Basic Math Examples

$\frac{1}{8 + \frac{1}{12 + \frac{1}{15}}}$

Step 1

Simplify the denominator.

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Step 1.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{1}{8 + \frac{1}{12 \cdot \frac{15}{15} + \frac{1}{15}}}$

Step 1.2

Combine $12$ and $\frac{15}{15}$ .

$\frac{1}{8 + \frac{1}{\frac{12 \cdot 15}{15} + \frac{1}{15}}}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{1}{8 + \frac{1}{\frac{12 \cdot 15 + 1}{15}}}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $12$ by $15$ .

$\frac{1}{8 + \frac{1}{\frac{180 + 1}{15}}}$

Step 1.4.2

Add $180$ and $1$ .

$\frac{1}{8 + \frac{1}{\frac{181}{15}}}$

Step 2

Simplify the denominator.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{8 + 1 (\frac{15}{181})}$

Step 2.1.2

Multiply $\frac{15}{181}$ by $1$ .

$\frac{1}{8 + \frac{15}{181}}$

Step 2.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{181}{181}$ .

$\frac{1}{8 \cdot \frac{181}{181} + \frac{15}{181}}$

Step 2.3

Combine $8$ and $\frac{181}{181}$ .

$\frac{1}{\frac{8 \cdot 181}{181} + \frac{15}{181}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{1}{\frac{8 \cdot 181 + 15}{181}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $8$ by $181$ .

$\frac{1}{\frac{1448 + 15}{181}}$

Step 2.5.2

Add $1448$ and $15$ .

$\frac{1}{\frac{1463}{181}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{181}{1463})$

Step 4

Multiply $\frac{181}{1463}$ by $1$ .

$\frac{181}{1463}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{181}{1463}$

Decimal Form:

$0.12371838 \dots$