Solve (((3/2+((1/4+(1/1-1/3)-frac{1}{6})*(frac{11}{3}-frac{6}{3}))))+frac{1}{1}+frac{2}{5}-frac{1}{3})*(((frac{2}{1}-frac{1}{3})div(frac{3}{5}+frac{1}{1})))

$$((( \frac{ 3 }{ 2 } +(( \frac{ 1 }{ 4 } +( \frac{ 1 }{ 1 } - \frac{ 1 }{ 3 } )- \frac{ 1 }{ 6 } ) \times ( \frac{ 11 }{ 3 } - \frac{ 6 }{ 3 } ))))+ \frac{ 1 }{ 1 } + \frac{ 2 }{ 5 } - \frac{ 1 }{ 3 } ) \times ((( \frac{ 2 }{ 1 } - \frac{ 1 }{ 3 } ) \div ( \frac{ 3 }{ 5 } + \frac{ 1 }{ 1 } )))$$

Evaluate

$$\frac{1145}{288}\approx 3.975694444$$

Solution Steps

Divide 1 by 1 to get 1.

$$\left(\frac{3}{2}+\left(\frac{1}{4}+1-\frac{1}{3}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+\frac{1}{1}+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+\frac{1}{1}}$$

Divide 1 by 1 to get 1.

$$\left(\frac{3}{2}+\left(\frac{1}{4}+1-\frac{1}{3}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+\frac{1}{1}}$$

Divide 1 by 1 to get 1.

$$\left(\frac{3}{2}+\left(\frac{1}{4}+1-\frac{1}{3}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Convert 1 to fraction \frac{4}{4}.

$$\left(\frac{3}{2}+\left(\frac{1}{4}+\frac{4}{4}-\frac{1}{3}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Since \frac{1}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\left(\frac{3}{2}+\left(\frac{1+4}{4}-\frac{1}{3}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Add 1 and 4 to get 5.

$$\left(\frac{3}{2}+\left(\frac{5}{4}-\frac{1}{3}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{1}{3} to fractions with denominator 12.

$$\left(\frac{3}{2}+\left(\frac{15}{12}-\frac{4}{12}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Since \frac{15}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3}{2}+\left(\frac{15-4}{12}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Subtract 4 from 15 to get 11.

$$\left(\frac{3}{2}+\left(\frac{11}{12}-\frac{1}{6}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Least common multiple of 12 and 6 is 12. Convert \frac{11}{12} and \frac{1}{6} to fractions with denominator 12.

$$\left(\frac{3}{2}+\left(\frac{11}{12}-\frac{2}{12}\right)\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Since \frac{11}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3}{2}+\frac{11-2}{12}\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Subtract 2 from 11 to get 9.

$$\left(\frac{3}{2}+\frac{9}{12}\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\left(\frac{3}{2}+\frac{3}{4}\left(\frac{11}{3}-\frac{6}{3}\right)+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Since \frac{11}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3}{2}+\frac{3}{4}\times \frac{11-6}{3}+1+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Subtract 6 from 11 to get 5.

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

Multiply \frac{3}{4} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{5}{4} to fractions with denominator 4.

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

Since \frac{6}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

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

Add 6 and 5 to get 11.

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

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{11}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

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

Add 11 and 4 to get 15.

$$\left(\frac{15}{4}+\frac{2}{5}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Least common multiple of 4 and 5 is 20. Convert \frac{15}{4} and \frac{2}{5} to fractions with denominator 20.

$$\left(\frac{75}{20}+\frac{8}{20}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Since \frac{75}{20} and \frac{8}{20} have the same denominator, add them by adding their numerators.

$$\left(\frac{75+8}{20}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Add 75 and 8 to get 83.

$$\left(\frac{83}{20}-\frac{1}{3}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Least common multiple of 20 and 3 is 60. Convert \frac{83}{20} and \frac{1}{3} to fractions with denominator 60.

$$\left(\frac{249}{60}-\frac{20}{60}\right)\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Since \frac{249}{60} and \frac{20}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{249-20}{60}\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Subtract 20 from 249 to get 229.

$$\frac{229}{60}\times \frac{\frac{2}{1}-\frac{1}{3}}{\frac{3}{5}+1}$$

Anything divided by one gives itself.

$$\frac{229}{60}\times \frac{2-\frac{1}{3}}{\frac{3}{5}+1}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{229}{60}\times \frac{\frac{6}{3}-\frac{1}{3}}{\frac{3}{5}+1}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{229}{60}\times \frac{\frac{6-1}{3}}{\frac{3}{5}+1}$$

Subtract 1 from 6 to get 5.

$$\frac{229}{60}\times \frac{\frac{5}{3}}{\frac{3}{5}+1}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{229}{60}\times \frac{\frac{5}{3}}{\frac{3}{5}+\frac{5}{5}}$$

Since \frac{3}{5} and \frac{5}{5} have the same denominator, add them by adding their numerators.

$$\frac{229}{60}\times \frac{\frac{5}{3}}{\frac{3+5}{5}}$$

Add 3 and 5 to get 8.

$$\frac{229}{60}\times \frac{\frac{5}{3}}{\frac{8}{5}}$$

Divide \frac{5}{3} by \frac{8}{5} by multiplying \frac{5}{3} by the reciprocal of \frac{8}{5}.

$$\frac{229}{60}\times \frac{5}{3}\times \frac{5}{8}$$

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

$$\frac{229}{60}\times \frac{5\times 5}{3\times 8}$$

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

$$\frac{229}{60}\times \frac{25}{24}$$

Multiply \frac{229}{60} times \frac{25}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{229\times 25}{60\times 24}$$

Do the multiplications in the fraction \frac{229\times 25}{60\times 24}.

$$\frac{5725}{1440}$$

Reduce the fraction \frac{5725}{1440} to lowest terms by extracting and canceling out 5.

$$\frac{1145}{288}$$

Factor

$$\frac{5 \cdot 229}{2 ^ {5} \cdot 3 ^ {2}} = 3\frac{281}{288} = 3.9756944444444446$$