Finite Math Examples

$\frac{\frac{5}{9}}{1 - \frac{5}{9}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{9} \cdot \frac{1}{1 - \frac{5}{9}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{5}{9} \cdot \frac{1}{\frac{9}{9} - \frac{5}{9}}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{5}{9} \cdot \frac{1}{\frac{9 - 5}{9}}$

Step 2.3

Subtract $5$ from $9$ .

$\frac{5}{9} \cdot \frac{1}{\frac{4}{9}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{9} (1 (\frac{9}{4}))$

Step 4

Multiply $\frac{9}{4}$ by $1$ .

$\frac{5}{9} \cdot \frac{9}{4}$

Step 5

Cancel the common factor of $9$ .

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Step 5.1

Cancel the common factor.

$\frac{5}{9} \cdot \frac{9}{4}$

Step 5.2

Rewrite the expression.

$5 (\frac{1}{4})$

Step 6

Combine $5$ and $\frac{1}{4}$ .

$\frac{5}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$