Solve 13/9-1/3-frac{13{9}}

$$\frac{ \frac{ 13 }{ 9 } -1 }{ 3- \frac{ 13 }{ 9 } }$$

Evaluate

$$\frac{2}{7}\approx 0.285714286$$

Solution Steps

Convert 1 to fraction \frac{9}{9}.

$$\frac{\frac{13}{9}-\frac{9}{9}}{3-\frac{13}{9}}$$

Since \frac{13}{9} and \frac{9}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13-9}{9}}{3-\frac{13}{9}}$$

Subtract 9 from 13 to get 4.

$$\frac{\frac{4}{9}}{3-\frac{13}{9}}$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{\frac{4}{9}}{\frac{27}{9}-\frac{13}{9}}$$

Since \frac{27}{9} and \frac{13}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{9}}{\frac{27-13}{9}}$$

Subtract 13 from 27 to get 14.

$$\frac{\frac{4}{9}}{\frac{14}{9}}$$

Divide \frac{4}{9} by \frac{14}{9} by multiplying \frac{4}{9} by the reciprocal of \frac{14}{9}.

$$\frac{4}{9}\times \frac{9}{14}$$

Multiply \frac{4}{9} times \frac{9}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 9}{9\times 14}$$

Cancel out 9 in both numerator and denominator.

$$\frac{4}{14}$$

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

$$\frac{2}{7}$$

Factor

$$\frac{2}{7} = 0.2857142857142857$$