Solve 11/2div[52/5-{23/5+(21/12divfrac{1}{2}+frac{1}{3})}]

$$1 \frac { 1 } { 2 } \div [ 5 \frac { 2 } { 5 } - \{ 2 \frac { 3 } { 5 } + ( 2 \frac { 1 } { 12 } \div \frac { 1 } { 2 } + \frac { 1 } { 3 } ) \} ]$$

Evaluate

$$-\frac{15}{17}\approx -0.882352941$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{\frac{2+1}{2}}{\frac{5\times 5+2}{5}-\left(\frac{2\times 5+3}{5}+\frac{\frac{2\times 12+1}{12}}{\frac{1}{2}}+\frac{1}{3}\right)}$$

Add 2 and 1 to get 3.

$$\frac{\frac{3}{2}}{\frac{5\times 5+2}{5}-\left(\frac{2\times 5+3}{5}+\frac{\frac{2\times 12+1}{12}}{\frac{1}{2}}+\frac{1}{3}\right)}$$

Multiply 5 and 5 to get 25.

$$\frac{\frac{3}{2}}{\frac{25+2}{5}-\left(\frac{2\times 5+3}{5}+\frac{\frac{2\times 12+1}{12}}{\frac{1}{2}}+\frac{1}{3}\right)}$$

Add 25 and 2 to get 27.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{2\times 5+3}{5}+\frac{\frac{2\times 12+1}{12}}{\frac{1}{2}}+\frac{1}{3}\right)}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{10+3}{5}+\frac{\frac{2\times 12+1}{12}}{\frac{1}{2}}+\frac{1}{3}\right)}$$

Add 10 and 3 to get 13.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{13}{5}+\frac{\frac{2\times 12+1}{12}}{\frac{1}{2}}+\frac{1}{3}\right)}$$

Divide \frac{2\times 12+1}{12} by \frac{1}{2} by multiplying \frac{2\times 12+1}{12} by the reciprocal of \frac{1}{2}.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{13}{5}+\frac{\left(2\times 12+1\right)\times 2}{12}+\frac{1}{3}\right)}$$

Multiply 2 and 12 to get 24.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{13}{5}+\frac{\left(24+1\right)\times 2}{12}+\frac{1}{3}\right)}$$

Add 24 and 1 to get 25.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{13}{5}+\frac{25\times 2}{12}+\frac{1}{3}\right)}$$

Multiply 25 and 2 to get 50.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{13}{5}+\frac{50}{12}+\frac{1}{3}\right)}$$

Reduce the fraction \frac{50}{12} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{13}{5}+\frac{25}{6}+\frac{1}{3}\right)}$$

Least common multiple of 5 and 6 is 30. Convert \frac{13}{5} and \frac{25}{6} to fractions with denominator 30.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{78}{30}+\frac{125}{30}+\frac{1}{3}\right)}$$

Since \frac{78}{30} and \frac{125}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{78+125}{30}+\frac{1}{3}\right)}$$

Add 78 and 125 to get 203.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{203}{30}+\frac{1}{3}\right)}$$

Least common multiple of 30 and 3 is 30. Convert \frac{203}{30} and \frac{1}{3} to fractions with denominator 30.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\left(\frac{203}{30}+\frac{10}{30}\right)}$$

Since \frac{203}{30} and \frac{10}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\frac{203+10}{30}}$$

Add 203 and 10 to get 213.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\frac{213}{30}}$$

Reduce the fraction \frac{213}{30} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{2}}{\frac{27}{5}-\frac{71}{10}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{27}{5} and \frac{71}{10} to fractions with denominator 10.

$$\frac{\frac{3}{2}}{\frac{54}{10}-\frac{71}{10}}$$

Since \frac{54}{10} and \frac{71}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{2}}{\frac{54-71}{10}}$$

Subtract 71 from 54 to get -17.

$$\frac{\frac{3}{2}}{-\frac{17}{10}}$$

Divide \frac{3}{2} by -\frac{17}{10} by multiplying \frac{3}{2} by the reciprocal of -\frac{17}{10}.

$$\frac{3}{2}\left(-\frac{10}{17}\right)$$

Multiply \frac{3}{2} times -\frac{10}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-10\right)}{2\times 17}$$

Do the multiplications in the fraction \frac{3\left(-10\right)}{2\times 17}.

$$\frac{-30}{34}$$

Reduce the fraction \frac{-30}{34} to lowest terms by extracting and canceling out 2.

$$-\frac{15}{17}$$

Factor

$$-\frac{15}{17} = -0.8823529411764706$$