Solve (-3/5)*(-5/9):(-1+1/3)+1/2

$$( - \frac { 3 } { 5 } ) \cdot ( - \frac { 5 } { 9 } ) : ( - 1 + \frac { 1 } { 3 } ) + \frac { 1 } { 2 }$$

Evaluate

$$0$$

Solution Steps

Multiply -\frac{3}{5} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-3\left(-5\right)}{5\times 9}}{-1+\frac{1}{3}}+\frac{1}{2}$$

Do the multiplications in the fraction \frac{-3\left(-5\right)}{5\times 9}.

$$\frac{\frac{15}{45}}{-1+\frac{1}{3}}+\frac{1}{2}$$

Reduce the fraction \frac{15}{45} to lowest terms by extracting and canceling out 15.

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

Convert -1 to fraction -\frac{3}{3}.

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

Since -\frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add -3 and 1 to get -2.

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

Divide \frac{1}{3} by -\frac{2}{3} by multiplying \frac{1}{3} by the reciprocal of -\frac{2}{3}.

$$\frac{1}{3}\left(-\frac{3}{2}\right)+\frac{1}{2}$$

Multiply \frac{1}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-3\right)}{3\times 2}.

$$\frac{-3}{6}+\frac{1}{2}$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

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

Add -\frac{1}{2} and \frac{1}{2} to get 0.

$$0$$

Factor

$$0$$