Solve -6/7+1/3/frac{3{4}+2/9}divfrac{frac{1}{11}-1}{frac{3}{4}+frac{7}{3}}

$$\frac { - \frac { 6 } { 7 } + \frac { 1 } { 3 } } { \frac { 3 } { 4 } + \frac { 2 } { 9 } } \div \frac { \frac { 1 } { 11 } - 1 } { \frac { 3 } { 4 } + \frac { 7 } { 3 } }$$

Evaluate

$$\frac{4477}{2450}\approx 1.827346939$$

Solution Steps

Divide \frac{-\frac{6}{7}+\frac{1}{3}}{\frac{3}{4}+\frac{2}{9}} by \frac{\frac{1}{11}-1}{\frac{3}{4}+\frac{7}{3}} by multiplying \frac{-\frac{6}{7}+\frac{1}{3}}{\frac{3}{4}+\frac{2}{9}} by the reciprocal of \frac{\frac{1}{11}-1}{\frac{3}{4}+\frac{7}{3}}.

$$\frac{\left(-\frac{6}{7}+\frac{1}{3}\right)\left(\frac{3}{4}+\frac{7}{3}\right)}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Least common multiple of 7 and 3 is 21. Convert -\frac{6}{7} and \frac{1}{3} to fractions with denominator 21.

$$\frac{\left(-\frac{18}{21}+\frac{7}{21}\right)\left(\frac{3}{4}+\frac{7}{3}\right)}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Since -\frac{18}{21} and \frac{7}{21} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-18+7}{21}\left(\frac{3}{4}+\frac{7}{3}\right)}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Add -18 and 7 to get -11.

$$\frac{-\frac{11}{21}\left(\frac{3}{4}+\frac{7}{3}\right)}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{7}{3} to fractions with denominator 12.

$$\frac{-\frac{11}{21}\left(\frac{9}{12}+\frac{28}{12}\right)}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Since \frac{9}{12} and \frac{28}{12} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{11}{21}\times \frac{9+28}{12}}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Add 9 and 28 to get 37.

$$\frac{-\frac{11}{21}\times \frac{37}{12}}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Multiply -\frac{11}{21} times \frac{37}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-11\times 37}{21\times 12}}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Do the multiplications in the fraction \frac{-11\times 37}{21\times 12}.

$$\frac{\frac{-407}{252}}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Fraction \frac{-407}{252} can be rewritten as -\frac{407}{252} by extracting the negative sign.

$$\frac{-\frac{407}{252}}{\left(\frac{3}{4}+\frac{2}{9}\right)\left(\frac{1}{11}-1\right)}$$

Least common multiple of 4 and 9 is 36. Convert \frac{3}{4} and \frac{2}{9} to fractions with denominator 36.

$$\frac{-\frac{407}{252}}{\left(\frac{27}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

Since \frac{27}{36} and \frac{8}{36} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{407}{252}}{\frac{27+8}{36}\left(\frac{1}{11}-1\right)}$$

Add 27 and 8 to get 35.

$$\frac{-\frac{407}{252}}{\frac{35}{36}\left(\frac{1}{11}-1\right)}$$

Convert 1 to fraction \frac{11}{11}.

$$\frac{-\frac{407}{252}}{\frac{35}{36}\left(\frac{1}{11}-\frac{11}{11}\right)}$$

Since \frac{1}{11} and \frac{11}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{407}{252}}{\frac{35}{36}\times \frac{1-11}{11}}$$

Subtract 11 from 1 to get -10.

$$\frac{-\frac{407}{252}}{\frac{35}{36}\left(-\frac{10}{11}\right)}$$

Multiply \frac{35}{36} times -\frac{10}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{407}{252}}{\frac{35\left(-10\right)}{36\times 11}}$$

Do the multiplications in the fraction \frac{35\left(-10\right)}{36\times 11}.

$$\frac{-\frac{407}{252}}{\frac{-350}{396}}$$

Reduce the fraction \frac{-350}{396} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{407}{252}}{-\frac{175}{198}}$$

Divide -\frac{407}{252} by -\frac{175}{198} by multiplying -\frac{407}{252} by the reciprocal of -\frac{175}{198}.

$$-\frac{407}{252}\left(-\frac{198}{175}\right)$$

Multiply -\frac{407}{252} times -\frac{198}{175} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-407\left(-198\right)}{252\times 175}$$

Do the multiplications in the fraction \frac{-407\left(-198\right)}{252\times 175}.

$$\frac{80586}{44100}$$

Reduce the fraction \frac{80586}{44100} to lowest terms by extracting and canceling out 18.

$$\frac{4477}{2450}$$

Factor

$$\frac{11 ^ {2} \cdot 37}{2 \cdot 5 ^ {2} \cdot 7 ^ {2}} = 1\frac{2027}{2450} = 1.8273469387755101$$