Solve 15/frac{-10{13}}+1/frac{-13{10}}

$$\frac { 15 } { \frac { - 10 } { 13 } } + \frac { 1 } { \frac { - 13 } { 10 } }$$

Evaluate

$$-\frac{527}{26}\approx -20.269230769$$

Solution Steps

Divide 15 by \frac{-10}{13} by multiplying 15 by the reciprocal of \frac{-10}{13}.

$$\frac{15\times 13}{-10}+\frac{1}{\frac{-13}{10}}$$

Multiply 15 and 13 to get 195.

$$\frac{195}{-10}+\frac{1}{\frac{-13}{10}}$$

Reduce the fraction \frac{195}{-10} to lowest terms by extracting and canceling out 5.

$$-\frac{39}{2}+\frac{1}{\frac{-13}{10}}$$

Divide 1 by \frac{-13}{10} by multiplying 1 by the reciprocal of \frac{-13}{10}.

$$-\frac{39}{2}+\frac{10}{-13}$$

Fraction \frac{10}{-13} can be rewritten as -\frac{10}{13} by extracting the negative sign.

$$-\frac{39}{2}-\frac{10}{13}$$

Least common multiple of 2 and 13 is 26. Convert -\frac{39}{2} and \frac{10}{13} to fractions with denominator 26.

$$-\frac{507}{26}-\frac{20}{26}$$

Since -\frac{507}{26} and \frac{20}{26} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-507-20}{26}$$

Subtract 20 from -507 to get -527.

$$-\frac{527}{26}$$

Factor

$$-\frac{527}{26} = -20\frac{7}{26} = -20.26923076923077$$