Solve (1-1/5):(1+1/5)

$$( 1 - \frac { 1 } { 5 } ) : ( 1 + \frac { 1 } { 5 } )$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

$$\frac{\frac{5}{5}-\frac{1}{5}}{1+\frac{1}{5}}$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-1}{5}}{1+\frac{1}{5}}$$

Subtract 1 from 5 to get 4.

$$\frac{\frac{4}{5}}{1+\frac{1}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{\frac{4}{5}}{\frac{5}{5}+\frac{1}{5}}$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4}{5}}{\frac{5+1}{5}}$$

Add 5 and 1 to get 6.

$$\frac{\frac{4}{5}}{\frac{6}{5}}$$

Divide \frac{4}{5} by \frac{6}{5} by multiplying \frac{4}{5} by the reciprocal of \frac{6}{5}.

$$\frac{4}{5}\times \frac{5}{6}$$

Multiply \frac{4}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 5}{5\times 6}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Factor

$$\frac{2}{3} = 0.6666666666666666$$