Evaluate (1-1/7)/(1+6/7)

$\frac{1 - \frac{1}{7}}{1 + \frac{6}{7}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $7$ .

Multiply $\frac{1 - \frac{1}{7}}{1 + \frac{6}{7}}$ by $\frac{7}{7}$ .

$\frac{7}{7} \cdot \frac{1 - \frac{1}{7}}{1 + \frac{6}{7}}$

Combine.

$\frac{7 (1 - \frac{1}{7})}{7 (1 + \frac{6}{7})}$

Step 2

Apply the distributive property.

$\frac{7 \cdot 1 + 7 (- \frac{1}{7})}{7 \cdot 1 + 7 (\frac{6}{7})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{1}{7}$ into the numerator.

$\frac{7 \cdot 1 + 7 (\frac{- 1}{7})}{7 \cdot 1 + 7 (\frac{6}{7})}$

Cancel the common factor.

$\frac{7 \cdot 1 + 7 (\frac{- 1}{7})}{7 \cdot 1 + 7 (\frac{6}{7})}$

Rewrite the expression.

$\frac{7 \cdot 1 - 1}{7 \cdot 1 + 7 (\frac{6}{7})}$

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 \cdot 1 - 1}{7 \cdot 1 + 7 (\frac{6}{7})}$

Rewrite the expression.

$\frac{7 \cdot 1 - 1}{7 \cdot 1 + 6}$

Step 4

Simplify the numerator.

Multiply $7$ by $1$ .

$\frac{7 - 1}{7 \cdot 1 + 6}$

Subtract $1$ from $7$ .

$\frac{6}{7 \cdot 1 + 6}$

Step 5

Simplify the denominator.

Multiply $7$ by $1$ .

$\frac{6}{7 + 6}$

Add $7$ and $6$ .

$\frac{6}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{13}$

Decimal Form:

$0.\overline{461538}$