Solve (3/4-1/3)2/3/(1-frac{1{6})div5}*3+frac{frac{2}{frac{4}{3}+frac{1}{2}}}{frac{frac{1}{2}-frac{2}{5}}{2}}

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

Evaluate

$$\frac{295}{11}\approx 26.818181818$$

Solution Steps

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

$$\frac{\left(\frac{9}{12}-\frac{4}{12}\right)\times \frac{2}{3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-4}{12}\times \frac{2}{3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Subtract 4 from 9 to get 5.

$$\frac{\frac{5}{12}\times \frac{2}{3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Multiply \frac{5}{12} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 2}{12\times 3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Do the multiplications in the fraction \frac{5\times 2}{12\times 3}.

$$\frac{\frac{10}{36}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Reduce the fraction \frac{10}{36} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{5}{18}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{\frac{5}{18}}{\frac{\frac{6}{6}-\frac{1}{6}}{5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

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

$$\frac{\frac{5}{18}}{\frac{\frac{6-1}{6}}{5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Subtract 1 from 6 to get 5.

$$\frac{\frac{5}{18}}{\frac{\frac{5}{6}}{5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Express \frac{\frac{5}{6}}{5} as a single fraction.

$$\frac{\frac{5}{18}}{\frac{5}{6\times 5}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{5}{18}}{\frac{1}{6}}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Divide \frac{5}{18} by \frac{1}{6} by multiplying \frac{5}{18} by the reciprocal of \frac{1}{6}.

$$\frac{5}{18}\times 6\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Express \frac{5}{18}\times 6 as a single fraction.

$$\frac{5\times 6}{18}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Multiply 5 and 6 to get 30.

$$\frac{30}{18}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Reduce the fraction \frac{30}{18} to lowest terms by extracting and canceling out 6.

$$\frac{5}{3}\times 3+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Cancel out 3 and 3.

$$5+\frac{\frac{2}{\frac{4}{3}+\frac{1}{2}}}{\frac{\frac{1}{2}-\frac{2}{5}}{2}}$$

Divide \frac{2}{\frac{4}{3}+\frac{1}{2}} by \frac{\frac{1}{2}-\frac{2}{5}}{2} by multiplying \frac{2}{\frac{4}{3}+\frac{1}{2}} by the reciprocal of \frac{\frac{1}{2}-\frac{2}{5}}{2}.

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

Multiply 2 and 2 to get 4.

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

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$5+\frac{4}{\left(\frac{8}{6}+\frac{3}{6}\right)\left(\frac{1}{2}-\frac{2}{5}\right)}$$

Since \frac{8}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$5+\frac{4}{\frac{8+3}{6}\left(\frac{1}{2}-\frac{2}{5}\right)}$$

Add 8 and 3 to get 11.

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

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

$$5+\frac{4}{\frac{11}{6}\left(\frac{5}{10}-\frac{4}{10}\right)}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$5+\frac{4}{\frac{11}{6}\times \frac{5-4}{10}}$$

Subtract 4 from 5 to get 1.

$$5+\frac{4}{\frac{11}{6}\times \frac{1}{10}}$$

Multiply \frac{11}{6} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$5+\frac{4}{\frac{11\times 1}{6\times 10}}$$

Do the multiplications in the fraction \frac{11\times 1}{6\times 10}.

$$5+\frac{4}{\frac{11}{60}}$$

Divide 4 by \frac{11}{60} by multiplying 4 by the reciprocal of \frac{11}{60}.

$$5+4\times \frac{60}{11}$$

Express 4\times \frac{60}{11} as a single fraction.

$$5+\frac{4\times 60}{11}$$

Multiply 4 and 60 to get 240.

$$5+\frac{240}{11}$$

Convert 5 to fraction \frac{55}{11}.

$$\frac{55}{11}+\frac{240}{11}$$

Since \frac{55}{11} and \frac{240}{11} have the same denominator, add them by adding their numerators.

$$\frac{55+240}{11}$$

Add 55 and 240 to get 295.

$$\frac{295}{11}$$

Factor

$$\frac{5 \cdot 59}{11} = 26\frac{9}{11} = 26.818181818181817$$