Basic Math Examples

$1 - \frac{1}{1 - \frac{1}{1 - \frac{1}{2}}}$

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.

$1 - \frac{1}{1 - \frac{1}{\frac{2}{2} - \frac{1}{2}}}$

Step 1.1.2

Combine the numerators over the common denominator.

$1 - \frac{1}{1 - \frac{1}{\frac{2 - 1}{2}}}$

Step 1.1.3

Subtract $1$ from $2$ .

$1 - \frac{1}{1 - \frac{1}{\frac{1}{2}}}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Multiply the numerator by the reciprocal of the denominator.

$1 - \frac{1}{1 - (1 \cdot 2)}$

Step 1.2.2

Multiply $- (1 \cdot 2)$ .

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Step 1.2.2.1

Multiply $2$ by $1$ .

$1 - \frac{1}{1 - 1 \cdot 2}$

Step 1.2.2.2

Multiply $- 1$ by $2$ .

$1 - \frac{1}{1 - 2}$

Step 1.2.3

Subtract $2$ from $1$ .

$1 - \frac{1}{- 1}$

Step 1.3

Divide $1$ by $- 1$ .

$1 - - 1$

Step 1.4

Multiply $- 1$ by $- 1$ .

$1 + 1$

Step 2

Add $1$ and $1$ .

$2$