Solve left(1/2+13/7+5/6right)left(4/15-frac{3}{20}right)div1frac{14}{15}*frac{11}{18}

$$\left( \frac{ 1 }{ 2 } +1 \frac{ 3 }{ 7 } + \frac{ 5 }{ 6 } \right) \left( \frac{ 4 }{ 15 } - \frac{ 3 }{ 20 } \right) \div 1 \frac{ 14 }{ 15 } \times \frac{ 11 }{ 18 }$$

Evaluate

$$\frac{11}{108}\approx 0.101851852$$

Solution Steps

Multiply 1 and 7 to get 7.

$$\frac{\left(\frac{1}{2}+\frac{7+3}{7}+\frac{5}{6}\right)\left(\frac{4}{15}-\frac{3}{20}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Add 7 and 3 to get 10.

$$\frac{\left(\frac{1}{2}+\frac{10}{7}+\frac{5}{6}\right)\left(\frac{4}{15}-\frac{3}{20}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{10}{7} to fractions with denominator 14.

$$\frac{\left(\frac{7}{14}+\frac{20}{14}+\frac{5}{6}\right)\left(\frac{4}{15}-\frac{3}{20}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Since \frac{7}{14} and \frac{20}{14} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{7+20}{14}+\frac{5}{6}\right)\left(\frac{4}{15}-\frac{3}{20}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Add 7 and 20 to get 27.

$$\frac{\left(\frac{27}{14}+\frac{5}{6}\right)\left(\frac{4}{15}-\frac{3}{20}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Least common multiple of 14 and 6 is 42. Convert \frac{27}{14} and \frac{5}{6} to fractions with denominator 42.

$$\frac{\left(\frac{81}{42}+\frac{35}{42}\right)\left(\frac{4}{15}-\frac{3}{20}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Since \frac{81}{42} and \frac{35}{42} have the same denominator, add them by adding their numerators.

$$\frac{\frac{81+35}{42}\left(\frac{4}{15}-\frac{3}{20}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Add 81 and 35 to get 116.

$$\frac{\frac{116}{42}\left(\frac{4}{15}-\frac{3}{20}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Reduce the fraction \frac{116}{42} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{58}{21}\left(\frac{4}{15}-\frac{3}{20}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Least common multiple of 15 and 20 is 60. Convert \frac{4}{15} and \frac{3}{20} to fractions with denominator 60.

$$\frac{\frac{58}{21}\left(\frac{16}{60}-\frac{9}{60}\right)}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Since \frac{16}{60} and \frac{9}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{58}{21}\times \frac{16-9}{60}}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Subtract 9 from 16 to get 7.

$$\frac{\frac{58}{21}\times \frac{7}{60}}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Multiply \frac{58}{21} times \frac{7}{60} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{58\times 7}{21\times 60}}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Do the multiplications in the fraction \frac{58\times 7}{21\times 60}.

$$\frac{\frac{406}{1260}}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Reduce the fraction \frac{406}{1260} to lowest terms by extracting and canceling out 14.

$$\frac{\frac{29}{90}}{\frac{1\times 15+14}{15}}\times \frac{11}{18}$$

Multiply 1 and 15 to get 15.

$$\frac{\frac{29}{90}}{\frac{15+14}{15}}\times \frac{11}{18}$$

Add 15 and 14 to get 29.

$$\frac{\frac{29}{90}}{\frac{29}{15}}\times \frac{11}{18}$$

Divide \frac{29}{90} by \frac{29}{15} by multiplying \frac{29}{90} by the reciprocal of \frac{29}{15}.

$$\frac{29}{90}\times \frac{15}{29}\times \frac{11}{18}$$

Multiply \frac{29}{90} times \frac{15}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 15}{90\times 29}\times \frac{11}{18}$$

Cancel out 29 in both numerator and denominator.

$$\frac{15}{90}\times \frac{11}{18}$$

Reduce the fraction \frac{15}{90} to lowest terms by extracting and canceling out 15.

$$\frac{1}{6}\times \frac{11}{18}$$

Multiply \frac{1}{6} times \frac{11}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 11}{6\times 18}$$

Do the multiplications in the fraction \frac{1\times 11}{6\times 18}.

$$\frac{11}{108}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 3 ^ {3}} = 0.10185185185185185$$