Solve 13/6-35/66+27/121*5/3-(frac{14}{15}+frac{8}{165})*(frac{2}{9}+frac{11}{18})

$$\frac { 13 } { 6 } - \frac { 35 } { 66 } + \frac { 27 } { 121 } \cdot \frac { 5 } { 3 } - ( \frac { 14 } { 15 } + \frac { 8 } { 165 } ) \cdot ( \frac { 2 } { 9 } + \frac { 11 } { 18 } )$$

Evaluate

$$\frac{144}{121}\approx 1.190082645$$

Solution Steps

Least common multiple of 6 and 66 is 66. Convert \frac{13}{6} and \frac{35}{66} to fractions with denominator 66.

$$\frac{143}{66}-\frac{35}{66}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Since \frac{143}{66} and \frac{35}{66} have the same denominator, subtract them by subtracting their numerators.

$$\frac{143-35}{66}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Subtract 35 from 143 to get 108.

$$\frac{108}{66}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Reduce the fraction \frac{108}{66} to lowest terms by extracting and canceling out 6.

$$\frac{18}{11}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Multiply \frac{27}{121} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18}{11}+\frac{27\times 5}{121\times 3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Do the multiplications in the fraction \frac{27\times 5}{121\times 3}.

$$\frac{18}{11}+\frac{135}{363}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Reduce the fraction \frac{135}{363} to lowest terms by extracting and canceling out 3.

$$\frac{18}{11}+\frac{45}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Least common multiple of 11 and 121 is 121. Convert \frac{18}{11} and \frac{45}{121} to fractions with denominator 121.

$$\frac{198}{121}+\frac{45}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Since \frac{198}{121} and \frac{45}{121} have the same denominator, add them by adding their numerators.

$$\frac{198+45}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Add 198 and 45 to get 243.

$$\frac{243}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Least common multiple of 15 and 165 is 165. Convert \frac{14}{15} and \frac{8}{165} to fractions with denominator 165.

$$\frac{243}{121}-\left(\frac{154}{165}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Since \frac{154}{165} and \frac{8}{165} have the same denominator, add them by adding their numerators.

$$\frac{243}{121}-\frac{154+8}{165}\left(\frac{2}{9}+\frac{11}{18}\right)$$

Add 154 and 8 to get 162.

$$\frac{243}{121}-\frac{162}{165}\left(\frac{2}{9}+\frac{11}{18}\right)$$

Reduce the fraction \frac{162}{165} to lowest terms by extracting and canceling out 3.

$$\frac{243}{121}-\frac{54}{55}\left(\frac{2}{9}+\frac{11}{18}\right)$$

Least common multiple of 9 and 18 is 18. Convert \frac{2}{9} and \frac{11}{18} to fractions with denominator 18.

$$\frac{243}{121}-\frac{54}{55}\left(\frac{4}{18}+\frac{11}{18}\right)$$

Since \frac{4}{18} and \frac{11}{18} have the same denominator, add them by adding their numerators.

$$\frac{243}{121}-\frac{54}{55}\times \frac{4+11}{18}$$

Add 4 and 11 to get 15.

$$\frac{243}{121}-\frac{54}{55}\times \frac{15}{18}$$

Reduce the fraction \frac{15}{18} to lowest terms by extracting and canceling out 3.

$$\frac{243}{121}-\frac{54}{55}\times \frac{5}{6}$$

Multiply \frac{54}{55} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{243}{121}-\frac{54\times 5}{55\times 6}$$

Do the multiplications in the fraction \frac{54\times 5}{55\times 6}.

$$\frac{243}{121}-\frac{270}{330}$$

Reduce the fraction \frac{270}{330} to lowest terms by extracting and canceling out 30.

$$\frac{243}{121}-\frac{9}{11}$$

Least common multiple of 121 and 11 is 121. Convert \frac{243}{121} and \frac{9}{11} to fractions with denominator 121.

$$\frac{243}{121}-\frac{99}{121}$$

Since \frac{243}{121} and \frac{99}{121} have the same denominator, subtract them by subtracting their numerators.

$$\frac{243-99}{121}$$

Subtract 99 from 243 to get 144.

$$\frac{144}{121}$$

Factor

$$\frac{2 ^ {4} \cdot 3 ^ {2}}{11 ^ {2}} = 1\frac{23}{121} = 1.1900826446280992$$