Solve -18/21+7/21/frac{18{36}+8/36}divfrac{frac{1}{11}-frac{11}{11}}{frac{9}{12}+frac{28}{12}}

$$\frac { \frac { - 18 } { 21 } + \frac { 7 } { 21 } } { \frac { 18 } { 36 } + \frac { 8 } { 36 } } \div \frac { \frac { 1 } { 11 } - \frac { 11 } { 11 } } { \frac { 9 } { 12 } + \frac { 28 } { 12 } }$$

Evaluate

$$\frac{4477}{1820}\approx 2.45989011$$

Solution Steps

Divide 11 by 11 to get 1.

$$\frac{\frac{\frac{-18}{21}+\frac{7}{21}}{\frac{18}{36}+\frac{8}{36}}}{\frac{\frac{1}{11}-1}{\frac{9}{12}+\frac{28}{12}}}$$

Divide \frac{\frac{-18}{21}+\frac{7}{21}}{\frac{18}{36}+\frac{8}{36}} by \frac{\frac{1}{11}-1}{\frac{9}{12}+\frac{28}{12}} by multiplying \frac{\frac{-18}{21}+\frac{7}{21}}{\frac{18}{36}+\frac{8}{36}} by the reciprocal of \frac{\frac{1}{11}-1}{\frac{9}{12}+\frac{28}{12}}.

$$\frac{\left(\frac{-18}{21}+\frac{7}{21}\right)\left(\frac{9}{12}+\frac{28}{12}\right)}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

Reduce the fraction \frac{-18}{21} to lowest terms by extracting and canceling out 3.

$$\frac{\left(-\frac{6}{7}+\frac{7}{21}\right)\left(\frac{9}{12}+\frac{28}{12}\right)}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

Reduce the fraction \frac{7}{21} to lowest terms by extracting and canceling out 7.

$$\frac{\left(-\frac{6}{7}+\frac{1}{3}\right)\left(\frac{9}{12}+\frac{28}{12}\right)}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

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

$$\frac{\left(-\frac{18}{21}+\frac{7}{21}\right)\left(\frac{9}{12}+\frac{28}{12}\right)}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

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

$$\frac{\frac{-18+7}{21}\left(\frac{9}{12}+\frac{28}{12}\right)}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

Add -18 and 7 to get -11.

$$\frac{-\frac{11}{21}\left(\frac{9}{12}+\frac{28}{12}\right)}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

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

$$\frac{-\frac{11}{21}\times \frac{9+28}{12}}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

Add 9 and 28 to get 37.

$$\frac{-\frac{11}{21}\times \frac{37}{12}}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

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

$$\frac{\frac{-11\times 37}{21\times 12}}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

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

$$\frac{\frac{-407}{252}}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

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

$$\frac{-\frac{407}{252}}{\left(\frac{18}{36}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

Reduce the fraction \frac{18}{36} to lowest terms by extracting and canceling out 18.

$$\frac{-\frac{407}{252}}{\left(\frac{1}{2}+\frac{8}{36}\right)\left(\frac{1}{11}-1\right)}$$

Reduce the fraction \frac{8}{36} to lowest terms by extracting and canceling out 4.

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

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{2}{9} to fractions with denominator 18.

$$\frac{-\frac{407}{252}}{\left(\frac{9}{18}+\frac{4}{18}\right)\left(\frac{1}{11}-1\right)}$$

Since \frac{9}{18} and \frac{4}{18} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{407}{252}}{\frac{9+4}{18}\left(\frac{1}{11}-1\right)}$$

Add 9 and 4 to get 13.

$$\frac{-\frac{407}{252}}{\frac{13}{18}\left(\frac{1}{11}-1\right)}$$

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

$$\frac{-\frac{407}{252}}{\frac{13}{18}\left(\frac{1}{11}-\frac{11}{11}\right)}$$

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

$$\frac{-\frac{407}{252}}{\frac{13}{18}\times \frac{1-11}{11}}$$

Subtract 11 from 1 to get -10.

$$\frac{-\frac{407}{252}}{\frac{13}{18}\left(-\frac{10}{11}\right)}$$

Multiply \frac{13}{18} times -\frac{10}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{407}{252}}{\frac{13\left(-10\right)}{18\times 11}}$$

Do the multiplications in the fraction \frac{13\left(-10\right)}{18\times 11}.

$$\frac{-\frac{407}{252}}{\frac{-130}{198}}$$

Reduce the fraction \frac{-130}{198} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{407}{252}}{-\frac{65}{99}}$$

Divide -\frac{407}{252} by -\frac{65}{99} by multiplying -\frac{407}{252} by the reciprocal of -\frac{65}{99}.

$$-\frac{407}{252}\left(-\frac{99}{65}\right)$$

Multiply -\frac{407}{252} times -\frac{99}{65} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-407\left(-99\right)}{252\times 65}$$

Do the multiplications in the fraction \frac{-407\left(-99\right)}{252\times 65}.

$$\frac{40293}{16380}$$

Reduce the fraction \frac{40293}{16380} to lowest terms by extracting and canceling out 9.

$$\frac{4477}{1820}$$

Factor

$$\frac{11 ^ {2} \cdot 37}{2 ^ {2} \cdot 5 \cdot 7 \cdot 13} = 2\frac{837}{1820} = 2.45989010989011$$