Solve 5/2/frac{5{2}+5/7}

$$\frac{ \frac{ 5 }{ 2 } }{ \frac{ 5 }{ 2 } + \frac{ 5 }{ 7 } }$$

Evaluate

$$\frac{7}{9}\approx 0.777777778$$

Solution Steps

Least common multiple of 2 and 7 is 14. Convert \frac{5}{2} and \frac{5}{7} to fractions with denominator 14.

$$\frac{\frac{5}{2}}{\frac{35}{14}+\frac{10}{14}}$$

Since \frac{35}{14} and \frac{10}{14} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{2}}{\frac{35+10}{14}}$$

Add 35 and 10 to get 45.

$$\frac{\frac{5}{2}}{\frac{45}{14}}$$

Divide \frac{5}{2} by \frac{45}{14} by multiplying \frac{5}{2} by the reciprocal of \frac{45}{14}.

$$\frac{5}{2}\times \frac{14}{45}$$

Multiply \frac{5}{2} times \frac{14}{45} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 14}{2\times 45}$$

Do the multiplications in the fraction \frac{5\times 14}{2\times 45}.

$$\frac{70}{90}$$

Reduce the fraction \frac{70}{90} to lowest terms by extracting and canceling out 10.

$$\frac{7}{9}$$

Factor

$$\frac{7}{3 ^ {2}} = 0.7777777777777778$$