Solve 3/5*-10/3/frac{1{3}-1/2}

$$\frac{ \frac{ 3 }{ 5 } \times - \frac{ 10 }{ 3 } }{ \frac{ 1 }{ 3 } - \frac{ 1 }{ 2 } }$$

Evaluate

$$12$$

Solution Steps

Multiply \frac{3}{5} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\left(-10\right)}{5\times 3}}{\frac{1}{3}-\frac{1}{2}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{-10}{5}}{\frac{1}{3}-\frac{1}{2}}$$

Divide -10 by 5 to get -2.

$$\frac{-2}{\frac{1}{3}-\frac{1}{2}}$$

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

$$\frac{-2}{\frac{2}{6}-\frac{3}{6}}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2}{\frac{2-3}{6}}$$

Subtract 3 from 2 to get -1.

$$\frac{-2}{-\frac{1}{6}}$$

Divide -2 by -\frac{1}{6} by multiplying -2 by the reciprocal of -\frac{1}{6}.

$$-2\left(-6\right)$$

Multiply -2 and -6 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$