Solve 1/5+(3/5*25/6)-2divfrac{4/9}{frac{4}{9}left(frac{1}{5}-2right)-frac{1}{3}}

$$\frac{ \frac{ 1 }{ 5 } +( \frac{ 3 }{ 5 } \times \frac{ 25 }{ 6 } )-2 \div \frac{ 4 }{ 9 } }{ \frac{ 4 }{ 9 } \left( \frac{ 1 }{ 5 } -2 \right) - \frac{ 1 }{ 3 } }$$

Evaluate

$$\frac{27}{17}\approx 1.588235294$$

Solution Steps

Multiply \frac{3}{5} times \frac{25}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{5}+\frac{3\times 25}{5\times 6}-\frac{2}{\frac{4}{9}}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Do the multiplications in the fraction \frac{3\times 25}{5\times 6}.

$$\frac{\frac{1}{5}+\frac{75}{30}-\frac{2}{\frac{4}{9}}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Reduce the fraction \frac{75}{30} to lowest terms by extracting and canceling out 15.

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

Least common multiple of 5 and 2 is 10. Convert \frac{1}{5} and \frac{5}{2} to fractions with denominator 10.

$$\frac{\frac{2}{10}+\frac{25}{10}-\frac{2}{\frac{4}{9}}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Since \frac{2}{10} and \frac{25}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2+25}{10}-\frac{2}{\frac{4}{9}}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Add 2 and 25 to get 27.

$$\frac{\frac{27}{10}-\frac{2}{\frac{4}{9}}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Divide 2 by \frac{4}{9} by multiplying 2 by the reciprocal of \frac{4}{9}.

$$\frac{\frac{27}{10}-2\times \frac{9}{4}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Express 2\times \frac{9}{4} as a single fraction.

$$\frac{\frac{27}{10}-\frac{2\times 9}{4}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Multiply 2 and 9 to get 18.

$$\frac{\frac{27}{10}-\frac{18}{4}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{27}{10}-\frac{9}{2}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Least common multiple of 10 and 2 is 10. Convert \frac{27}{10} and \frac{9}{2} to fractions with denominator 10.

$$\frac{\frac{27}{10}-\frac{45}{10}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Since \frac{27}{10} and \frac{45}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27-45}{10}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Subtract 45 from 27 to get -18.

$$\frac{\frac{-18}{10}}{\frac{4}{9}\left(\frac{1}{5}-2\right)-\frac{1}{3}}$$

Reduce the fraction \frac{-18}{10} to lowest terms by extracting and canceling out 2.

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

Convert 2 to fraction \frac{10}{5}.

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

Since \frac{1}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{9}{5}}{\frac{4}{9}\times \frac{1-10}{5}-\frac{1}{3}}$$

Subtract 10 from 1 to get -9.

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

Multiply \frac{4}{9} times -\frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{4\left(-9\right)}{9\times 5}.

$$\frac{-\frac{9}{5}}{\frac{-36}{45}-\frac{1}{3}}$$

Reduce the fraction \frac{-36}{45} to lowest terms by extracting and canceling out 9.

$$\frac{-\frac{9}{5}}{-\frac{4}{5}-\frac{1}{3}}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{4}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{-\frac{9}{5}}{-\frac{12}{15}-\frac{5}{15}}$$

Since -\frac{12}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{9}{5}}{\frac{-12-5}{15}}$$

Subtract 5 from -12 to get -17.

$$\frac{-\frac{9}{5}}{-\frac{17}{15}}$$

Divide -\frac{9}{5} by -\frac{17}{15} by multiplying -\frac{9}{5} by the reciprocal of -\frac{17}{15}.

$$-\frac{9}{5}\left(-\frac{15}{17}\right)$$

Multiply -\frac{9}{5} times -\frac{15}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9\left(-15\right)}{5\times 17}$$

Do the multiplications in the fraction \frac{-9\left(-15\right)}{5\times 17}.

$$\frac{135}{85}$$

Reduce the fraction \frac{135}{85} to lowest terms by extracting and canceling out 5.

$$\frac{27}{17}$$

Factor

$$\frac{3 ^ {3}}{17} = 1\frac{10}{17} = 1.588235294117647$$