Finite Math Examples

$1 + \frac{1}{1 + \frac{1}{2}}$

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

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

$1 + \frac{1}{\frac{2}{2} + \frac{1}{2}}$

Step 1.1.2

Combine the numerators over the common denominator.

$1 + \frac{1}{\frac{2 + 1}{2}}$

Step 1.1.3

Add $2$ and $1$ .

$1 + \frac{1}{\frac{3}{2}}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$1 + 1 (\frac{2}{3})$

Step 1.3

Multiply $\frac{2}{3}$ by $1$ .

$1 + \frac{2}{3}$

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Add $3$ and $2$ .

$\frac{5}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$