Solve [3/5+(4/5-1/6):(1+9/10)+(frac{4}{3}-frac{3}{5})*(2-frac{4}{11})]:frac{8}{5}

$$[ \frac { 3 } { 5 } + ( \frac { 4 } { 5 } - \frac { 1 } { 6 } ) : ( 1 + \frac { 9 } { 10 } ) + ( \frac { 4 } { 3 } - \frac { 3 } { 5 } ) \cdot ( 2 - \frac { 4 } { 11 } ) ] : \frac { 8 } { 5 }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Least common multiple of 5 and 6 is 30. Convert \frac{4}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{\frac{3}{5}+\frac{\frac{24}{30}-\frac{5}{30}}{1+\frac{9}{10}}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Since \frac{24}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{5}+\frac{\frac{24-5}{30}}{1+\frac{9}{10}}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Subtract 5 from 24 to get 19.

$$\frac{\frac{3}{5}+\frac{\frac{19}{30}}{1+\frac{9}{10}}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{\frac{3}{5}+\frac{\frac{19}{30}}{\frac{10}{10}+\frac{9}{10}}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Since \frac{10}{10} and \frac{9}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{5}+\frac{\frac{19}{30}}{\frac{10+9}{10}}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Add 10 and 9 to get 19.

$$\frac{\frac{3}{5}+\frac{\frac{19}{30}}{\frac{19}{10}}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Divide \frac{19}{30} by \frac{19}{10} by multiplying \frac{19}{30} by the reciprocal of \frac{19}{10}.

$$\frac{\frac{3}{5}+\frac{19}{30}\times \frac{10}{19}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Multiply \frac{19}{30} times \frac{10}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{5}+\frac{19\times 10}{30\times 19}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Cancel out 19 in both numerator and denominator.

$$\frac{\frac{3}{5}+\frac{10}{30}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Reduce the fraction \frac{10}{30} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{3}{5}+\frac{1}{3}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{\frac{9}{15}+\frac{5}{15}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Since \frac{9}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+5}{15}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Add 9 and 5 to get 14.

$$\frac{\frac{14}{15}+\left(\frac{4}{3}-\frac{3}{5}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{\frac{14}{15}+\left(\frac{20}{15}-\frac{9}{15}\right)\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Since \frac{20}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14}{15}+\frac{20-9}{15}\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Subtract 9 from 20 to get 11.

$$\frac{\frac{14}{15}+\frac{11}{15}\left(2-\frac{4}{11}\right)}{\frac{8}{5}}$$

Convert 2 to fraction \frac{22}{11}.

$$\frac{\frac{14}{15}+\frac{11}{15}\left(\frac{22}{11}-\frac{4}{11}\right)}{\frac{8}{5}}$$

Since \frac{22}{11} and \frac{4}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14}{15}+\frac{11}{15}\times \frac{22-4}{11}}{\frac{8}{5}}$$

Subtract 4 from 22 to get 18.

$$\frac{\frac{14}{15}+\frac{11}{15}\times \frac{18}{11}}{\frac{8}{5}}$$

Multiply \frac{11}{15} times \frac{18}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{14}{15}+\frac{11\times 18}{15\times 11}}{\frac{8}{5}}$$

Cancel out 11 in both numerator and denominator.

$$\frac{\frac{14}{15}+\frac{18}{15}}{\frac{8}{5}}$$

Since \frac{14}{15} and \frac{18}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{14+18}{15}}{\frac{8}{5}}$$

Add 14 and 18 to get 32.

$$\frac{\frac{32}{15}}{\frac{8}{5}}$$

Divide \frac{32}{15} by \frac{8}{5} by multiplying \frac{32}{15} by the reciprocal of \frac{8}{5}.

$$\frac{32}{15}\times \frac{5}{8}$$

Multiply \frac{32}{15} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32\times 5}{15\times 8}$$

Do the multiplications in the fraction \frac{32\times 5}{15\times 8}.

$$\frac{160}{120}$$

Reduce the fraction \frac{160}{120} to lowest terms by extracting and canceling out 40.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$