Solve (-15)div(1/3-3/2-3)*6

$$( - 15 ) \div ( \frac { 1 } { 3 } - \frac { 3 } { 2 } - 3 ) \times 6$$

Evaluate

$$\frac{108}{5}=21.6$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{-15}{\frac{2}{6}-\frac{9}{6}-3}\times 6$$

Since \frac{2}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15}{\frac{2-9}{6}-3}\times 6$$

Subtract 9 from 2 to get -7.

$$\frac{-15}{-\frac{7}{6}-3}\times 6$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{-15}{-\frac{7}{6}-\frac{18}{6}}\times 6$$

Since -\frac{7}{6} and \frac{18}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15}{\frac{-7-18}{6}}\times 6$$

Subtract 18 from -7 to get -25.

$$\frac{-15}{-\frac{25}{6}}\times 6$$

Divide -15 by -\frac{25}{6} by multiplying -15 by the reciprocal of -\frac{25}{6}.

$$-15\left(-\frac{6}{25}\right)\times 6$$

Express -15\left(-\frac{6}{25}\right) as a single fraction.

$$\frac{-15\left(-6\right)}{25}\times 6$$

Multiply -15 and -6 to get 90.

$$\frac{90}{25}\times 6$$

Reduce the fraction \frac{90}{25} to lowest terms by extracting and canceling out 5.

$$\frac{18}{5}\times 6$$

Express \frac{18}{5}\times 6 as a single fraction.

$$\frac{18\times 6}{5}$$

Multiply 18 and 6 to get 108.

$$\frac{108}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {3}}{5} = 21\frac{3}{5} = 21.6$$