Evaluate (1/2)/(1/2+1)-1

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

Step 1

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

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

Simplify the denominator.

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

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

Combine the numerators over the common denominator.

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

Add $1$ and $2$ .

$\frac{1}{2} \cdot \frac{1}{\frac{3}{2}} - 1$

Multiply the numerator by the reciprocal of the denominator.

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

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

$\frac{1}{2} \cdot \frac{2}{3} - 1$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2}{3} - 1$

Rewrite the expression.

$\frac{1}{3} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{3} - 1 \cdot \frac{3}{3}$

Step 3

Combine $- 1$ and $\frac{3}{3}$ .

$\frac{1}{3} + \frac{- 1 \cdot 3}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 - 1 \cdot 3}{3}$

Step 5

Simplify the numerator.

Multiply $- 1$ by $3$ .

$\frac{1 - 3}{3}$

Subtract $3$ from $1$ .

$\frac{- 2}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$