Solve operatorname{le}(1-2/5)*((1/2+1/3-1/4)*(frac{1}{2}-frac{1}{13})+frac{3}{4}:frac{9}{2}]

$$\operatorname { le } ( 1 - \frac { 2 } { 5 } ) \cdot ( ( \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 4 } ) \cdot ( \frac { 1 } { 2 } - \frac { 1 } { 13 } ) + \frac { 3 } { 4 } : \frac { 9 } { 2 } ]$$

Evaluate

$$\frac{129el}{520}$$

Solution Steps

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

$$le\left(\frac{5}{5}-\frac{2}{5}\right)\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$le\times \frac{5-2}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Subtract 2 from 5 to get 3.

$$le\times \frac{3}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

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

$$le\times \frac{3}{5}\left(\left(\frac{3}{6}+\frac{2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$le\times \frac{3}{5}\left(\left(\frac{3+2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Add 3 and 2 to get 5.

$$le\times \frac{3}{5}\left(\left(\frac{5}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$le\times \frac{3}{5}\left(\left(\frac{10}{12}-\frac{3}{12}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$le\times \frac{3}{5}\left(\frac{10-3}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Subtract 3 from 10 to get 7.

$$le\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Least common multiple of 2 and 13 is 26. Convert \frac{1}{2} and \frac{1}{13} to fractions with denominator 26.

$$le\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{13}{26}-\frac{2}{26}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Since \frac{13}{26} and \frac{2}{26} have the same denominator, subtract them by subtracting their numerators.

$$le\times \frac{3}{5}\left(\frac{7}{12}\times \frac{13-2}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Subtract 2 from 13 to get 11.

$$le\times \frac{3}{5}\left(\frac{7}{12}\times \frac{11}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Multiply \frac{7}{12} times \frac{11}{26} by multiplying numerator times numerator and denominator times denominator.

$$le\times \frac{3}{5}\left(\frac{7\times 11}{12\times 26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Do the multiplications in the fraction \frac{7\times 11}{12\times 26}.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Divide \frac{3}{4} by \frac{9}{2} by multiplying \frac{3}{4} by the reciprocal of \frac{9}{2}.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{3}{4}\times \frac{2}{9}\right)$$

Multiply \frac{3}{4} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{3\times 2}{4\times 9}\right)$$

Do the multiplications in the fraction \frac{3\times 2}{4\times 9}.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{6}{36}\right)$$

Reduce the fraction \frac{6}{36} to lowest terms by extracting and canceling out 6.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{1}{6}\right)$$

Least common multiple of 312 and 6 is 312. Convert \frac{77}{312} and \frac{1}{6} to fractions with denominator 312.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{52}{312}\right)$$

Since \frac{77}{312} and \frac{52}{312} have the same denominator, add them by adding their numerators.

$$le\times \frac{3}{5}\times \frac{77+52}{312}$$

Add 77 and 52 to get 129.

$$le\times \frac{3}{5}\times \frac{129}{312}$$

Reduce the fraction \frac{129}{312} to lowest terms by extracting and canceling out 3.

$$le\times \frac{3}{5}\times \frac{43}{104}$$

Multiply \frac{3}{5} times \frac{43}{104} by multiplying numerator times numerator and denominator times denominator.

$$le\times \frac{3\times 43}{5\times 104}$$

Do the multiplications in the fraction \frac{3\times 43}{5\times 104}.

$$le\times \frac{129}{520}$$

Expand

$$\frac{129el}{520}$$

Solution Steps

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

$$le\left(\frac{5}{5}-\frac{2}{5}\right)\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$le\times \frac{5-2}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Subtract 2 from 5 to get 3.

$$le\times \frac{3}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

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

$$le\times \frac{3}{5}\left(\left(\frac{3}{6}+\frac{2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$le\times \frac{3}{5}\left(\left(\frac{3+2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Add 3 and 2 to get 5.

$$le\times \frac{3}{5}\left(\left(\frac{5}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$le\times \frac{3}{5}\left(\left(\frac{10}{12}-\frac{3}{12}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$le\times \frac{3}{5}\left(\frac{10-3}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Subtract 3 from 10 to get 7.

$$le\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Least common multiple of 2 and 13 is 26. Convert \frac{1}{2} and \frac{1}{13} to fractions with denominator 26.

$$le\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{13}{26}-\frac{2}{26}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Since \frac{13}{26} and \frac{2}{26} have the same denominator, subtract them by subtracting their numerators.

$$le\times \frac{3}{5}\left(\frac{7}{12}\times \frac{13-2}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Subtract 2 from 13 to get 11.

$$le\times \frac{3}{5}\left(\frac{7}{12}\times \frac{11}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Multiply \frac{7}{12} times \frac{11}{26} by multiplying numerator times numerator and denominator times denominator.

$$le\times \frac{3}{5}\left(\frac{7\times 11}{12\times 26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Do the multiplications in the fraction \frac{7\times 11}{12\times 26}.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Divide \frac{3}{4} by \frac{9}{2} by multiplying \frac{3}{4} by the reciprocal of \frac{9}{2}.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{3}{4}\times \frac{2}{9}\right)$$

Multiply \frac{3}{4} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{3\times 2}{4\times 9}\right)$$

Do the multiplications in the fraction \frac{3\times 2}{4\times 9}.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{6}{36}\right)$$

Reduce the fraction \frac{6}{36} to lowest terms by extracting and canceling out 6.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{1}{6}\right)$$

Least common multiple of 312 and 6 is 312. Convert \frac{77}{312} and \frac{1}{6} to fractions with denominator 312.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{52}{312}\right)$$

Since \frac{77}{312} and \frac{52}{312} have the same denominator, add them by adding their numerators.

$$le\times \frac{3}{5}\times \frac{77+52}{312}$$

Add 77 and 52 to get 129.

$$le\times \frac{3}{5}\times \frac{129}{312}$$

Reduce the fraction \frac{129}{312} to lowest terms by extracting and canceling out 3.

$$le\times \frac{3}{5}\times \frac{43}{104}$$

Multiply \frac{3}{5} times \frac{43}{104} by multiplying numerator times numerator and denominator times denominator.

$$le\times \frac{3\times 43}{5\times 104}$$

Do the multiplications in the fraction \frac{3\times 43}{5\times 104}.

$$le\times \frac{129}{520}$$