Solve -4/5+5/13/frac{3{5}-5/13}

$$\frac { - \frac { 4 } { 5 } + \frac { 5 } { 13 } } { \frac { 3 } { 5 } - \frac { 5 } { 13 } }$$

Evaluate

$$-\frac{27}{14}\approx -1.928571429$$

Solution Steps

Least common multiple of 5 and 13 is 65. Convert -\frac{4}{5} and \frac{5}{13} to fractions with denominator 65.

$$\frac{-\frac{52}{65}+\frac{25}{65}}{\frac{3}{5}-\frac{5}{13}}$$

Since -\frac{52}{65} and \frac{25}{65} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-52+25}{65}}{\frac{3}{5}-\frac{5}{13}}$$

Add -52 and 25 to get -27.

$$\frac{-\frac{27}{65}}{\frac{3}{5}-\frac{5}{13}}$$

Least common multiple of 5 and 13 is 65. Convert \frac{3}{5} and \frac{5}{13} to fractions with denominator 65.

$$\frac{-\frac{27}{65}}{\frac{39}{65}-\frac{25}{65}}$$

Since \frac{39}{65} and \frac{25}{65} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{27}{65}}{\frac{39-25}{65}}$$

Subtract 25 from 39 to get 14.

$$\frac{-\frac{27}{65}}{\frac{14}{65}}$$

Divide -\frac{27}{65} by \frac{14}{65} by multiplying -\frac{27}{65} by the reciprocal of \frac{14}{65}.

$$-\frac{27}{65}\times \frac{65}{14}$$

Multiply -\frac{27}{65} times \frac{65}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-27\times 65}{65\times 14}$$

Cancel out 65 in both numerator and denominator.

$$\frac{-27}{14}$$

Fraction \frac{-27}{14} can be rewritten as -\frac{27}{14} by extracting the negative sign.

$$-\frac{27}{14}$$

Factor

$$-\frac{27}{14} = -1\frac{13}{14} = -1.9285714285714286$$