Solve 2/5left(3/4+1/6-2/3left(frac{4}{5}divfrac{5}{10}right)right)+frac{1}{3}

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

Evaluate

$$\frac{41}{150}\approx 0.273333333$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{2}{5}\left(\frac{9}{12}+\frac{2}{12}-\frac{2}{3}\times \frac{\frac{4}{5}}{\frac{5}{10}}\right)+\frac{1}{3}$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}\left(\frac{9+2}{12}-\frac{2}{3}\times \frac{\frac{4}{5}}{\frac{5}{10}}\right)+\frac{1}{3}$$

Add 9 and 2 to get 11.

$$\frac{2}{5}\left(\frac{11}{12}-\frac{2}{3}\times \frac{\frac{4}{5}}{\frac{5}{10}}\right)+\frac{1}{3}$$

Divide \frac{4}{5} by \frac{5}{10} by multiplying \frac{4}{5} by the reciprocal of \frac{5}{10}.

$$\frac{2}{5}\left(\frac{11}{12}-\frac{2}{3}\times \frac{4\times 10}{5\times 5}\right)+\frac{1}{3}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2}{5}\left(\frac{11}{12}-\frac{2}{3}\times \frac{2\times 4}{5}\right)+\frac{1}{3}$$

Multiply 2 and 4 to get 8.

$$\frac{2}{5}\left(\frac{11}{12}-\frac{2}{3}\times \frac{8}{5}\right)+\frac{1}{3}$$

Multiply \frac{2}{3} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}\left(\frac{11}{12}-\frac{2\times 8}{3\times 5}\right)+\frac{1}{3}$$

Do the multiplications in the fraction \frac{2\times 8}{3\times 5}.

$$\frac{2}{5}\left(\frac{11}{12}-\frac{16}{15}\right)+\frac{1}{3}$$

Least common multiple of 12 and 15 is 60. Convert \frac{11}{12} and \frac{16}{15} to fractions with denominator 60.

$$\frac{2}{5}\left(\frac{55}{60}-\frac{64}{60}\right)+\frac{1}{3}$$

Since \frac{55}{60} and \frac{64}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}\times \frac{55-64}{60}+\frac{1}{3}$$

Subtract 64 from 55 to get -9.

$$\frac{2}{5}\times \frac{-9}{60}+\frac{1}{3}$$

Reduce the fraction \frac{-9}{60} to lowest terms by extracting and canceling out 3.

$$\frac{2}{5}\left(-\frac{3}{20}\right)+\frac{1}{3}$$

Multiply \frac{2}{5} times -\frac{3}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-3\right)}{5\times 20}+\frac{1}{3}$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 20}.

$$\frac{-6}{100}+\frac{1}{3}$$

Reduce the fraction \frac{-6}{100} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{50}+\frac{1}{3}$$

Least common multiple of 50 and 3 is 150. Convert -\frac{3}{50} and \frac{1}{3} to fractions with denominator 150.

$$-\frac{9}{150}+\frac{50}{150}$$

Since -\frac{9}{150} and \frac{50}{150} have the same denominator, add them by adding their numerators.

$$\frac{-9+50}{150}$$

Add -9 and 50 to get 41.

$$\frac{41}{150}$$

Factor

$$\frac{41}{2 \cdot 3 \cdot 5 ^ {2}} = 0.2733333333333333$$