Solve 5/9/frac{3{5}+4/15}

$$\frac{ \frac{ 5 }{ 9 } }{ \frac{ 3 }{ 5 } + \frac{ 4 }{ 15 } }$$

Evaluate

$$\frac{25}{39}\approx 0.641025641$$

Solution Steps

Least common multiple of 5 and 15 is 15. Convert \frac{3}{5} and \frac{4}{15} to fractions with denominator 15.

$$\frac{\frac{5}{9}}{\frac{9}{15}+\frac{4}{15}}$$

Since \frac{9}{15} and \frac{4}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{9}}{\frac{9+4}{15}}$$

Add 9 and 4 to get 13.

$$\frac{\frac{5}{9}}{\frac{13}{15}}$$

Divide \frac{5}{9} by \frac{13}{15} by multiplying \frac{5}{9} by the reciprocal of \frac{13}{15}.

$$\frac{5}{9}\times \frac{15}{13}$$

Multiply \frac{5}{9} times \frac{15}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 15}{9\times 13}$$

Do the multiplications in the fraction \frac{5\times 15}{9\times 13}.

$$\frac{75}{117}$$

Reduce the fraction \frac{75}{117} to lowest terms by extracting and canceling out 3.

$$\frac{25}{39}$$

Factor

$$\frac{5 ^ {2}}{3 \cdot 13} = 0.6410256410256411$$