Solve 1/30-4/45)*sqrt{-27}+(-1+3/5)+1/50-sqrt{frac{25}{3}-frac{11}{9}}=sqrt{-frac{8}{125}}

$$\frac { 1 } { 30 } - \frac { 4 } { 45 } ) \times \sqrt { - 27 } + ( - 1 + \frac { 3 } { 5 } ) + \frac { 1 } { 50 } - \sqrt { \frac { 25 } { 3 } - \frac { 11 } { 9 } } = \sqrt { - \frac { 8 } { 125 } }$$

Evaluate

$$-\frac{1}{18}\approx -0.055555556$$

Solution Steps

Least common multiple of 30 and 45 is 90. Convert \frac{1}{30} and \frac{4}{45} to fractions with denominator 90.

$$\frac{3}{90}-\frac{8}{90}$$

Since \frac{3}{90} and \frac{8}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-8}{90}$$

Subtract 8 from 3 to get -5.

$$\frac{-5}{90}$$

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

$$-\frac{1}{18}$$

Factor

$$-\frac{1}{18} = -0.05555555555555555$$