Solve (-2/9-1/4)-[-5/18-(-1/2)]

$$( - \frac { 2 } { 9 } - \frac { 1 } { 4 } ) - [ - \frac { 5 } { 18 } - ( - \frac { 1 } { 2 } ) ]$$

Evaluate

$$-\frac{25}{36}\approx -0.694444444$$

Solution Steps

Least common multiple of 9 and 4 is 36. Convert -\frac{2}{9} and \frac{1}{4} to fractions with denominator 36.

$$-\frac{8}{36}-\frac{9}{36}-\left(-\frac{5}{18}-\left(-\frac{1}{2}\right)\right)$$

Since -\frac{8}{36} and \frac{9}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-8-9}{36}-\left(-\frac{5}{18}-\left(-\frac{1}{2}\right)\right)$$

Subtract 9 from -8 to get -17.

$$-\frac{17}{36}-\left(-\frac{5}{18}-\left(-\frac{1}{2}\right)\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$-\frac{17}{36}-\left(-\frac{5}{18}+\frac{1}{2}\right)$$

Least common multiple of 18 and 2 is 18. Convert -\frac{5}{18} and \frac{1}{2} to fractions with denominator 18.

$$-\frac{17}{36}-\left(-\frac{5}{18}+\frac{9}{18}\right)$$

Since -\frac{5}{18} and \frac{9}{18} have the same denominator, add them by adding their numerators.

$$-\frac{17}{36}-\frac{-5+9}{18}$$

Add -5 and 9 to get 4.

$$-\frac{17}{36}-\frac{4}{18}$$

Reduce the fraction \frac{4}{18} to lowest terms by extracting and canceling out 2.

$$-\frac{17}{36}-\frac{2}{9}$$

Least common multiple of 36 and 9 is 36. Convert -\frac{17}{36} and \frac{2}{9} to fractions with denominator 36.

$$-\frac{17}{36}-\frac{8}{36}$$

Since -\frac{17}{36} and \frac{8}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17-8}{36}$$

Subtract 8 from -17 to get -25.

$$-\frac{25}{36}$$

Factor

$$-\frac{25}{36} = -0.6944444444444444$$