Calculate: /(5) 7 / /(2) 5+/(-8) 14

Expression: $$\frac { 5 } { 7 } \div \frac { 2 } { 5 } + \frac { - 8 } { 14 }$$

Divide $\frac{5}{7}$ by $\frac{2}{5}$ by multiplying $\frac{5}{7}$ by the reciprocal of $\frac{2}{5}$.

$$\frac{5}{7}\times \left(\frac{5}{2}\right)+\frac{-8}{14}$$

Multiply $\frac{5}{7}$ times $\frac{5}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 5}{7\times 2}+\frac{-8}{14}$$

Do the multiplications in the fraction $\frac{5\times 5}{7\times 2}$.

$$\frac{25}{14}+\frac{-8}{14}$$

Reduce the fraction $\frac{-8}{14}$ to lowest terms by extracting and canceling out $2$.

$$\frac{25}{14}-\frac{4}{7}$$

Least common multiple of $14$ and $7$ is $14$. Convert $\frac{25}{14}$ and $\frac{4}{7}$ to fractions with denominator $14$.

$$\frac{25}{14}-\frac{8}{14}$$

Since $\frac{25}{14}$ and $\frac{8}{14}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-8}{14}$$

Subtract $8$ from $25$ to get $17$.

$$\frac{17}{14}$$