Solve 1/5+2/3*9*1/9-sqrt{1/3}sqrt{frac{1}{3}}

$$\frac{ 1 }{ 5 } + \frac{ 2 }{ 3 } \times 9 \times \frac{ 1 }{ 9 } - \sqrt{ \frac{ 1 }{ 3 } } \sqrt{ \frac{ 1 }{ 3 } }$$

Evaluate

$$\frac{8}{15}\approx 0.533333333$$

Solution Steps

Multiply \sqrt{\frac{1}{3}} and \sqrt{\frac{1}{3}} to get \frac{1}{3}.

$$\frac{1}{5}+\frac{2}{3}\times 9\times \frac{1}{9}-\frac{1}{3}$$

Express \frac{2}{3}\times 9 as a single fraction.

$$\frac{1}{5}+\frac{2\times 9}{3}\times \frac{1}{9}-\frac{1}{3}$$

Multiply 2 and 9 to get 18.

$$\frac{1}{5}+\frac{18}{3}\times \frac{1}{9}-\frac{1}{3}$$

Divide 18 by 3 to get 6.

$$\frac{1}{5}+6\times \frac{1}{9}-\frac{1}{3}$$

Multiply 6 and \frac{1}{9} to get \frac{6}{9}.

$$\frac{1}{5}+\frac{6}{9}-\frac{1}{3}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1}{5}+\frac{2}{3}-\frac{1}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{3}{15}+\frac{10}{15}-\frac{1}{3}$$

Since \frac{3}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{3+10}{15}-\frac{1}{3}$$

Add 3 and 10 to get 13.

$$\frac{13}{15}-\frac{1}{3}$$

Least common multiple of 15 and 3 is 15. Convert \frac{13}{15} and \frac{1}{3} to fractions with denominator 15.

$$\frac{13}{15}-\frac{5}{15}$$

Since \frac{13}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-5}{15}$$

Subtract 5 from 13 to get 8.

$$\frac{8}{15}$$

Factor

$$\frac{2 ^ {3}}{3 \cdot 5} = 0.5333333333333333$$