Solve lfloor{left(-5/3right)}^-1+{left(5/2right)}^-1rfloor

$$\lfloor { \left(- \frac{ 5 }{ 3 } \right) }^{ -1 } + { \left( \frac{ 5 }{ 2 } \right) }^{ -1 } \rfloor$$

Evaluate

$$-1$$

Solution Steps

Calculate -\frac{5}{3} to the power of -1 and get -\frac{3}{5}.

$$\lfloor -\frac{3}{5}+\left(\frac{5}{2}\right)^{-1}\rfloor$$

Calculate \frac{5}{2} to the power of -1 and get \frac{2}{5}.

$$\lfloor -\frac{3}{5}+\frac{2}{5}\rfloor$$

Add -\frac{3}{5} and \frac{2}{5} to get -\frac{1}{5}.

$$\lfloor -\frac{1}{5}\rfloor$$

Dividing -1 by 5 gives -1 and remainder 4. Rewrite -\frac{1}{5} as -1+\frac{4}{5}.

$$\lfloor -1+\frac{4}{5}\rfloor$$

The floor of a real number a is the largest integer number less than or equal to a. The floor of -1+\frac{4}{5} is -1.

$$-1$$

Factor

$$-1$$