Solve 2+1/2+1{2+frac{1/1+frac{1{11}}}}=67/24

$$2 + \frac { 1 } { 2 + \frac { 1 } { 2 + \frac { 1 } { 1 + \frac { 1 } { 11 } } } } = \frac { 67 } { 24 }$$

Verify

Solution Steps

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

$$2+\frac{1}{2+\frac{1}{2+\frac{1}{\frac{11}{11}+\frac{1}{11}}}}=\frac{67}{24}$$

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

$$2+\frac{1}{2+\frac{1}{2+\frac{1}{\frac{11+1}{11}}}}=\frac{67}{24}$$

Add 11 and 1 to get 12.

$$2+\frac{1}{2+\frac{1}{2+\frac{1}{\frac{12}{11}}}}=\frac{67}{24}$$

Divide 1 by \frac{12}{11} by multiplying 1 by the reciprocal of \frac{12}{11}.

$$2+\frac{1}{2+\frac{1}{2+1\times \frac{11}{12}}}=\frac{67}{24}$$

Multiply 1 and \frac{11}{12} to get \frac{11}{12}.

$$2+\frac{1}{2+\frac{1}{2+\frac{11}{12}}}=\frac{67}{24}$$

Convert 2 to fraction \frac{24}{12}.

$$2+\frac{1}{2+\frac{1}{\frac{24}{12}+\frac{11}{12}}}=\frac{67}{24}$$

Since \frac{24}{12} and \frac{11}{12} have the same denominator, add them by adding their numerators.

$$2+\frac{1}{2+\frac{1}{\frac{24+11}{12}}}=\frac{67}{24}$$

Add 24 and 11 to get 35.

$$2+\frac{1}{2+\frac{1}{\frac{35}{12}}}=\frac{67}{24}$$

Divide 1 by \frac{35}{12} by multiplying 1 by the reciprocal of \frac{35}{12}.

$$2+\frac{1}{2+1\times \frac{12}{35}}=\frac{67}{24}$$

Multiply 1 and \frac{12}{35} to get \frac{12}{35}.

$$2+\frac{1}{2+\frac{12}{35}}=\frac{67}{24}$$

Convert 2 to fraction \frac{70}{35}.

$$2+\frac{1}{\frac{70}{35}+\frac{12}{35}}=\frac{67}{24}$$

Since \frac{70}{35} and \frac{12}{35} have the same denominator, add them by adding their numerators.

$$2+\frac{1}{\frac{70+12}{35}}=\frac{67}{24}$$

Add 70 and 12 to get 82.

$$2+\frac{1}{\frac{82}{35}}=\frac{67}{24}$$

Divide 1 by \frac{82}{35} by multiplying 1 by the reciprocal of \frac{82}{35}.

$$2+1\times \frac{35}{82}=\frac{67}{24}$$

Multiply 1 and \frac{35}{82} to get \frac{35}{82}.

$$2+\frac{35}{82}=\frac{67}{24}$$

Convert 2 to fraction \frac{164}{82}.

$$\frac{164}{82}+\frac{35}{82}=\frac{67}{24}$$

Since \frac{164}{82} and \frac{35}{82} have the same denominator, add them by adding their numerators.

$$\frac{164+35}{82}=\frac{67}{24}$$

Add 164 and 35 to get 199.

$$\frac{199}{82}=\frac{67}{24}$$

Least common multiple of 82 and 24 is 984. Convert \frac{199}{82} and \frac{67}{24} to fractions with denominator 984.

$$\frac{2388}{984}=\frac{2747}{984}$$

Compare \frac{2388}{984} and \frac{2747}{984}.

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