Solve 1+2/5/2+frac{3{5}}

$$\frac { 1 + \frac { 2 } { 5 } } { 2 + \frac { 3 } { 5 } }$$

Evaluate

$$\frac{7}{13}\approx 0.538461538$$

Solution Steps

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

$$\frac{\frac{5}{5}+\frac{2}{5}}{2+\frac{3}{5}}$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+2}{5}}{2+\frac{3}{5}}$$

Add 5 and 2 to get 7.

$$\frac{\frac{7}{5}}{2+\frac{3}{5}}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{7}{5}}{\frac{10}{5}+\frac{3}{5}}$$

Since \frac{10}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{5}}{\frac{10+3}{5}}$$

Add 10 and 3 to get 13.

$$\frac{\frac{7}{5}}{\frac{13}{5}}$$

Divide \frac{7}{5} by \frac{13}{5} by multiplying \frac{7}{5} by the reciprocal of \frac{13}{5}.

$$\frac{7}{5}\times \frac{5}{13}$$

Multiply \frac{7}{5} times \frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 5}{5\times 13}$$

Cancel out 5 in both numerator and denominator.

$$\frac{7}{13}$$

Factor

$$\frac{7}{13} = 0.5384615384615384$$