Solve sqrt{1-5/9}-{left(15/10right)}^-2+5/18-7/9-frac{22}{9}=

$$\sqrt{ 1- \frac{ 5 }{ 9 } } - { \left( \frac{ 15 }{ 10 } \right) }^{ -2 } + \frac{ 5 }{ 18 } - \frac{ 7 }{ 9 } - \frac{ 22 }{ 9 } =$$

Evaluate

$$-\frac{49}{18}\approx -2.722222222$$

Solution Steps

Subtract \frac{5}{9} from 1 to get \frac{4}{9}.

$$\sqrt{\frac{4}{9}}-\left(\frac{15}{10}\right)^{-2}+\frac{5}{18}-\frac{7}{9}-\frac{22}{9}$$

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{2}{3}-\left(\frac{15}{10}\right)^{-2}+\frac{5}{18}-\frac{7}{9}-\frac{22}{9}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{2}{3}-\left(\frac{3}{2}\right)^{-2}+\frac{5}{18}-\frac{7}{9}-\frac{22}{9}$$

Calculate \frac{3}{2} to the power of -2 and get \frac{4}{9}.

$$\frac{2}{3}-\frac{4}{9}+\frac{5}{18}-\frac{7}{9}-\frac{22}{9}$$

Subtract \frac{4}{9} from \frac{2}{3} to get \frac{2}{9}.

$$\frac{2}{9}+\frac{5}{18}-\frac{7}{9}-\frac{22}{9}$$

Add \frac{2}{9} and \frac{5}{18} to get \frac{1}{2}.

$$\frac{1}{2}-\frac{7}{9}-\frac{22}{9}$$

Subtract \frac{7}{9} from \frac{1}{2} to get -\frac{5}{18}.

$$-\frac{5}{18}-\frac{22}{9}$$

Subtract \frac{22}{9} from -\frac{5}{18} to get -\frac{49}{18}.

$$-\frac{49}{18}$$

Factor

$$-\frac{49}{18} = -2\frac{13}{18} = -2.7222222222222223$$