Solve 1+1/2/3+1-frac{1/3/2}{frac{2^1/2}{5/6}-frac{1/3}{1/8}}*(23^1/2divfrac{47}{12})

$$\frac { \frac { 1 + \frac { 1 } { 2 } } { 3 } + \frac { 1 - \frac { 1 } { 3 } } { 2 } } { \frac { 2 ^ { 1 } / 2 } { 5 / 6 } - \frac { 1 / 3 } { 1 / 8 } } \times ( 23 ^ { 1 } / 2 \div \frac { 47 } { 12 } )$$

Evaluate

$$-\frac{1725}{1034}\approx -1.66827853$$

Solution Steps

Divide 2^{1} by 2 to get 1.

$$\frac{\frac{1+\frac{1}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{\frac{2}{2}+\frac{1}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{2+1}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{\frac{3}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Express \frac{\frac{3}{2}}{3} as a single fraction.

$$\frac{\frac{3}{2\times 3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{2}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{1}{2}+\frac{\frac{3}{3}-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{2}+\frac{\frac{3-1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Subtract 1 from 3 to get 2.

$$\frac{\frac{1}{2}+\frac{\frac{2}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Express \frac{\frac{2}{3}}{2} as a single fraction.

$$\frac{\frac{1}{2}+\frac{2}{3\times 2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{3}{6}+\frac{2}{6}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+2}{6}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{6}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Divide 1 by \frac{5}{6} by multiplying 1 by the reciprocal of \frac{5}{6}.

$$\frac{\frac{5}{6}}{1\times \frac{6}{5}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Multiply 1 and \frac{6}{5} to get \frac{6}{5}.

$$\frac{\frac{5}{6}}{\frac{6}{5}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Divide \frac{1}{3} by \frac{1}{8} by multiplying \frac{1}{3} by the reciprocal of \frac{1}{8}.

$$\frac{\frac{5}{6}}{\frac{6}{5}-\frac{1}{3}\times 8}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Multiply \frac{1}{3} and 8 to get \frac{8}{3}.

$$\frac{\frac{5}{6}}{\frac{6}{5}-\frac{8}{3}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{6}{5} and \frac{8}{3} to fractions with denominator 15.

$$\frac{\frac{5}{6}}{\frac{18}{15}-\frac{40}{15}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Since \frac{18}{15} and \frac{40}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{6}}{\frac{18-40}{15}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Subtract 40 from 18 to get -22.

$$\frac{\frac{5}{6}}{-\frac{22}{15}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Divide \frac{5}{6} by -\frac{22}{15} by multiplying \frac{5}{6} by the reciprocal of -\frac{22}{15}.

$$\frac{5}{6}\left(-\frac{15}{22}\right)\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Multiply \frac{5}{6} times -\frac{15}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-15\right)}{6\times 22}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Do the multiplications in the fraction \frac{5\left(-15\right)}{6\times 22}.

$$\frac{-75}{132}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Reduce the fraction \frac{-75}{132} to lowest terms by extracting and canceling out 3.

$$-\frac{25}{44}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Divide \frac{23^{1}}{2} by \frac{47}{12} by multiplying \frac{23^{1}}{2} by the reciprocal of \frac{47}{12}.

$$-\frac{25}{44}\times \frac{23^{1}\times 12}{2\times 47}$$

Cancel out 2 in both numerator and denominator.

$$-\frac{25}{44}\times \frac{6\times 23^{1}}{47}$$

Calculate 23 to the power of 1 and get 23.

$$-\frac{25}{44}\times \frac{6\times 23}{47}$$

Multiply 6 and 23 to get 138.

$$-\frac{25}{44}\times \frac{138}{47}$$

Multiply -\frac{25}{44} times \frac{138}{47} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-25\times 138}{44\times 47}$$

Do the multiplications in the fraction \frac{-25\times 138}{44\times 47}.

$$\frac{-3450}{2068}$$

Reduce the fraction \frac{-3450}{2068} to lowest terms by extracting and canceling out 2.

$$-\frac{1725}{1034}$$

Factor

$$-\frac{1725}{1034} = -1\frac{691}{1034} = -1.6682785299806577$$