Solve 1+1/3/1+frac{2{2-frac{1/2}}+2-frac{1/3}{1-frac{2}{1+frac{1}{2}}}}{7+frac{1}{1-frac{1}{1+frac{7}{6}}}}

$$\frac { \frac { 1 + \frac { 1 } { 3 } } { 1 + \frac { 2 } { 2 - \frac { 1 } { 2 } } } + \frac { 2 - \frac { 1 } { 3 } } { 1 - \frac { 2 } { 1 + \frac { 1 } { 2 } } } } { 7 + \frac { 1 } { 1 - \frac { 1 } { 1 + \frac { 7 } { 6 } } } }$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

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

$$\frac{\frac{\frac{3}{3}+\frac{1}{3}}{1+\frac{2}{2-\frac{1}{2}}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{\frac{3+1}{3}}{1+\frac{2}{2-\frac{1}{2}}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Add 3 and 1 to get 4.

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

Convert 2 to fraction \frac{4}{2}.

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

Since \frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 4 to get 3.

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

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

$$\frac{\frac{\frac{4}{3}}{1+2\times \frac{2}{3}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{\frac{4}{3}}{1+\frac{2\times 2}{3}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Multiply 2 and 2 to get 4.

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

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

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

Since \frac{3}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

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

Add 3 and 4 to get 7.

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

Divide \frac{4}{3} by \frac{7}{3} by multiplying \frac{4}{3} by the reciprocal of \frac{7}{3}.

$$\frac{\frac{4}{3}\times \frac{3}{7}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Multiply \frac{4}{3} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 3}{3\times 7}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Cancel out 3 in both numerator and denominator.

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

Convert 2 to fraction \frac{6}{3}.

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

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 6 to get 5.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2}{\frac{2}{2}+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2}{\frac{2+1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2}{\frac{3}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-2\times \frac{2}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2\times 2}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{4}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{\frac{3}{3}-\frac{4}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Since \frac{3}{3} and \frac{4}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{\frac{3-4}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Subtract 4 from 3 to get -1.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{-\frac{1}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Divide \frac{5}{3} by -\frac{1}{3} by multiplying \frac{5}{3} by the reciprocal of -\frac{1}{3}.

$$\frac{\frac{4}{7}+\frac{5}{3}\left(-3\right)}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Express \frac{5}{3}\left(-3\right) as a single fraction.

$$\frac{\frac{4}{7}+\frac{5\left(-3\right)}{3}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Multiply 5 and -3 to get -15.

$$\frac{\frac{4}{7}+\frac{-15}{3}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Divide -15 by 3 to get -5.

$$\frac{\frac{4}{7}-5}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Convert 5 to fraction \frac{35}{7}.

$$\frac{\frac{4}{7}-\frac{35}{7}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Since \frac{4}{7} and \frac{35}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-35}{7}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Subtract 35 from 4 to get -31.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{\frac{6}{6}+\frac{7}{6}}}}$$

Since \frac{6}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{\frac{6+7}{6}}}}$$

Add 6 and 7 to get 13.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{\frac{13}{6}}}}$$

Divide 1 by \frac{13}{6} by multiplying 1 by the reciprocal of \frac{13}{6}.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-1\times \frac{6}{13}}}$$

Multiply 1 and \frac{6}{13} to get \frac{6}{13}.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{6}{13}}}$$

Convert 1 to fraction \frac{13}{13}.

$$\frac{-\frac{31}{7}}{7+\frac{1}{\frac{13}{13}-\frac{6}{13}}}$$

Since \frac{13}{13} and \frac{6}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{31}{7}}{7+\frac{1}{\frac{13-6}{13}}}$$

Subtract 6 from 13 to get 7.

$$\frac{-\frac{31}{7}}{7+\frac{1}{\frac{7}{13}}}$$

Divide 1 by \frac{7}{13} by multiplying 1 by the reciprocal of \frac{7}{13}.

$$\frac{-\frac{31}{7}}{7+1\times \frac{13}{7}}$$

Multiply 1 and \frac{13}{7} to get \frac{13}{7}.

$$\frac{-\frac{31}{7}}{7+\frac{13}{7}}$$

Convert 7 to fraction \frac{49}{7}.

$$\frac{-\frac{31}{7}}{\frac{49}{7}+\frac{13}{7}}$$

Since \frac{49}{7} and \frac{13}{7} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{31}{7}}{\frac{49+13}{7}}$$

Add 49 and 13 to get 62.

$$\frac{-\frac{31}{7}}{\frac{62}{7}}$$

Divide -\frac{31}{7} by \frac{62}{7} by multiplying -\frac{31}{7} by the reciprocal of \frac{62}{7}.

$$-\frac{31}{7}\times \frac{7}{62}$$

Multiply -\frac{31}{7} times \frac{7}{62} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-31\times 7}{7\times 62}$$

Cancel out 7 in both numerator and denominator.

$$\frac{-31}{62}$$

Reduce the fraction \frac{-31}{62} to lowest terms by extracting and canceling out 31.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$