Evaluate (1/7)/(1/7+1)-1

$\frac{\frac{1}{7}}{\frac{1}{7} + 1} - 1$

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{7} \cdot \frac{1}{\frac{1}{7} + 1} - 1$

Simplify the denominator.

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

$\frac{1}{7} \cdot \frac{1}{\frac{1}{7} + \frac{7}{7}} - 1$

Combine the numerators over the common denominator.

$\frac{1}{7} \cdot \frac{1}{\frac{1 + 7}{7}} - 1$

Add $1$ and $7$ .

$\frac{1}{7} \cdot \frac{1}{\frac{8}{7}} - 1$

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{7} (1 (\frac{7}{8})) - 1$

Multiply $\frac{7}{8}$ by $1$ .

$\frac{1}{7} \cdot \frac{7}{8} - 1$

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{1}{7} \cdot \frac{7}{8} - 1$

Rewrite the expression.

$\frac{1}{8} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{8} - 1 \cdot \frac{8}{8}$

Combine $- 1$ and $\frac{8}{8}$ .

$\frac{1}{8} + \frac{- 1 \cdot 8}{8}$

Combine the numerators over the common denominator.

$\frac{1 - 1 \cdot 8}{8}$

Simplify the numerator.

Multiply $- 1$ by $8$ .

$\frac{1 - 8}{8}$

Subtract $8$ from $1$ .

$\frac{- 7}{8}$

Move the negative in front of the fraction.

$- \frac{7}{8}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{8}$

Decimal Form:

$- 0.875$