Solve 3/3-2/5[1/sqrt{9}-4/3(frac{1}{2}+frac{5}{3}-frac{4}{2}+frac{3}{2}divfrac{1}{6})-frac{2}{4}]

$$\frac { 3 } { 3 } - \frac { 2 } { 5 } [ \frac { 1 } { \sqrt { 9 } } - \frac { 4 } { 3 } ( \frac { 1 } { 2 } + \frac { 5 } { 3 } - \frac { 4 } { 2 } + \frac { 3 } { 2 } \div \frac { 1 } { 6 } ) - \frac { 2 } { 4 } ]$$

Evaluate

$$\frac{268}{45}\approx 5.955555556$$

Solution Steps

Divide 3 by 3 to get 1.

$$1-\frac{2}{5}\left(\frac{1}{\sqrt{9}}-\frac{4}{3}\left(\frac{1}{2}+\frac{5}{3}-\frac{4}{2}+\frac{\frac{3}{2}}{\frac{1}{6}}\right)-\frac{2}{4}\right)$$

Calculate the square root of 9 and get 3.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{1}{2}+\frac{5}{3}-\frac{4}{2}+\frac{\frac{3}{2}}{\frac{1}{6}}\right)-\frac{2}{4}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{5}{3} to fractions with denominator 6.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{3}{6}+\frac{10}{6}-\frac{4}{2}+\frac{\frac{3}{2}}{\frac{1}{6}}\right)-\frac{2}{4}\right)$$

Since \frac{3}{6} and \frac{10}{6} have the same denominator, add them by adding their numerators.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{3+10}{6}-\frac{4}{2}+\frac{\frac{3}{2}}{\frac{1}{6}}\right)-\frac{2}{4}\right)$$

Add 3 and 10 to get 13.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{13}{6}-\frac{4}{2}+\frac{\frac{3}{2}}{\frac{1}{6}}\right)-\frac{2}{4}\right)$$

Divide 4 by 2 to get 2.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{13}{6}-2+\frac{\frac{3}{2}}{\frac{1}{6}}\right)-\frac{2}{4}\right)$$

Convert 2 to fraction \frac{12}{6}.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{13}{6}-\frac{12}{6}+\frac{\frac{3}{2}}{\frac{1}{6}}\right)-\frac{2}{4}\right)$$

Since \frac{13}{6} and \frac{12}{6} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{13-12}{6}+\frac{\frac{3}{2}}{\frac{1}{6}}\right)-\frac{2}{4}\right)$$

Subtract 12 from 13 to get 1.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{1}{6}+\frac{\frac{3}{2}}{\frac{1}{6}}\right)-\frac{2}{4}\right)$$

Divide \frac{3}{2} by \frac{1}{6} by multiplying \frac{3}{2} by the reciprocal of \frac{1}{6}.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{1}{6}+\frac{3}{2}\times 6\right)-\frac{2}{4}\right)$$

Express \frac{3}{2}\times 6 as a single fraction.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{1}{6}+\frac{3\times 6}{2}\right)-\frac{2}{4}\right)$$

Multiply 3 and 6 to get 18.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{1}{6}+\frac{18}{2}\right)-\frac{2}{4}\right)$$

Divide 18 by 2 to get 9.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{1}{6}+9\right)-\frac{2}{4}\right)$$

Convert 9 to fraction \frac{54}{6}.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\left(\frac{1}{6}+\frac{54}{6}\right)-\frac{2}{4}\right)$$

Since \frac{1}{6} and \frac{54}{6} have the same denominator, add them by adding their numerators.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\times \frac{1+54}{6}-\frac{2}{4}\right)$$

Add 1 and 54 to get 55.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4}{3}\times \frac{55}{6}-\frac{2}{4}\right)$$

Multiply \frac{4}{3} times \frac{55}{6} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{4\times 55}{3\times 6}-\frac{2}{4}\right)$$

Do the multiplications in the fraction \frac{4\times 55}{3\times 6}.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{220}{18}-\frac{2}{4}\right)$$

Reduce the fraction \frac{220}{18} to lowest terms by extracting and canceling out 2.

$$1-\frac{2}{5}\left(\frac{1}{3}-\frac{110}{9}-\frac{2}{4}\right)$$

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{110}{9} to fractions with denominator 9.

$$1-\frac{2}{5}\left(\frac{3}{9}-\frac{110}{9}-\frac{2}{4}\right)$$

Since \frac{3}{9} and \frac{110}{9} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{2}{5}\left(\frac{3-110}{9}-\frac{2}{4}\right)$$

Subtract 110 from 3 to get -107.

$$1-\frac{2}{5}\left(-\frac{107}{9}-\frac{2}{4}\right)$$

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

$$1-\frac{2}{5}\left(-\frac{107}{9}-\frac{1}{2}\right)$$

Least common multiple of 9 and 2 is 18. Convert -\frac{107}{9} and \frac{1}{2} to fractions with denominator 18.

$$1-\frac{2}{5}\left(-\frac{214}{18}-\frac{9}{18}\right)$$

Since -\frac{214}{18} and \frac{9}{18} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{2}{5}\times \frac{-214-9}{18}$$

Subtract 9 from -214 to get -223.

$$1-\frac{2}{5}\left(-\frac{223}{18}\right)$$

Multiply \frac{2}{5} times -\frac{223}{18} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{2\left(-223\right)}{5\times 18}$$

Do the multiplications in the fraction \frac{2\left(-223\right)}{5\times 18}.

$$1-\frac{-446}{90}$$

Reduce the fraction \frac{-446}{90} to lowest terms by extracting and canceling out 2.

$$1-\left(-\frac{223}{45}\right)$$

The opposite of -\frac{223}{45} is \frac{223}{45}.

$$1+\frac{223}{45}$$

Convert 1 to fraction \frac{45}{45}.

$$\frac{45}{45}+\frac{223}{45}$$

Since \frac{45}{45} and \frac{223}{45} have the same denominator, add them by adding their numerators.

$$\frac{45+223}{45}$$

Add 45 and 223 to get 268.

$$\frac{268}{45}$$

Factor

$$\frac{2 ^ {2} \cdot 67}{3 ^ {2} \cdot 5} = 5\frac{43}{45} = 5.955555555555556$$