Solve -1/3lfloor2/5-1/2(1/3-frac{1}{5})rfloor

$$- \frac{ 1 }{ 3 } \lfloor \frac{ 2 }{ 5 } - \frac{ 1 }{ 2 } ( \frac{ 1 }{ 3 } - \frac{ 1 }{ 5 } ) \rfloor$$

Evaluate

$$0$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$-\frac{1}{3}\lfloor \frac{2}{5}-\frac{1}{2}\left(\frac{5}{15}-\frac{3}{15}\right)\rfloor$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}\lfloor \frac{2}{5}-\frac{1}{2}\times \frac{5-3}{15}\rfloor$$

Subtract 3 from 5 to get 2.

$$-\frac{1}{3}\lfloor \frac{2}{5}-\frac{1}{2}\times \frac{2}{15}\rfloor$$

Multiply \frac{1}{2} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{3}\lfloor \frac{2}{5}-\frac{2}{2\times 15}\rfloor$$

Cancel out 2 in both numerator and denominator.

$$-\frac{1}{3}\lfloor \frac{2}{5}-\frac{1}{15}\rfloor$$

Least common multiple of 5 and 15 is 15. Convert \frac{2}{5} and \frac{1}{15} to fractions with denominator 15.

$$-\frac{1}{3}\lfloor \frac{6}{15}-\frac{1}{15}\rfloor$$

Since \frac{6}{15} and \frac{1}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}\lfloor \frac{6-1}{15}\rfloor$$

Subtract 1 from 6 to get 5.

$$-\frac{1}{3}\lfloor \frac{5}{15}\rfloor$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{3}\lfloor \frac{1}{3}\rfloor$$

The floor of a real number a is the largest integer number less than or equal to a. The floor of 0+\frac{1}{3} is 0.

$$-\frac{1}{3}\times 0$$

Multiply -\frac{1}{3} and 0 to get 0.

$$0$$

Factor

$$0$$