Solve (-1/4)*{1/3-(-5/9)}

$$( - \frac { 1 } { 4 } ) \times \{ \frac { 1 } { 3 } - ( - \frac { 5 } { 9 } ) \}$$

Evaluate

$$-\frac{2}{9}\approx -0.222222222$$

Solution Steps

The opposite of -\frac{5}{9} is \frac{5}{9}.

$$-\frac{1}{4}\left(\frac{1}{3}+\frac{5}{9}\right)$$

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{5}{9} to fractions with denominator 9.

$$-\frac{1}{4}\left(\frac{3}{9}+\frac{5}{9}\right)$$

Since \frac{3}{9} and \frac{5}{9} have the same denominator, add them by adding their numerators.

$$-\frac{1}{4}\times \frac{3+5}{9}$$

Add 3 and 5 to get 8.

$$-\frac{1}{4}\times \frac{8}{9}$$

Multiply -\frac{1}{4} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8}{4\times 9}$$

Do the multiplications in the fraction \frac{-8}{4\times 9}.

$$\frac{-8}{36}$$

Reduce the fraction \frac{-8}{36} to lowest terms by extracting and canceling out 4.

$$-\frac{2}{9}$$

Factor

$$-\frac{2}{9} = -0.2222222222222222$$