Solve 12/5-{[10/9-1/3*(5/4+1)-frac{1}{3}]:[frac{1}{6}+frac{2}{5}*(frac{1}{9}+1)-frac{11}{12}]}*(-frac{33}{10})

$$\frac { 12 } { 5 } - \{ [ \frac { 10 } { 9 } - \frac { 1 } { 3 } \cdot ( \frac { 5 } { 4 } + 1 ) - \frac { 1 } { 3 } ] : [ \frac { 1 } { 6 } + \frac { 2 } { 5 } \cdot ( \frac { 1 } { 9 } + 1 ) - \frac { 11 } { 12 } ] \} \cdot ( - \frac { 33 } { 10 } )$$

Evaluate

$$\frac{21}{10}=2.1$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$\frac{12}{5}-\frac{\frac{10}{9}-\frac{1}{3}\left(\frac{5}{4}+\frac{4}{4}\right)-\frac{1}{3}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Since \frac{5}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{12}{5}-\frac{\frac{10}{9}-\frac{1}{3}\times \frac{5+4}{4}-\frac{1}{3}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Add 5 and 4 to get 9.

$$\frac{12}{5}-\frac{\frac{10}{9}-\frac{1}{3}\times \frac{9}{4}-\frac{1}{3}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Multiply \frac{1}{3} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}-\frac{\frac{10}{9}-\frac{1\times 9}{3\times 4}-\frac{1}{3}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Do the multiplications in the fraction \frac{1\times 9}{3\times 4}.

$$\frac{12}{5}-\frac{\frac{10}{9}-\frac{9}{12}-\frac{1}{3}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{12}{5}-\frac{\frac{10}{9}-\frac{3}{4}-\frac{1}{3}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Least common multiple of 9 and 4 is 36. Convert \frac{10}{9} and \frac{3}{4} to fractions with denominator 36.

$$\frac{12}{5}-\frac{\frac{40}{36}-\frac{27}{36}-\frac{1}{3}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Since \frac{40}{36} and \frac{27}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{5}-\frac{\frac{40-27}{36}-\frac{1}{3}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Subtract 27 from 40 to get 13.

$$\frac{12}{5}-\frac{\frac{13}{36}-\frac{1}{3}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Least common multiple of 36 and 3 is 36. Convert \frac{13}{36} and \frac{1}{3} to fractions with denominator 36.

$$\frac{12}{5}-\frac{\frac{13}{36}-\frac{12}{36}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Since \frac{13}{36} and \frac{12}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{5}-\frac{\frac{13-12}{36}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Subtract 12 from 13 to get 1.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+1\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{1}{6}+\frac{2}{5}\left(\frac{1}{9}+\frac{9}{9}\right)-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Since \frac{1}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{1}{6}+\frac{2}{5}\times \frac{1+9}{9}-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Add 1 and 9 to get 10.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{1}{6}+\frac{2}{5}\times \frac{10}{9}-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Multiply \frac{2}{5} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{1}{6}+\frac{2\times 10}{5\times 9}-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Do the multiplications in the fraction \frac{2\times 10}{5\times 9}.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{1}{6}+\frac{20}{45}-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Reduce the fraction \frac{20}{45} to lowest terms by extracting and canceling out 5.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{1}{6}+\frac{4}{9}-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Least common multiple of 6 and 9 is 18. Convert \frac{1}{6} and \frac{4}{9} to fractions with denominator 18.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{3}{18}+\frac{8}{18}-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Since \frac{3}{18} and \frac{8}{18} have the same denominator, add them by adding their numerators.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{3+8}{18}-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Add 3 and 8 to get 11.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{11}{18}-\frac{11}{12}}\left(-\frac{33}{10}\right)$$

Least common multiple of 18 and 12 is 36. Convert \frac{11}{18} and \frac{11}{12} to fractions with denominator 36.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{22}{36}-\frac{33}{36}}\left(-\frac{33}{10}\right)$$

Since \frac{22}{36} and \frac{33}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{5}-\frac{\frac{1}{36}}{\frac{22-33}{36}}\left(-\frac{33}{10}\right)$$

Subtract 33 from 22 to get -11.

$$\frac{12}{5}-\frac{\frac{1}{36}}{-\frac{11}{36}}\left(-\frac{33}{10}\right)$$

Divide \frac{1}{36} by -\frac{11}{36} by multiplying \frac{1}{36} by the reciprocal of -\frac{11}{36}.

$$\frac{12}{5}-\frac{1}{36}\left(-\frac{36}{11}\right)\left(-\frac{33}{10}\right)$$

Multiply \frac{1}{36} times -\frac{36}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}-\frac{1\left(-36\right)}{36\times 11}\left(-\frac{33}{10}\right)$$

Do the multiplications in the fraction \frac{1\left(-36\right)}{36\times 11}.

$$\frac{12}{5}-\frac{-36}{396}\left(-\frac{33}{10}\right)$$

Reduce the fraction \frac{-36}{396} to lowest terms by extracting and canceling out 36.

$$\frac{12}{5}-\left(-\frac{1}{11}\left(-\frac{33}{10}\right)\right)$$

Multiply -\frac{1}{11} times -\frac{33}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}-\frac{-\left(-33\right)}{11\times 10}$$

Do the multiplications in the fraction \frac{-\left(-33\right)}{11\times 10}.

$$\frac{12}{5}-\frac{33}{110}$$

Reduce the fraction \frac{33}{110} to lowest terms by extracting and canceling out 11.

$$\frac{12}{5}-\frac{3}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{12}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{24}{10}-\frac{3}{10}$$

Since \frac{24}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-3}{10}$$

Subtract 3 from 24 to get 21.

$$\frac{21}{10}$$

Factor

$$\frac{3 \cdot 7}{2 \cdot 5} = 2\frac{1}{10} = 2.1$$