64 \cdot 8} - \frac{1}{512}$

Step 1.8

Multiply $8$ by $64$ .

$\frac{512}{512} - \frac{64}{512} + \frac{8}{64 \cdot 8} - \frac{1}{512}$

Step 1.9

Reorder the factors of $64 \cdot 8$ .

$\frac{512}{512} - \frac{64}{512} + \frac{8}{8 \cdot 64} - \frac{1}{512}$

Step 1.10

Multiply $8$ by $64$ .

$\frac{512}{512} - \frac{64}{512} + \frac{8}{512} - \frac{1}{512}$

Step 2

Combine the numerators over the common denominator.

$\frac{512 - 64 + 8 - 1}{512}$

Step 3

Simplify by adding and subtracting.

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Step 3.1

Subtract $64$ from $512$ .

$\frac{448 + 8 - 1}{512}$

Step 3.2

Add $448$ and $8$ .

$\frac{456 - 1}{512}$

Step 3.3

Subtract $1$ from $456$ .

$\frac{455}{512}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{455}{512}$

Decimal Form:

$0.88867187 \dots$